Well, it fell into an empty slot.

Well, imagine that we have a game cube with 64 sides and 160 throws, more throws means repetitions will occur. Next, for each of 64 we divide by 128, that is, we take a cube with 8192 sides so that there are no repetitions.

10000000000000000000000000000000 00000000000000000000000000000000 1   pz 2 
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 3 
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 4 
10000000000000000000000000000000 00000000000000000000000000000000 1   pz 5 
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 6 
00000000000000000000000000000000 00000000000001000000000000000000 46  pz 7 
00000000000000000000000000100000 00000000000000000000000000000000 27  pz 8 
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 9 
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 10
00100000000000000000000000000000 00000000000000000000000000000000 3   pz 11
00000000000000000000010000000000 00000000000000000000000000000000 22  pz 12
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 13
00000000000000000000000000000000 10000000000000000000000000000000 33  pz 14
00000000000000000000000000000000 01000000000000000000000000000000 34  pz 15
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 16
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 17
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 18
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 19
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 20
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 21
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 22
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 23
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 24
00000000000000000000000000000000 00000000000000000000000000000010 63  pz 25
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 26
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 27
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 28
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 29
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 30
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 31
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 32
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 33
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 34
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 35
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 36
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 37
00000000000000010000000000000000 00000000000000000000000000000000 16  pz 38
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 39
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 40
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 41
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 42
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 43
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 44
00000000000000000000001000000000 00000000000000000000000000000000 23  pz 45
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 46
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 47
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 48
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 49
00000000000000000100000000000000 00000000000000000000000000000000 18  pz 50
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 51
00000000000000000000000000000000 00000000000000000000000000100000 59  pz 52
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 53
00000000000000000001000000000000 00000000000000000000000000000000 20  pz 54
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 55
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 56
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 57
00000000000000000000000000000000 00000010000000000000000000000000 39  pz 58
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 59
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 60
00000000000000000000000000000010 00000000000000000000000000000000 31  pz 61
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 62
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 63
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 64
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 65
00000000000000000000000000000001 00000000000000000000000000000000 32  pz 66

...............x.x.x.xx..x...xxx xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.                               pz 67

00000000000000000000000000000000 00000100000000000000000000000000 38  pz 70
00000000000000000000000000000000 00000000000000000000000010000000 57  pz 75
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 80
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 85
00000000000000000000000000000000 00000000000000001000000000000000 49  pz 90
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 95
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 100
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 105
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 110
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 115
                                                                                                              pz 120
                                                                                                             pz 125


for example, 43, 51, 52, 53, 58, 61 have already fallen out 4 times.

sides not yet rolled in a 64-sided die (128 each for 8192)

free missing sides and possible space

1-15
(√(2^66)/8192×129)^2+2^66;  8192/128 73805273267836026880
(√(2^66)/8192×1921)^2+2^66; 8192/128 77844439183633940480

17
(√(2^66)/8192×2177)^2+2^66; 8192/128 78997923638194208768
(√(2^66)/8192×2305)^2+2^66; 8192/128 79628709061002788864

19
(√(2^66)/8192×2433)^2+2^66; 8192/128 80295523280830332928
(√(2^66)/8192×2561)^2+2^66; 8192/128 80998366297676840960

21
(√(2^66)/8192×2689)^2+2^66; 8192/128 81737238111542312960
(√(2^66)/8192×2817)^2+2^66; 8192/128 82512138722426748928

24
(√(2^66)/8192×3073)^2+2^66; 8192/128 84170026335252512768
(√(2^66)/8192×3201)^2+2^66; 8192/128 85053013337193840640

25
(√(2^66)/8192×3201)^2+2^66; 8192/128 85053013337193840640
(√(2^66)/8192×3329)^2+2^66; 8192/128 85972029136154132480

27
(√(2^66)/8192×3457)^2+2^66; 8192/128 86927073732133388288
(√(2^66)/8192×3585)^2+2^66; 8192/128 87918147125131608064

28
(√(2^66)/8192×3585)^2+2^66; 8192/128 87918147125131608064
(√(2^66)/8192×3713)^2+2^66; 8192/128 88945249315148791808

29
(√(2^66)/8192×3713)^2+2^66; 8192/128 88945249315148791808
(√(2^66)/8192×3841)^2+2^66; 8192/128 90008380302184939520

37
(√(2^66)/8192×4736)^2+2^66; 8192/128 98448687854319042560
(√(2^66)/8192×4864)^2+2^66; 8192/128 99799767742530191360 

40
(√(2^66)/8192×5120)^2+2^66; 8192/128 102610013910009380864
(√(2^66)/8192×5248)^2+2^66; 8192/128 104069180189277421568

41
(√(2^66)/8192×5248)^2+2^66; 8192/128 104069180189277421568
(√(2^66)/8192×5376)^2+2^66; 8192/128 105564375265564426240

46
(√(2^66)/8192×5888)^2+2^66; 8192/128 111905443540902084608
(√(2^66)/8192×6016)^2+2^66; 8192/128 113580782602283909120

47
(√(2^66)/8192×6016)^2+2^66; 8192/128 113580782602283909120
(√(2^66)/8192×6144)^2+2^66; 8192/128 115292150460684697600

56
(√(2^66)/8192×7168)^2+2^66; 8192/128 130280130020573708288
(√(2^66)/8192×7296)^2+2^66; 8192/128 132315757052145172480

60
(√(2^66)/8192×7680)^2+2^66; 8192/128 138638810928973348864
(√(2^66)/8192×7808)^2+2^66; 8192/128 140818553148620668928

 

 bald chupacabras method...

for example, we take the square roots of the spaces and the keys themselves

pz65

2^64 √(18446744073709551616)    4294967296
30568377312064202855-18446744073709551616 12121633238354651239
√(12121633238354651239)         3481613596,933
2^63 √(9223372036854775808)     3037000499,976
                                        
4294967296/8                    536870912     
3481613596/8                    435201699,5   
536870912×x=3481613596          x = 6,485
3481613596/536870912                6,485

---

(4294967296/64)×x=(3481613596) x = 51,880085408687591552734375 pz 65

2^64 √(18446744073709551616) 4294967296
     √(12121633238354651239) 3481613596,933                              pz65
      12121633231852051216  3481613596×3481613596
      30568377305561602832  12121633231852051216+18446744073709551616   pz65
      30568377312064202855                                              pz65



and divide into parts, by 2, by 3, by 64, 128, 1024, 2048, 4096, etc.

we catch such a divider into parts so that there are no repetitions

for 64 and 2 table

               0                                1
            1                                0

_______________1________________|_______________2_______________     2

_______1_______|________2_______|_______3_______|_______4_______     4
 
___1____|___2___|___3___|___4___|___5___|___6___|___7___|___8___     8

|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_     64


00000000000000000000010000000000 00000000000000000000000000000000 22  pz 12   0
00000000000000000000000000000000 00100000000000000000000000000000 35  pz 13   1
00000000000000000000000000000000 10000000000000000000000000000000 33  pz 14   1
00000000000000000000000000000000 01000000000000000000000000000000 34  pz 15   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 16   1
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 17   1
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 18   1
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 19   1
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 20   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 21   1
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 22   1
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 23   1
00000000000000000000000000000000 00000000000000000000010000000000 54  pz 24   1
00000000000000000000000000000000 00000000000000000000000000000010 63  pz 25   1
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 26   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 27   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 28   1
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 29   1
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 30   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 31   1
00000000000000000000000000000000 00000000010000000000000000000000 42  pz 32   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 33   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 34   1
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 35   0
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 36   0
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 37   1
00000000000000010000000000000000 00000000000000000000000000000000 16  pz 38   0
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 39   0
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 40   1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 41   1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 42   1
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 43   1
00000000000000000000000000000000 00000000000000000000001000000000 55  pz 44   1
00000000000000000000001000000000 00000000000000000000000000000000 23  pz 45   0
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 46   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 47   1
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 48   1
00000000000000000000000000000000 00000000001000000000000000000000 43  pz 49   1
00000000000000000100000000000000 00000000000000000000000000000000 18  pz 50   0
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 51   1
00000000000000000000000000000000 00000000000000000000000000100000 59  pz 52   1
00000000000000000000000000000000 00000000000010000000000000000000 45  pz 53   1
00000000000000000001000000000000 00000000000000000000000000000000 20  pz 54   0
00000000000000000000000000000000 00000000000000000001000000000000 52  pz 55   1
00000000000000000000000000000100 00000000000000000000000000000000 30  pz 56   0
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 57   1
00000000000000000000000000000000 00000010000000000000000000000000 39  pz 58   1
00000000000000000000000000000000 00000000000000000000000001000000 58  pz 59   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 60   1
00000000000000000000000000000010 00000000000000000000000000000000 31  pz 61   0
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 62   1
00000000000000000000000000000000 00000000000000000000000000000100 62  pz 63   1
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 64   1
00000000000000000000000000000000 00000000000000000010000000000000 51  pz 65   1
                           ...............x.x.x.xx..x...xx. xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.     pz 66   
00000000000000000000000000000000 00000100000000000000000000000000 38  pz 70   1
00000000000000000000000000000000 00000000000000000000000010000000 57  pz 75   1
00000000000000000000000001000000 00000000000000000000000000000000 26  pz 80   0
00000000000000000000000000000000 00000000000000000000000000001000 61  pz 85   1
00000000000000000000000000000000 00000000000000001000000000000000 49  pz 90   1
00000000000000000000000000000000 00000000000000000000100000000000 53  pz 95   1
00000000000000000000000000000000 00000000000000000100000000000000 50  pz 100  1
00000000000000000000000000000000 00000000000000010000000000000000 48  pz 105  1
00000000000000000000000000000000 00010000000000000000000000000000 36  pz 110  1
00000000000000000000000000000000 00000000000100000000000000000000 44  pz 115  1
                                                                      pz 120
                         xxxx.xx..xxxx..xxxxxxxx.xxx.xxx.     pz 125


for example, at 1664 repetitions stop falling out

1664 , 1664/2 832 ,1664/64 26, 26×x=1348 x = 51,846 pz 65

                                          pz20
[572,924,858,887,1326,1250,1131,1190,1001,1337,1418,1096,1411,1645,1315,1360,1388,1168,1599,1628,1104,1353,1336,687,804,1127,438,701,
1511,950,936,1376,1442,615,1129,1392,996,1120,486,1514,1554,1178,545,1359,793,1594,1035,1508,1637,809,1387,1621,1604,1348,992,1494,
688,1587,1286,1403,1320,1251,941,1158]

35935527204195940 ~2^54

3+3+3+1+4+1+3+4+4+2+0+2+2+4+4+2+3+2+0+0+0+2+3+4+3+1+3+4+0+1+3+1 72 , 84-72 12,

3   3    3   1   4   1    3   4   4   2    0    2    2   4   4   2    3    2    0    0     0    2    3   4   3    1    3    4    0    1    3   1

x    x   x   x   .   x    x   .   .   x    x    x    x   .   .   x    x    x    x    x     x    x    x   .   x    x    x    .    x    x    x   .
33   34  35  36  37  38   39  40  41  42   43   44   45  46  47  48   49   50   51   52    53   54   55  56  57   58   59   60   61   62   63  64

858 887 924  941     992 1035        1104 1120 1158 1178        1251 1286 1320 1337 1359  1403 1411 1442    1494 1508 1554      1587 1621 1645
             936     996             1096 1129 1168 1190        1250      1315 1348 1376  1387 1418              1514           1604 1637
           950    1001              1127                           1336 1353  1392                   1511           1594 1628
                                1131                            1326 1360  1388                                  1599

                                                            1327                          1482 1509 1534 1560 1586 1612 1638
                                                                               1328                         1483 1510 1535 1561 1588 1613 1639
                                                                               1329                         1484 1512 1536 1562 1589 1614 1640
                                                                               1330                         1485 1513 1537 1563 1590 1615 1641
                                                                               1331                         1486 1515 1538 1564 1591 1616 1642
                                                                               1332                         1487 1516 1539 1565 1592 1617 1643
                                                                               1333                         1488 1517 1540 1566 1593 1618 1644
                                                                               1334                         1489 1518 1541 1567 1595 1619 1646
                                                                               1335                         1490 1519 1542 1568 1596 1620 1647
                                                                               1338                         1491 1520 1543 1569 1597 1622 1648
                                                                               1339                         1492 1521 1544 1570 1598 1623 1649
                                                                               1340                         1493 1522 1545 1571 1600 1624 1650
                                                                               1341                         1495 1523 1546 1572 1601 1625 1651
                                                                               1342                         1496 1524 1547 1573 1602 1626 1652
                                                                               1343                         1497 1525 1548 1574 1603 1627 1653
                                                                               1344                         1498 1526 1549 1575 1605 1629 1654
                                                                               1345                         1499 1527 1550 1576 1606 1630 1655
                                                                               1346                         1500 1528 1551 1577 1607 1631 1656
                                                                               1347                         1501 1529 1552 1578 1608 1632 1657
                                                                               1349                         1502 1530 1553 1579 1609 1633 1658
                                                                               1350                         1503 1531 1555 1580 1610 1634 1659
                                                                               1351                         1504 1532 1556 1581 1611 1635 1660
                                                                                                              1505 1533 1557 1582         1636 1661
                                                                                                                      1506 1558 1583                1662
                                                                                                                      1507  1559 1584               1663
                                                                                                                                      1585

in general, everything is slipping somewhere, meaning that taking large divisors, we look in the table for 64 where they will fall out and so we select the spaces for the search.

the main thing is that more drops out on the right side than on the left if the table is divided into 2 equal sides, those that have already fallen out will not fall out, but you need to determine where exactly they can fall out, for example, there are parts that have not yet fallen out of 64, for example 37 40 41 46 47 56 60

we take the ones that haven't dropped yet and fit our search spots to them in the next puzzles

37 40 41 46 47 56 60 for 1664/2 832

833-1664

26×x=1348 x = 51,846 pz 65

962 37 
963 37
964 37
965 37
966 37
967 37
968 37
969 37
970 37
971 37
972 37
973 37
974 37
975 37
976 37
977 37
978 37
979 37
980 37
981 37
982 37
983 37
984 37
985 37
986 37
987 37

1560 60
1561 60
1562 60
1563 60
1564 60
1565 60
1566 60
1567 60
1568 60
1569 60
1570 60
1571 60
1572 60
1573 60
1574 60
1575 60
1576 60
1577 60
1578 60
1579 60
1580 60
1581 60
1582 60
1583 60
1584 60
1585 60

etc

and so we are looking for where nothing has fallen out at all

pz67
(√(2^66)/2^30×536870912)^2+2^66 92233720368547758080
(√(2^66)/2^30×536870913)^2+2^66 92233720437267234880
92233720437267234880−92233720368547758080 68719476800  ~2^36

pz68
(√(2^67)/2^30×536870912)^2+2^67 184467440737095516160
(√(2^67)/2^30×536870913)^2+2^67 184467440874534469760
184467440874534469760-184467440737095516160 137438953600 ~2^37

pz69
(√(2^68)/2^30×536870912)^2+2^68 368934881474191032320
(√(2^68)/2^30×536870913)^2+2^68 368934881749068939520
368934881749068939520-368934881474191032320 274877907200 ~2^38


pz67
(√(2^66)/2^30×(2^30/2+0))^2+2^66 92233720368547758080
(√(2^66)/2^30×(2^30/2+1))^2+2^66 92233720437267234880
92233720437267234880−92233720368547758080 68719476800  ~2^36

pz68
(√(2^67)/2^31×(2^31/2+0))^2+2^67 184467440737095516160
(√(2^67)/2^31×(2^31/2+1))^2+2^67 184467440805814992928
184467440805814992928-184467440737095516160 68719476768 ~2^36

pz69
(√(2^68)/2^32×(2^32/2+0))^2+2^68 368934881474191032320
(√(2^68)/2^32×(2^32/2+1))^2+2^68 368934881542910509072
368934881542910509072-368934881474191032320 68719476752 ~2^36


***

pz65
(√(2^64)/1664×1348)^2+2^64 30552526466155465467,455
                           30568377312064202855
(√(2^64)/1664×1349)^2+2^64 30570494229757563437,443
30570494229757563437−30552526466155465467 17967763602097970  ~2^53

pz65
(√(2^64)/2048×1660)^2+2^64 30566001039707734016
                           30568377312064202855
(√(2^64)/2048×1661)^2+2^64 30580606952171110400
30580606952171110400−30566001039707734016 14605912463376384  ~2^53


pz66
(√(2^65)/2048×1660)^2+2^65 61132002079415468032
(√(2^65)/2048×1661)^2+2^65 61161213904342220800
61161213904342220800-61132002079415468032 29211824926752768 ~2^54

pz66
(√(2^65)/1664×1348)^2+2^65 61105052932310930934,911
(√(2^65)/1664×1349)^2+2^65 61140988459515126874,887
61140988459515126874-61105052932310930934 35935527204195940 ~2^54
                                          18014398509481984 2^54
                                          36028797018963968 2^55
                               
pz66
(√(2^65)/4096×3320)^2+2^65 61132002079415468032
(√(2^65)/4096×3321)^2+2^65 61146605792855588864
61146605792855588864-61132002079415468032 14603713440120832
                                          18014398509481984 2^54                       

pz67                       
(√(2^66)/2048×1660)^2+2^66 122264004158830936064
(√(2^66)/2048×1661)^2+2^66 122322427808684441600
122322427808684441600-122264004158830936064 58423649853505536 ~2^56   
                                            36028797018963968 2^55

(√(2^66)/4096×3320)^2+2^66 122264004158830936064
(√(2^66)/4096×3321)^2+2^66 122293211585711177728
122293211585711177728-122264004158830936064 29207426880241664 ~2^54   
                                            36028797018963968 2^55

pz68                       
(√(2^67)/2048×1660)^2+2^67 244528008317661872128
(√(2^67)/2048×1661)^2+2^67 244644855617368883200
244644855617368883200-244528008317661872128 116847299707011072 ~2^56   
                                            144115188075855872 2^57
pz68                       
(√(2^67)/4096×3320)^2+2^67 244528008317661872128
(√(2^67)/4096×3321)^2+2^67 244586423171422355456
244586423171422355456-244528008317661872128 58414853760483328 ~2^56   
                                            144115188075855872 2^57

pz69                       
(√(2^68)/2048×1660)^2+2^68 489056016635323744256
(√(2^68)/2048×1661)^2+2^68 489289711234737766400
489289711234737766400-489056016635323744256 233694599414022144 ~2^56   
                                   288230376151711744 2^58
                                 36028797018963968  2^55

                                            103864266406232064    3072 48-64 ((√(2^68)/3072×1661)^2+2^68)−((√(2^68)/3072×1660)^2+2^68)
                                 82065593209862371,555 3456 54-64 ((√(2^68)/3456×1661)^2+2^68)−((√(2^68)/3456×1660)^2+2^68)
                                 58423649853505536     4096 64-64 ((√(2^68)/4096×1661)^2+2^68)−((√(2^68)/4096×1660)^2+2^68)
pz69                       
(√(2^68)/4096×3320)^2+2^68 489056016635323744256
(√(2^68)/4096×3321)^2+2^68 489172846342844710912
489172846342844710912-489056016635323744256 116829707520966656 ~2^56   
                                   288230376151711744 2^58

who is fast in programming, try to make such an analysis.

for example rmd160 puzzle 66 like this

13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so 20d45a6a762535700ce9e0b216e31994335db8a5
0010000011010100010110100110101001110110001001010011010101110000000011001110100 1111000001011001000010110111000110001100110010100001100110101110110111000101001 01 160 len

"1" 73, "0" 87

according to this criterion

160!/73!/87!
50039953558241343191231898620403129563706328000

50039953558241343191231898620403129563706328000/2^65 1356335658972975302954605575

2^160/50039953558241343191231898620403129563706328000 29
2^65/29 1272189246462727697

2^65/2^20 35184372088832

2^160/2^65 39614081257132168796771975168
50039953558241343191231898620403129563706328000/39614081257132168796771975168  1263186017957493013   \
                                                                                           35184372088832×35968 1265511495291109376     > 2^60-2^61 
                                                                                                                 2^65/29 1272189246462727697   /

for every 1048576 step of puzzle 66, will fall around ~36000 "1" 73, "0" 87 and if we add fishing on the first 20 bits (for example)
001000001101010001011010011010100111011000100101001101010111000000001100111010011110000010110010000 1011011100011000110011001010000110011010111011011100010100101

then, based on the probability of dropping 20 bits, you need 1048576 outcomes

1048576/36000 29

1048576 × 30 31457280
1048576 × 29 30408704  there will be only 1 00100000110101000101 "1" 73, "0" 87
1048576 × 28 29360128

what is a full turn for example by 3

001
100
010

010
100
001

100
001
010

there may be such

100
100
001

001
001
001

etc

but in theory, when hashing, the data is simply shuffled, that is, rotated

this means that 20 bits (1048576  steps) in the first 00100000110101000101 will simply move to another place in the second (1048576  steps), third (1048576  steps), etc.

1048576×1048576 = 1099511627776 1 twist

2^65/1048576 = 35184372088832

35184372088832/1099511627776 32 twists for all puzzle 66


1048576×32 = 33554432 (there will be only 1 00100000110101000101 "1" 73, "0" 87)

2^65/33554432 = 1099511627776

all puzzle be

33554432 steps by 1099511627776 len or

1099511627776 steps by 33554432 len 

during the analysis, 1-3 drops out on such steps

we can rotate this space as we like, even take a square

6074001000
6074001000

imagine that we fill with zeros those addresses that do not suit us according to the sorting criterion and mark 1 those that do

we will get a similar picture

000001000001000100000000000000000001000000100000000000000001
001000000000000010000000000110000000000000000100000000100000
etc...

if we take another piece of 20 bits from the address, it will behave similarly

11011011100010100101

so these pieces will jump around the whole puzzle according to the random distribution and in total, as I wrote above, there will be 32 full turns

the idea is to take and randomly generate all possible collisions

select statistics from the puzzle space and try to jump by sorting the template


2^10*2^10                                                                        abbreviated example  2^65/33554432 = 1099511627776 (33554432  can be divided into 1024 parts)

001 010                                                                      000    <  000000000000000000000000000000000000001000000000000000000000000000  33554432 step
100 100                                                                      000    <  000000000000000000000000000000000000000000000000000000000000000001  33554432 step
010 001                                                                      000    <  000000000000000000000001000000000000000000000000000000000000000000  33554432 step
 

That's right, but we don't know what he specifically did and in what program. What entropy was used 128-256 bit. 128bit enropy 12 words, still get 256bit private key. Let's say we start iterating over the entire enropy of 128bit and, by derivation, generate 256 addresses and cut them off in front, as the creator of the puzzle did. We have to iterate over all 128bits (12 worlds, 2048^12). https://github.com/Mizogg/python-mnemonic For each of 2048 to 2048^11 etc.But the generation itself (if he did not use the words brainwallets) 128bit number was caused by some data for seed() ("some garbage" > Mersenne twister 2^19937 bit > seed() > 128bit > address), what size of "some garbage" for the swirl was used. Maybe the size of the "some garbage" was less than 128bit, maybe more. If he manually cut 256 addresses for the deep puzzle, then how did he get addresses from them.

zahid888 He also wrote that he used a "It is just consecutive keys from a deterministic wallet (masked with leading 000...0001 to set difficulty)" this means that he could use anything, but most likely a regular random 2^256 address. He could create the keys a month before filling, or a week. And one time is not enough to shove all the devilry there, the clock counters... all this nonsense has a range "Mersenne twister 2^19937 bit (624·32 (2^32 = 4294967296) — 31)".

***

test

it took to open the first 3 puzzles through seed()

        a = random.seed(1,15000000)

        a1 = random.randrange(512,1024)
        if a1 == 514:

            a2 = random.randrange(256,512)
            if a2 == 467:               

                a3 = random.randrange(128,256)
                if a3 == 224:

14429208 steps, 514, 467, 224

for 4 it's been a long time to search 1,1000000000...

because when finding the first one, it is necessary to iterate over all the first ones until it suits the second one, etc.

1024×1024×1024 = 1073741824

probably needed for the whole puzzle 160-66=94, (2^160)^94 ~ 2^15040

2^15040 all pz
2^19937 twister

And how does this random.seed() work?

set some value and then Mersenne twister...

Mersenne twister 19937 bit (624·32 (2^32 = 4294967296) — 31)

for example, we take 3 random

random.seed(blablabla)
random.randrange(1,10)
random.randrange(1,10)
random.randrange(1,10)

we get for each of the 3 in order from the vortex of the first three?

                                 1— 31
random.randrange(1,10) 1,4294967296 (624·2)
random.randrange(1,10) 1,4294967296 (624·3)
random.randrange(1,10) 1,4294967296 (624·4)

and if we take 624 random.randrange(1,10) period ends and a new one begins again

                                 1— 31
random.randrange(1,10) 1,4294967296 (624·2) (625)624·2
random.randrange(1,10) 1,4294967296 (624·3) (626)624·2
random.randrange(1,10) 1,4294967296 (624·4) (627)624·2

or he these 19937 bit takes it all at once

in other words, to complete all puzzles with 1 seed() we need to iterate over this seed() to iterate over all variations of this 2^19937 bit?

Well, for 6-7 years, all possible options have already been sorted out, or combinatorics to sort out (shuffle 111112233... 222221133.. 332222211... etc) or to be smart about something with collisions.

for example, we can choose from a random house any number of times


random.seed(36893488147419103232,73786976294838206464)
random.randrange(36893488147419103232,73786976294838206464,1)

etc

36893488147419103232×36893488147419103232 = 1361129467683753853853498429727072845824

random.seed(36893488147419103232,1361129467683753853853498429727072845824)
random.randrange(36893488147419103232,73786976294838206464,1)

etc

in other words, there 1361129467683753853853498429727072845824 are so many collisions 36893488147419103232

now we take this number and we need to fish out the collisions we need

random.seed(36893488147419103232,73786976294838206464)
random.randrange(1,1361129467683753853853498429727072845824 ,1)

to

random.seed(random.randrange(1,1361129467683753853853498429727072845824 ,1))
random.seed(36893488147419103232,73786976294838206464)


1361129467683753853853498429727072845824×1361129467683753853853498429727072845824 = 1852673427797059126777135760139006525652319754650249024631321344126610074238976

there will be such sections in this number where the first step by step will be collisions (36893488147419103232×36893488147419103232 = 1361129467683753853853498429727072845824)

36893488147419103232×36893488147419103232 = 1361129467683753853853498429727072845824
****************** ___________________      ****************** ___________________

there will be areas

****************** ___________________

**********___________________*********

_______*******_______********_________

*_*_*_*_*_*_*_*_**__**__**__***___***

etc...

well, according to the law of uniform distribution, somehow jump there, random means uniform distribution over space.

He could use programming languages, python, c++... or, if possible, hardware wallets Leger etc... in this case, if possible, you need to work in this direction with the processor of the Leger itself or emulate its processor (and through seed selection). Moreover, we do not know where these funds (+10x) come from, they can be stolen from the exchange, etc., but the author did not appear.

you still don't understand the meaning sense of the hash function? "more light" > what is random? you take a coin and flip it 1 time, it may come up heads or tails. what happens if you flip a coin 10 times in a row, according to the theory of probability, either 10 heads or 10 tails can fall out. if you want to get 5 heads and 5 tails (in any order) you will need to flip a coin in series of 10, 2^10 = 1024 (1024 by 10). to drop all possible combinations from 10 heads in a row to 10 tails in a row, for all tosses in a row 1024 by 10, you need to flip a coin, 1024^1024=... when we start looking at the numbers generated when creating a bitcoin address (any or the address itself or its private key or its 160 hash in any form, hex, dec, bin) we get some parts of this huge number 2^10 = 1024 (1024 by 10) <> 1024^1024=... if you take 3 bits, 2^3=8, 8^8=16777216, then we start looking from 1 to 2^160 what we have in rmd160 hash in hex or dec

someting blablabla
...

1111101110010000010011001101000011011011000101101111100110000011100011011110010 1101011011011101111100000100100110000001010101110011001000000111000100000111101
1111101110010000010011011101010001011110010001010101111001100100101001001001000 1010001010111001000001111010110110000110010101010100001100011111100000110111111
1111101110010000010000101000101001011101000101100110011001100110111110110010000 0011000111101001111110011101100110100010110011110100110011111010000101000000010
1111101110010000010011110100011011001001011101100011111101001110111010000111011 0001001100010000010011000110111010111010110010011001001111010010100000010100001
1111101110010000010011111001001101010000001111001001110001101011110000111011011 0111000010010000111110000100000111010010001000110010111010110111000110000011111
1111101110010000010011000111010011111010010100001000011000001100110010010110001 1010100111011011111111001101001111100000101000101000000110011010110110110111000
1111101110010000010000000110100101101111101110001100000111111001100110111011111 0010000010110100011110101010101010101000100110101100010001111000000000111110001
1111101110010000010000011010010110100011111111100110001101001111001000110101011 0010100010010101100111100010000000110101000001101101111001011101010100101010101

the principle is preserved that vertically and horizontally > 2^3=8, 8^8=16777216


11111011
11111011
11111011
111
111
111
111
111

how many such sections will fit into 2:160 > 1461501637330902918203684832716283019655932542976 / 16777216 = 87112285931760246646623899502532662132736

we will split our 160 bits by 3 bits into sections


111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...
111 110 111 001...



11111011 10010000 01001100...
11111011 10010000 01001101...
11111011 10010000 01000010...

11111011 10010000 01001111...
11111011 10010000 01001111...
11111011 10010000 01001100...



of course we can't look further from where they fall from for each row > 16777216^16777216=...

with a horizontal representation, we get 160hesh/8bits = 20 parts.

8 bit 2^8 = 256, 256/20 = 12,8

256^256=... huge number 3231700607131100730071487668866995196044410266971548403213034542752465513886789 0893197201411522913463688717960921898019494119559150490921095088152386448283120 6308773673009960917501977503896521067960576383840675682767922186426197561618380 9433847617047058164585203630504288757589154106580860755239912393038552191433338 9668342420684974786564569494856176035326322058077805659331026192708460314150258 5928641771167259436037184618573575983511523016459044036976132332872312271256847 1082020972515710172693132346967854258065669793504599726835299863821552516638943 7335543602135433229604645318478604952148193555853611059596230656


16777216/12,8 =  1310720 steps, 2^1 to 2^160, 1461501637330902918203684832716283019655932542976 / 1310720 = 1115037259926531157076785913632418075299020,8

256^256=... huge number / 1115037259926531157076785913632418075299020,8

3231700607131100730071487668866995196044410266971548403213034542752465513886789 0893197201411522913463688717960921898019494119559150490921095088152386448283120 6308773673009960917501977503896521067960576383840675682767922186426197561618380 9433847617047058164585203630504288757589154106580860755239912393038552191433338 9668342420684974786564569494856176035326322058077805659331026192708460314150258 5928641771167259436037184618573575983511523016459044036976132332872312271256847 1082020972515710172693132346967854258065669793504599726835299863821552516638943 7335543602135433229604645318478604952148193555853611059596230656 / 1115037259926531157076785913632418075299020,8 =~

2898289342675449871993098867672270812704240074863894775739976204579701715524344 5980591244385169006487474859731523184059403721470360895667790293862650383583527 8052308371150131655537851476057700318587873331791124614866020470257907019747447 1073288393330068706379548507509145858817458460347497468230852750261100385960260 0438313585964807278885206604007966494048122967982378718514987992376064111499830 2154324000491294951584421374564447449664912755949011836586456519390866498333142 8684237600062725568520340756025511278116285953620110095472786524359663371614992 7614893228693106196480

in general our 2^3=8, 8^8=16777216 fall into their position from the general 256^256=... huge number...

in the first column, theirs fall out all over, in the second one, etc. when presented vertically and similarly when recalculating and converting in horizontal...

instead of constantly flipping a coin, we initiate with Mersenne twister and hash functions (256,160hashs) by initiating the creation of a bitcoin address using a number, we get a fixed result instead of randomly generating a constantly new one (but it randomly takes it from a large number), but this number itself 2^160 or 2^256 is still fixed and falls out of the total huge number that goes into infinity 2^3=8, 8^8=16777216, 16777216^16777216... etc

in general, everyone is picking something and looking for their own ways))

https://youtu.be/AYWoDqQmm1o?t=128

import random
from combi import *
import gmpy2

list2 = ["1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum"] # pz 20 > dec 863317 bit 11010010110001010101


F1="01"

aa1=F1[0]*50
aa2=F1[1]*50

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
   
    if M == len(l):
        return F1[1] * M

    result = ''   

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result



#ccount0 = 0

#a1 = "0"*22
#a2 = "1"*22
#a3 = a1+a2

#perm_space = PermSpace(a3)

#print(perm_space.length)
#print(perm_space.index(a4))
#( 44!/22!/22!)/2^20 2006625,140876770019531 collision
# 2104098963720 (44!/22!/22!)

#1048576×1048576 = 1099511627776
#1099511627776×1099511627776 = 1208925819614629174706176
#100!/50!/50!             100891344545564193334812497256                         
#44!/22!/22!       2104098963720


#aa = perm_space[2]
#aaa = "".join(aa)
       
#print(aaa)

pzbit = "11010010110001010101" #"11010010110001010101"
                                                                                 
for XXX in range(1000000,1048576,1):

    ccount0 = 0
   
    random.seed()
    gnoy= XXX #random.randrange(1000000,1048576,1) #1048576
    saki = 1099511627776 * gnoy #random.randrange(1,1048576,1) #2^256×2^256
   
    #print(gnoy,"1208925819614629174706176 //",saki,1208925819614629174706176//saki)
    #print("")

    X2=0 #X=10
    while X2 <= 100891344545564193334812497256-1:

        if X2 >= 1208925819614629174706176:
            break
        else:
            pass
       
        #count0 = 0
       
        X=X2 #X=10
        while X <= X2: #+100


            ccount0 += 1

            if ccount0 >= 1048576: #1048576 3000
                break
           
           
       
            #aa = perm_space[X]
            #aaa = "".join(aa)   
            #count0 += 1

            a3 = list(aa1+aa2)
            K = X #perm_int
            numberbit1 = len(aa1)
            numberbit0 = len(aa2)
            aa = find_permutation(a3,K,numberbit1,numberbit0)

            random.seed(aa)

            Nn = "0","1"

            RRR = [] #func()

            for RR in range(20): # "bit" set log2(x)=20 2^20 = 1048576, 1048576/20 = 52428,8
                DDD = random.choice(Nn)
                RRR.append(DDD)

            d = ''.join(RRR)
                #print(d,count0,aa,X)
            #print(bin(X)[2:],XXX,saki,"loop count","step",d,aa,X2,ccount0)
                #break

            if pzbit in d:
                print(bin(X)[2:],gnoy,"1099511627776 *",saki,"step",d,aa,X,X2,ccount0,XXX)
                #print("")
                #print("")
                break

            X=X+1


        X2=X2+saki
           
            #print("")
            #print(X2)
            #print("")


                 
print("pz end")
input() #"pause"


import random
from combi import *
import gmpy2
import time

list2 = ["1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum"] # pz 20 > dec 863317 bit 11010010110001010101


F1="01"

aa1=F1[0]*50
aa2=F1[1]*50

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
   
    if M == len(l):
        return F1[1] * M

    result = ''   

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result



#ccount0 = 0

#a1 = "0"*22
#a2 = "1"*22
#a3 = a1+a2

#perm_space = PermSpace(a3)

#print(perm_space.length)
#print(perm_space.index(a4))
#( 44!/22!/22!)/2^20 2006625,140876770019531 collision
# 2104098963720 (44!/22!/22!)

#1048576×1048576 = 1099511627776
#1099511627776×1099511627776 = 1208925819614629174706176
#100!/50!/50!             100891344545564193334812497256                         
#44!/22!/22!       2104098963720


#aa = perm_space[2]
#aaa = "".join(aa)
       
#print(aaa)

ccount20 = 0

pzbit = "11010010110001010101" #"11010010110001010101"
                                                                                 
for XXX in range(1,1208925819614629174706176,1):

    #print("loop start",ccount20)
    #print("")

    ccount0 = 0
   
    #random.seed()
    #gnoy= XXX #random.randrange(1000000,1048576,1) #1048576
    #saki = 1099511627776 * gnoy #random.randrange(1,1048576,1) #2^256×2^256
   
    #print(gnoy,"1208925819614629174706176 //",saki,1208925819614629174706176//saki)
    #print("")

    #X2=0 #X=10
    #while X2 <= 100891344545564193334812497256-1:

        #if X2 >= 1208925819614629174706176:
            #break
        #else:
            #pass
       
        #count0 = 0
       
        #X=X2 #X=10
        #while X <= X2: #+100


    #ccount0 += 1

            #if ccount0 >= 1048576:
                #break
   

    for S1 in range(20,40,1):
        for S2 in range(1):


            random.seed()
           
            Nn1 = "1","0","0","0","0","0"

            RRR1 = [] #func()

            for RR1 in range(S1): # bit len   1000000000000000000000000000000000000000000000000000000000000000000000000000000 00 1048576×1099511627776×1048576 = 1208925819614629174706176
                DDD1 = random.choice(Nn1)
                RRR1.append(DDD1)

            d1 = ''.join(RRR1)

            llen = bin(1208925819614629174706176)[2:]
            llen2 = len(llen)
           
           
           

            d0 = "0"
            d2 = "1"+d1 # bit len   1000000000000000000000000000000000000000000000000000000000000000000000000000000 00 1048576×1099511627776×1048576 = 1208925819614629174706176
            llen3 = llen2-len(d2)
            d3 = d2+d0*llen3
           

            f1=len(d3)
            while f1 >= len(d2):
               
               
                f2 = d3[0:f1]
                d4 = int(f2,2)
               
                ccount0 += 1
                ccount20 += 1

                if d4 <= 1208925819614629174706176:
                    #ccount0 += 1
                            #print(d3,d2)

                                #aa = perm_space[X]
                                #aaa = "".join(aa)   
                                #count0 += 1

                    a3 = list(aa1+aa2)
                    K = d4 #perm_int
                    numberbit1 = len(aa1)
                    numberbit0 = len(aa2)
                    aa = find_permutation(a3,K,numberbit1,numberbit0)

                    random.seed(aa)

                    Nn = "0","1"

                    RRR = [] #func()

                    for RR in range(20): # "bit" set log2(x)=20 2^20 = 1048576, 1048576/20 = 52428,8
                        DDD = random.choice(Nn)
                        RRR.append(DDD)

                    d = ''.join(RRR)
                                        #print(d,count0,aa,X)
                                    #print(bin(X)[2:],XXX,saki,"loop count","step",d,aa,X2,ccount0)
                                        #break

                           
                            #print(FD,d2,d3,aa,d,pzbit)
                    #print(S1,S2,"",ccount0,f2,d4,d,pzbit)

                    if pzbit in d:
                        print(S1,S2,"",ccount0,f2,d4,d,aa,d,pzbit,ccount20)
                        print("")
                        print("")
                        pass
                        #time.sleep(10.0)

                                    #X=X+1


                                #X2=X2+saki
                                   
                                    #print("")
                                    #print(X2)
                                    #print("")

                f1=f1-1

                         
print("pz end")
input() #"pause"


a couple of search scripts for 20 puzzles and a couple of scripts for searching 64 and other puzzles

from os import system
system("title "+__file__)
import random
import time
import gmpy2
import secp256k1 as ice

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]

#262!/131!/131! 364950428295639250777230977182937950631063637653015344224357416878384793565048
#               1461501637330902918203684832716283019655932542976 2^160
#               115792089237316195423570985008687907853269984665640564039457584007913129639936 2^256 (340282366920938463463374607431768211456*340282366920938463463374607431768211456 = 2^256)

F1="01"

aa1=F1[0]*131
aa2=F1[1]*131

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
   
    if M == len(l):
        return F1[1] * M

    result = ''   

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result


#ccount0 = 0

for XXX in range(1,1000000000000,1): # loop step

    llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
    llen2 = len(llen)
    d0 = "0"
   
    ccount0 = 0
   
    for S1 in range(2,128,1):   # half bit len for collision to dec set
        for S2 in range(1):    # random loop for ^ "half bit len for collision to dec set"

            random.seed()
           
            Nn1 = "0","1"  # ours dropout "1","0","0","0","0","0","0","0","0","0","0","0","0","0","0","0"

            RRR1 = []

            for RR1 in range(S1):
                DDD1 = random.choice(Nn1)
                RRR1.append(DDD1)

            d1 = ''.join(RRR1)

            #llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
            #llen2 = len(llen)
            #d0 = "0"
           
            d2 = "1"+d1 # bit len for collision to dec set , 18446744073709551616 * 18446744073709551616 = 340282366920938463463374607431768211456 , 18446744073709551616 * 340282366920938463463374607431768211456 * 18446744073709551616 = 115792089237316195423570985008687907853269984665640564039457584007913129639936

            llen3 = llen2-len(d2) # num zeros +

            d3 = d2+d0*llen3
           
            print(S1,S2,"",ccount0,d3)
           
            f1=len(d3)
            while f1 >= len(d2):
               
                f2 = d3[0:f1]
                d4 = int(f2,2)
                             
                if d4 <= 115792089237316195423570985008687907853269984665640564039457584007913129639936:
                    ccount0 += 1
                    a3 = list(aa1+aa2)
                    K = d4 #perm_int
                    numberbit1 = len(aa1)
                    numberbit0 = len(aa2)
                    aa = find_permutation(a3,K,numberbit1,numberbit0)

                    random.seed(aa) # init collision seed

                    Nn = "0","1"

                    RRR = [] #func()

                    for RR in range(160): # bit collision seeded len
                        DDD = random.choice(Nn)
                        RRR.append(DDD)

                    d = ''.join(RRR)

                    #print(S1,S2,"",ccount0,f2,d4,d,aa)

                    ii = 64
                    while ii <= 160:
                        dd = (d)[0:ii]
                        b = int(dd,2)
                        if b >= 9223372036854775807:
                           
                            #key = Key.from_int(b)
                            addr = ice.privatekey_to_address(0, True, b) #key.address
                                   
                            if addr in list2:
                                       
                                print ("found!!!",b,addr)
                                s1 = str(b)
                                s2 = addr
                                f=open("a.txt","a")
                                f.write(s1)
                                f.write(s2)       
                                f.close()
                                pass
                            else:
                               
                                #print(S1,S2,"",ccount0,f2,d4,d,aa,addr)
                                pass
                        ii=ii+1


                f1=f1-1

                         
print("pz end")
input() #"pause"


from os import system
system("title "+__file__)
import random
import time
import gmpy2
import secp256k1 as ice

list2 = ["16jY7qLJnxb7CHZyqBP8qca9d51gAjyXQN","13zb1hQbWVsc2S7ZTZnP2G4undNNpdh5so","1BY8GQbnueYofwSuFAT3USAhGjPrkxDdW9",
        "1MVDYgVaSN6iKKEsbzRUAYFrYJadLYZvvZ","19vkiEajfhuZ8bs8Zu2jgmC6oqZbWqhxhG","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF",
        "1PWo3JeB9jrGwfHDNpdGK54CRas7fsVzXU","1JTK7s9YVYywfm5XUH7RNhHJH1LshCaRFR","12VVRNPi4SJqUTsp6FmqDqY5sGosDtysn4",
        "1FWGcVDK3JGzCC3WtkYetULPszMaK2Jksv","1DJh2eHFYQfACPmrvpyWc8MSTYKh7w9eRF","1Bxk4CQdqL9p22JEtDfdXMsng1XacifUtE",
        "15qF6X51huDjqTmF9BJgxXdt1xcj46Jmhb","1ARk8HWJMn8js8tQmGUJeQHjSE7KRkn2t8","15qsCm78whspNQFydGJQk5rexzxTQopnHZ",
        "13zYrYhhJxp6Ui1VV7pqa5WDhNWM45ARAC","14MdEb4eFcT3MVG5sPFG4jGLuHJSnt1Dk2","1CMq3SvFcVEcpLMuuH8PUcNiqsK1oicG2D",
        "1K3x5L6G57Y494fDqBfrojD28UJv4s5JcK","1PxH3K1Shdjb7gSEoTX7UPDZ6SH4qGPrvq","16AbnZjZZipwHMkYKBSfswGWKDmXHjEpSf",
        "19QciEHbGVNY4hrhfKXmcBBCrJSBZ6TaVt","1EzVHtmbN4fs4MiNk3ppEnKKhsmXYJ4s74","1AE8NzzgKE7Yhz7BWtAcAAxiFMbPo82NB5",
        "17Q7tuG2JwFFU9rXVj3uZqRtioH3mx2Jad","1K6xGMUbs6ZTXBnhw1pippqwK6wjBWtNpL","15ANYzzCp5BFHcCnVFzXqyibpzgPLWaD8b",
        "18ywPwj39nGjqBrQJSzZVq2izR12MDpDr8","1CaBVPrwUxbQYYswu32w7Mj4HR4maNoJSX","1JWnE6p6UN7ZJBN7TtcbNDoRcjFtuDWoNL",
        "1CKCVdbDJasYmhswB6HKZHEAnNaDpK7W4n","1PXv28YxmYMaB8zxrKeZBW8dt2HK7RkRPX","1AcAmB6jmtU6AiEcXkmiNE9TNVPsj9DULf",
        "1EQJvpsmhazYCcKX5Au6AZmZKRnzarMVZu","18KsfuHuzQaBTNLASyj15hy4LuqPUo1FNB","15EJFC5ZTs9nhsdvSUeBXjLAuYq3SWaxTc",
        "1HB1iKUqeffnVsvQsbpC6dNi1XKbyNuqao","1GvgAXVCbA8FBjXfWiAms4ytFeJcKsoyhL","12JzYkkN76xkwvcPT6AWKZtGX6w2LAgsJg",
        "1824ZJQ7nKJ9QFTRBqn7z7dHV5EGpzUpH3","18A7NA9FTsnJxWgkoFfPAFbQzuQxpRtCos","1NeGn21dUDDeqFQ63xb2SpgUuXuBLA4WT4",
        "1NLbHuJebVwUZ1XqDjsAyfTRUPwDQbemfv","1MnJ6hdhvK37VLmqcdEwqC3iFxyWH2PHUV","1KNRfGWw7Q9Rmwsc6NT5zsdvEb9M2Wkj5Z",
        "1PJZPzvGX19a7twf5HyD2VvNiPdHLzm9F6","1GuBBhf61rnvRe4K8zu8vdQB3kHzwFqSy7","17s2b9ksz5y7abUm92cHwG8jEPCzK3dLnT",
        "1GDSuiThEV64c166LUFC9uDcVdGjqkxKyh","1Me3ASYt5JCTAK2XaC32RMeH34PdprrfDx","1CdufMQL892A69KXgv6UNBD17ywWqYpKut",
        "1BkkGsX9ZM6iwL3zbqs7HWBV7SvosR6m8N","1PXAyUB8ZoH3WD8n5zoAthYjN15yN5CVq5","1AWCLZAjKbV1P7AHvaPNCKiB7ZWVDMxFiz",
        "1G6EFyBRU86sThN3SSt3GrHu1sA7w7nzi4","1MZ2L1gFrCtkkn6DnTT2e4PFUTHw9gNwaj","1Hz3uv3nNZzBVMXLGadCucgjiCs5W9vaGz",
        "1Fo65aKq8s8iquMt6weF1rku1moWVEd5Ua","16zRPnT8znwq42q7XeMkZUhb1bKqgRogyy","1KrU4dHE5WrW8rhWDsTRjR21r8t3dsrS3R",
        "17uDfp5r4n441xkgLFmhNoSW1KWp6xVLD","13A3JrvXmvg5w9XGvyyR4JEJqiLz8ZySY3","16RGFo6hjq9ym6Pj7N5H7L1NR1rVPJyw2v",
        "1UDHPdovvR985NrWSkdWQDEQ1xuRiTALq","15nf31J46iLuK1ZkTnqHo7WgN5cARFK3RA","1Ab4vzG6wEQBDNQM1B2bvUz4fqXXdFk2WT",
        "1Fz63c775VV9fNyj25d9Xfw3YHE6sKCxbt","1QKBaU6WAeycb3DbKbLBkX7vJiaS8r42Xo","1CD91Vm97mLQvXhrnoMChhJx4TP9MaQkJo",
        "15MnK2jXPqTMURX4xC3h4mAZxyCcaWWEDD","13N66gCzWWHEZBxhVxG18P8wyjEWF9Yoi1","1NevxKDYuDcCh1ZMMi6ftmWwGrZKC6j7Ux",
        "19GpszRNUej5yYqxXoLnbZWKew3KdVLkXg","1M7ipcdYHey2Y5RZM34MBbpugghmjaV89P","18aNhurEAJsw6BAgtANpexk5ob1aGTwSeL",
        "1FwZXt6EpRT7Fkndzv6K4b4DFoT4trbMrV","1CXvTzR6qv8wJ7eprzUKeWxyGcHwDYP1i2","1MUJSJYtGPVGkBCTqGspnxyHahpt5Te8jy",
        "13Q84TNNvgcL3HJiqQPvyBb9m4hxjS3jkV","1LuUHyrQr8PKSvbcY1v1PiuGuqFjWpDumN","18192XpzzdDi2K11QVHR7td2HcPS6Qs5vg",
        "1NgVmsCCJaKLzGyKLFJfVequnFW9ZvnMLN","1AoeP37TmHdFh8uN72fu9AqgtLrUwcv2wJ","1FTpAbQa4h8trvhQXjXnmNhqdiGBd1oraE",
        "14JHoRAdmJg3XR4RjMDh6Wed6ft6hzbQe9","19z6waranEf8CcP8FqNgdwUe1QRxvUNKBG","14u4nA5sugaswb6SZgn5av2vuChdMnD9E5",
        "174SNxfqpdMGYy5YQcfLbSTK3MRNZEePoy", "1NBC8uXJy1GiJ6drkiZa1WuKn51ps7EPTv"]

#262!/131!/131! 364950428295639250777230977182937950631063637653015344224357416878384793565048
#               1461501637330902918203684832716283019655932542976 2^160
#               115792089237316195423570985008687907853269984665640564039457584007913129639936 2^256 (340282366920938463463374607431768211456*340282366920938463463374607431768211456 = 2^256)

F1="01"

aa1=F1[0]*131
aa2=F1[1]*131

def find_permutation(lst,K,numberbit1,numberbit0):

    l = lst

    N = numberbit0
    M = numberbit1

    if N == len(l):
        return F1[1] * N
   
    if M == len(l):
        return F1[1] * M

    result = ''   

    for i in range (0, len(lst)-1):
        K0 = gmpy2.comb(len(l)-1, M)

        if (K < K0):
            result += F1[0]
            l.remove (F1[0])
        else:
            result += F1[1]
            l.remove (F1[1])
            M -=1
            K = K - K0

    result += l[0]

    return result



def lexico_permute_string(s):
    a = list(s)
    n = len(a) - 1
    while True:
        yield ''.join(a)
        for j in range(n-1, -1, -1):
            if a[j] < a[j + 1]:
                break
        else:
            return
        v = a[j]
        for k in range(n, j, -1):
            if v < a[k]:
                break
        a[j], a[k] = a[k], a[j]
        a[j+1:] = a[j+1:][::-1]

       
s = "0000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000011" #128!/126!/2!  8128
sv = lexico_permute_string(s)
ccount0 = 0

for XXX in sv: # loop step

    llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
    llen2 = len(llen)
    d0 = "0"
   
    ccount0 += 1
   
   

    d1 = XXX #''.join(RRR1)

    #llen = bin(115792089237316195423570985008687907853269984665640564039457584007913129639936)[2:]
    #llen2 = len(llen)
    #d0 = "0"
           
    d2 = "1"+d1 # bit len for collision to dec set , 18446744073709551616 * 18446744073709551616 = 340282366920938463463374607431768211456 , 18446744073709551616 * 340282366920938463463374607431768211456 * 18446744073709551616 = 115792089237316195423570985008687907853269984665640564039457584007913129639936

    llen3 = llen2-len(d2) # num zeros +

    d3 = d2+d0*llen3
           
    print(XXX,"",ccount0,d3)
           
    f1=len(d3)
    while f1 >= len(d2):
               
        f2 = d3[0:f1]
        d4 = int(f2,2)
                             
        if d4 <= 115792089237316195423570985008687907853269984665640564039457584007913129639936:
            #ccount0 += 1
            a3 = list(aa1+aa2)
            K = d4 #perm_int
            numberbit1 = len(aa1)
            numberbit0 = len(aa2)
            aa = find_permutation(a3,K,numberbit1,numberbit0)

            random.seed(aa) # init collision seed

            Nn = "0","1"

            RRR = [] #func()

            for RR in range(160): # bit collision seeded len
                DDD = random.choice(Nn)
                RRR.append(DDD)

            d = ''.join(RRR)

            #print(d3,"",ccount0,f2,d4,d,aa)

            ii = 64
            while ii <= 160:
                dd = (d)[0:ii]
                b = int(dd,2)
                if b >= 9223372036854775807:
                           
                    #key = Key.from_int(b)
                    addr = ice.privatekey_to_address(0, True, b) #key.address
                                   
                    if addr in list2:
                                       
                        print ("found!!!",b,addr)
                        s1 = str(b)
                        s2 = addr
                        f=open("a.txt","a")
                        f.write(s1)
                        f.write(s2)       
                        f.close()
                        pass
                    else:
                               
                        #print(d3,"",ccount0,f2,d4,d,aa,addr)
                        pass
                ii=ii+1


        f1=f1-1

                         
print("pz end")
input() #"pause"

https://bitcointalk.org/index.php?topic=1306983.msg59102356#msg59102356 continuing the flight...

1048576×1048576             = 1099511627776
1099511627776×1099511627776 = 1208925819614629174706176

or the same

1048576×1099511627776×1048576 = 1208925819614629174706176

i.e. the 20th puzzle jumps within 1^2-2^20 blablabla

532368669374487342350336 484187 ×1099511627776×1000001
181088827760010590158848 164700 ×1099511627776×1000002
619892701383498689150976 563789 ×1099511627776×1000002
644019977303000002592768 585732 ×1099511627776×1000003
1120137428268770255699968 1018757 ×1099511627776×1000003
280959330078426262405120 255531 ×1099511627776×1000004
352372895955598358609920 320481 ×1099511627776×1000004
15992476587985050009600 14546 ×1099511627776×1000005
147981810864471083581440 134589 ×1099511627776×1000005
849455045036521008660480 772572 ×1099511627776×1000005
1092999181290656105496576 994072 ×1099511627776×1000006
142265848123988914470912 129390 ×1099511627776×1000008
520451395515858448023552 473345 ×1099511627776×1000008
852452687023533572751360 775296×1099511627776× 1000008
181419951836283866710016 165000 ×1099511627776×1000009
697292360654493845553152 634179 ×1099511627776×1000009
722959214526753365032960 657522×1099511627776× 1000010
...

in some it pops up several times

11011000101111010000110010010101010000000000000000000000000000000000000000         11010010110001010101 0000000000000000000110100111010101010100110111011111111001111110010001110011100 011011110001010111101  15992476587985050009600  14546 ×1099511627776× 1000005
11111010101100001110000101011101011000000000000000000000000000000000000000000      11010010110001010101 0000000000000000011111111011000011100000111110011001010110000101001111111101111 011001101010101011110  147981810864471083581440 134589 ×1099511627776×1000005
1011001111100001000011001101111000000111000000000000000000000000000000000000000 0   11010010110001010101 0000000000000001111101000000111100110111011100100001110000110000001111111111011 111101101011001111001  849455045036521008660480 772572 ×1099511627776×1000005

1000000000000000000000000000000000000000000000000000000000000000000000000000000 00      1208925819614629174706176 2^81-1
10000011001010111110101110111100110000000000000000000000000000000000000000             9678753217407715639296
10111011010111111110111010111111010000000000000000000000000000000000000000             13825815258173381017600
10010111001010110000000101001111000000000000000000000000000000000000000000             11154228800040674000896
10111110101100110011101011100000000000000000000000000000000000000000000                1758898127588428873728
11011000101111010000110010010101010000000000000000000000000000000000000000             15992476587985050009600
10110110000100000010110100011101100000000000000000000000000000000000000000             13433892166917160960000
10000111010010110111010111000001010000000000000000000000000000000000000000             9982991658226125111296
111011110101001111100011100100000000000000000000000000000000000000000000               4414816667071118573568
100001010011010001011111010101100000000000000000000000000000000000000000000            19657526330993040949248
10110110010000110111011111000100000000000000000000000000000000000000000000             13448675964968748711936
11110011011110011110111110111101010000000000000000000000000000000000000000             17965381037568078905344
1110111100000110010011001111000000000000000000000000000000000000000000000              8818451670323662159872
1000011000011011000000001000101100000000000000000000000000000000000000000              4947618827496440463360
100100111110101101001101011000000000000000000000000000000000000000000000               2728626692560540139520
11000100100110101011111100111100100000000000000000000000000000000000000000             14506850144679672938496
101001011000001000110101011100000000000000000000000000000000000000000000               3053095300706074624000
10010111100011000101000001101000000000000000000000000000000000000000000                1397784525321399173120
100100101010101100001111011010000000000000000000000000000000000000000000000            21644406558527521292288
10010011001100100110000001100100000000000000000000000000000000000000000000             10861205560344509939712
111010101001010001011011111100000000000000000000000000000000000000000000               4327228515271319748608
1100010100010110010101011011010100000000000000000000000000000000000000000              7271235947948482232320
1100010110011001000110101001110000000000000000000000000000000000000000000              7290081768563586105344
10011011010110100110101111001000000000000000000000000000000000000000000000             11463043410452910440448
11100100010110110011101101100110000000000000000000000000000000000000000                2106215804518520586240
1001000001011110000110111110101110000000000000000000000000000000000000000              5326224838426200375296
10011101011001011101011101111110110000000000000000000000000000000000000000             11613909172213287747584
100011001010110010110101111100100000000000000000000000000000000000000000000            20759914316371675054080
101011001001011100110101111111000000000000000000000000000000000000000000               3183735872628465860608
11010000101000001100111000100110100000000000000000000000000000000000000000             15394040034216221081600
100010111110000101001110001110011000000000000000000000000000000000000000000            20642659225394107908096
1011000110011010001111110011011110000000000000000000000000000000000000000              6552376728949719302144
11111111111011100001010100111000100000000000000000000000000000000000000000             18884301677095521615872
100000010100111110101011100111111000000000000000000000000000000000000000000            19082966744245204942848
11000001111011000000110000100100000000000000000000000000000000000000000000             14308922462804134330368
11010011100100001010100000001110100000000000000000000000000000000000000000             15610746387332732026880
111010111110110100001110001100010000000000000000000000000000000000000000               4352066501634477260800
100011100000001010111011111001101110000000000000000000000000000000000000000            20957077306601793126400
10110001010010011101100101011111000000000000000000000000000000000000000000             13081580359739640905728
1011110100011001100001010010011010000000000000000000000000000000000000000              6976547096570307280896
111110011011101000101011000001010000000000000000000000000000000000000000               4606654095766289645568
1011001000100111010000110010000000000000000000000000000000000000000000000              6572699170591182159872
1100001011101010111110000010001110000000000000000000000000000000000000000              7191199344262830358528
100101010011000100110110001111111100000000000000000000000000000000000000000            22016887670665522446336
11001111001000111101011000100100000000000000000000000000000000000000000000             15284233257106557370368
1101000000001101101100110110101000000000000000000000000000000000000000000              7675820033246287101952
11000010101101100101001001001000000000000000000000000000000000000000000                1795902996263741685760
1110000001110001100000010010110000000000000000000000000000000000000000000              8280499078575465431040
10100001010010101110011000011000000000000000000000000000000000000000000000             11901291293835867979776
11000100011110111001001101011111000000000000000000000000000000000000000000             14497865615155673432064
11101001011000111111011010011010000000000000000000000000000000000000000000             17221177932612567564288
10000111100011111110100111101001000000000000000000000000000000000000000000             10002722103015984070656
1001001001001001101101000011100000000000000000000000000000000000000000000              5397071132389644697600
100100011100100101011100000001010000000000000000000000000000000000000000               2689287368284924018688
1110111000101100110010100111101000000000000000000000000000000000000000000              8787105231532512509952
110010001100100111011100000000000000000000000000000000000000000000000000               3703894315638410182656
11110100011011110111011001111010100000000000000000000000000000000000000000             18036149182643067420672
11110010101111111001110011010000000000000000000000000000000000000000000000             17911676820374964666368
1111010000000000000110000011010000000000000000000000000000000000000000000              9002024733118352588800
10000111110011001000101110110101010000000000000000000000000000000000000000             10020198093771088330752
10011111110000001000001111100001000000000000000000000000000000000000000000             11787617945548664864768
1010001110110011110000010011101110000000000000000000000000000000000000000              6039543966877786046464
101110100100101111111101100001010000000000000000000000000000000000000000               3436570076666975485952
1010110000001110111111101100001100000000000000000000000000000000000000000              6347840992086851584000
1100010101101100111001010101010000000000000000000000000000000000000000000              7283710705611042717696
101011010101100010001101001000000000000000000000000000000000000000000                  399708439522897297408
10101000011100000110000001011100000000000000000000000000000000000000000000             12428602310673146314752
10101110011010111011001010111101110000000000000000000000000000000000000000             12869975770262824550400
100000011110011101111001101001000000000000000000000000000000000000000000000            19170476228187059650560
11011110110001010110110001110101000000000000000000000000000000000000000000             16437612233317349851136
100010101100000011110011000011000000000000000000000000000000000000000000000            20476433214725444075520
100010100000100110000000010010010100000000000000000000000000000000000000000            20370682478836041383936
100100001011101101010011110110001000000000000000000000000000000000000000000            21358636137332818837504
11010000000100110010011010001001010000000000000000000000000000000000000000             15353210834301573136384
11000110111110000010011010001100000000000000000000000000000000000000000                1835168229948320120832
10001000001101001010010111010000000000000000000000000000000000000000000000             10050203443936188432384
1011110010011110111101010000000100000000000000000000000000000000000000000              6958883896368388112384
11001110111110111110101010010110100000000000000000000000000000000000000000             15272727063634951274496
10000000001010101111011001011010010000000000000000000000000000000000000000             9457116009838443233280
110000010101011101101100000110110000000000000000000000000000000000000000               3566521045891541893120
10100000110100110011100101110011000000000000000000000000000000000000000000             11866797498612163018752
100010101110110110000001011001111000000000000000000000000000000000000000000            20502118048242849546240
1100001000101100001110000100001010000000000000000000000000000000000000000              7163709440307081773056
10101011111010101101011111101111000000000000000000000000000000000000000000             12685261974049921171456
11110011000110111001101001101110000000000000000000000000000000000000000000             17938191332172550373376
10110100001010001010100110010001100000000000000000000000000000000000000000             13293375865116969402368
11110000101110111110100100010000000000000000000000000000000000000000000000             17763035796148578156544
1001011100000100000001010101000000000000000000000000000000000000000000                 696437020210526945280
101101000000010110101000011000000000000000000000000000000000000000000000               3320821614587112587264
10101000001010011100111101010110000000000000000000000000000000000000000                1551032862808469405696
10100000111111001111000110010010000000000000000000000000000000000000000000             11878822245956684087296
10101111001111101110010100100111000000000000000000000000000000000000000000             12930849137520573153280
10110011111100111000001110100101100000000000000000000000000000000000000000             13278056958945398882304
100001011011001101011101100101100000000000000000000000000000000000000000000            19730732905885901783040
1101000001111011010110001101111000000000000000000000000000000000000000000              7691621730575567552512
110011001111001111001011001100000000000000000000000000000000000000000000               3780702978584795414528
111000011000010000010101110001100000000000000000000000000000000000000000               4160035147675468824576
1111101110001110011100100000110000000000000000000000000000000000000000                 1160099260548991942656
1110000101101100110110011111000000000000000000000000000000000000000000                 1039590245173370552320
10101000011010100101110000100100000000000000000000000000000000000000000000             12426868178526004051968
11111010111111011000010101010010000000000000000000000000000000000000000                2314977058025419833344
100100000010100011100110000100100000000000000000000000000000000000000000000            21274225675292362407936
110001111000010110010011110101100000000000000000000000000000000000000000               3680527342792309997568
110100110101010111001001110000000000000000000000000000000000000000000                  487305585327811330048
100011101001000001011000011101000000000000000000000000000000000000000000               2629838849349517312000
10000101000110111000011001100101000000000000000000000000000000000000000000             9821601382159792209920
10110000111010001100100001110000000000000000000000000000000000000000000                1631700368465162403840
100011100001011010110110101001100100000000000000000000000000000000000000000            20968594694201281609728
10001000111110100010000110001110000000000000000000000000000000000000000000             10107124149355454398464

1100000110000100101111100111101010000000000000000000000000000000000000000000000        456932713417561520209920
10010001101110110111011101011111110000000000000000000000000000000000000000             10753145046293777743872
100100001011010011001010011011001011110000000000000000000000000000000000000000         170838943426624490569728
111010100110110000000001100001111010010000000000000000000000000000000000000000         276756528897123353100288
1001111001011100110110010011101000000100000000000000000000000000000000000000000 0       747846657576038148603904
1101010111001010100011111010011110011100000000000000000000000000000000000000000 0       1009600654567916108251136

1110000101110111100001101101101110110100000000000000000000000000000000000000000        532368669374487342350336
100110010110001101100001010011011101100000000000000000000000000000000000000000         181088827760010590158848
1000001101000100011100110101111110011000000000000000000000000000000000000000000 0       619892701383498689150976
1000100001100000011001001001011011001001000000000000000000000000000000000000000 0       644019977303000002592768
1110110100110010110001011000101110001100000000000000000000000000000000000000000 0       1120137428268770255699968
111011011111101101010111110111001010000000000000000000000000000000000000000000         280959330078426262405120
1001010100111100010110001000111100000000000000000000000000000000000000000000000        352372895955598358609920
11011000101111010000110010010101010000000000000000000000000000000000000000             15992476587985050009600
11111010101100001110000101011101011000000000000000000000000000000000000000000          147981810864471083581440
1011001111100001000011001101111000000111000000000000000000000000000000000000000 0       849455045036521008660480

1011111111111110011001000000000000000000000000000000000000000000000                    110676840451932160000         100661×1099511627776×1000
1110000001100000001111110010000000000000000000000000000000000000000000                 1034751492411621376000        941102×1099511627776×1000
10001100010010001001010111110000000000000000000000000000000000000000                   161735907546524286976         146952×1099511627776×1001
1000000111110101111110111000110000000000000000000000000000000000000000                 599338725049651691520         543466×1099511627776×1003
1010111010110111000001100000000000000000000000000000000000000000000000                 805730424346065764352         729889×1099511627776×1004
1101111111110000011000000010000000000000000000000000000000000000000000                 1032736201947117256704        935527×1099511627776×1004
110010110111111010100000011000000000000000000000000000000000000000000                  469226680670150983680         424637×1099511627776×1005
1110010010110010000110001000110000000000000000000000000000000000000000                 1054672702468899471360        954448×1099511627776×1005

10000000000000000000000000000000000000000                                              1099511627776
1000000000000000000000000000000000000000000000000000000000000000000000000000000 00      1208925819614629174706176

1000000111110101111110111000110000000000000000000000000000000000000000
1110010010110010000110001000110000000000000000000000000000000000000000
1__00_0_1_110______110__100011

10000000000000000000000000000000000000000                                              1×1099511627776×1
100000000000000000000000000000000000000000                                             1×1099511627776×2
110000000000000000000000000000000000000000                                             1×1099511627776×3
1000000000000000000000000000000000000000000                                            1×1099511627776×4
1010000000000000000000000000000000000000000                                            1×1099511627776×5
100000000000000000000000000000000000000000                                             2×1099511627776×1
110000000000000000000000000000000000000000                                             3×1099511627776×1
1000000000000000000000000000000000000000000                                            4×1099511627776×1
1010000000000000000000000000000000000000000                                            5×1099511627776×1
1100100000000000000000000000000000000000000000                                         50×1099511627776×1
1111101000000000000000000000000000000000000000000                                      500×1099511627776×1
1111101010000000000000000000000000000000000000000                                      501×1099511627776×1
11111010100000000000000000000000000000000000000000                                     501×1099511627776×2
1001110010010000000000000000000000000000000000000000                                   501×1099511627776×5
1111111100000000000000000000000000000000000000000                                      510×1099511627776×1
111111110             510
10011100010000000000000000000000000000000000000000000                                  5000×1099511627776×1
1001110001000         5000
11000011010100000000000000000000000000000000000000000000                               50000×1099511627776×1
1100001101010000      50000
110000110101000000000000000000000000000000000000000000000                              50000×1099511627776×2
11011011101110100000000000000000000000000000000000000000000                            50000×1099511627776×9
11110100001001000000000000000000000000000000000000000000000                            50000×1099511627776×10
11110100001001000000000000000000000000000000000000000000000                            500000×1099511627776×1
1111010000100100000   500000
101010101110011000000000000000000000000000000000000000000000                           700000×1099511627776×1
110110111011101000000000000000000000000000000000000000000000                           900000×1099511627776×1
111101000010010000000000000000000000000000000000000000000000                           1000000×1099511627776×1
11110100001001000000  1000000
1000000000000000000000000000000000000000000000000000000000000                          1048576×1099511627776×1
100000000000000000000 1048576
111111111111111111110000000000000000000000000000000000000000                           1048575×1099511627776×1
11111111111111111111  1048575
1111111111111111111100000000000000000000000000000000000000000000000000000000000 000000000000000000000 1048575×1208925819614629174706176×1
1011111010111100001000000000000000000000000000000000000000000000000                    1000000×1099511627776×100
1111000110000100100111010000000000000000000000000000000000000000000000                 1000000×1099511627776×1013
100110101001001001010000000000000000000000000000000000000000000                        5000×1099511627776×1013


1099511627776×1099511627776 1208925819614629174706176
1208925819614629174706176×1208925819614629174706176 1461501637330902918203684832716283019655932542976

1011111010111100001000000000000000000000000000000000000000000000000                                          1000000×1099511627776×100
1011111010111100001000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000  1000000×1208925819614629174706176×100
1011111010111100001000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000000000000 1000000×1461501637330902918203684832716283019655932542976×100

262!/131!/131! 364950428295639250777230977182937950631063637653015344224357416878384793565048
1048575×1208925819614629174706176×1048575 1329225460484924342264618696048640000  1208925819614629174706176×1099511627776 1329227995784915872903807060280344576
80!/40!/40!                               107507208733336176461620
100!/50!/50!                              100891344545564193334812497256
140!/70!/70!                              93820969697840041204785894580506297666600
120!/60!/60!                              96614908840363322603893139521372656
130!/65!/65!                              95067625827960698145584333020095113100



here it turns out so zeros are added for 20 puzzles, this is 40 + 40 zeros


1000000000000000000000000000000000000000000000000000000000000000000000000000000 00      1208925819614629174706176
1111111111111111111111111111111111111111111111111111111111111111111111111111111 1       1208925819614629174706176(-1)

10000011000100100000100001000000101000000000000000                                     576453884411904             11010010110001010101 0000000000000000000000000000000000111011111111101010111110111101010101110111011 011110111101101111011 1450500
1000011000100111000001000000000000000000000000000000000                                18880272506290176           11010010110001010101 0000000000000000000000000000000101110101101100111110101011110100011001011111111 111101111111111011101 1700914
10000000000011010000011100000000000000000000                                           8799590023168               11010010110001010101 0000000000000000000000000000000000000111111101101111110111011111111111011111110 111000101111111010011 3402713
100101000000000010010000000000001000000000000000000000000000000000000000000            21841269246843326300160     11010010110001010101 0000000000000000000111110110110000111100110111001010100011010011110100011111100 110101011110111110011 231490
100000001111000100000100000000000000000000000000000000000000                           580700744018034688          11010010110001010101 0000000000000000000000000000100011111111111111011011011111110110010111111000110 111101100101111001010 258790
1000000000000010010000101100000000001000000000000000000000000000                       9224008379343568896         11010010110001010101 0000000000000000000000000010111110111111101101010111000110110111110110101100110 111111100110111010010 3224774
1010000100000100000000000000000001000000000                                            5532454748672               11010010110001010101 0000000000000000000000000000000000000111010001110111111110111111100111111110110 111111111011001111111 3464692
10001010000110000000100100000000000000000000000000                                     607343339372544             11010010110001010101 0000000000000000000000000000000000111101011101010110111010111100111101111001111 110111010111111111111 845038
101000000000100111001000000010000000000000000000000000000000000                        5765984128772079616         11010010110001010101 0000000000000000000000000010000111010111110011011100110111111001000110111110111 000111101111111111011 531959
1011100000000010011010001100100110000000000000000                                      404640974962688             11010010110001010101 0000000000000000000000000000000000110101011111110110111111111111111111110010100 001001101111111101111 624928
10101000100000100100000101000000000000000000000                                        92638696964096              11010010110001010101 0000000000000000000000000000000000011010011111011110111111111001111111110111100 011101010111011111111 1363131
100000000000000101001010010010000000000                                                274888729600                11010010110001010101 0000000000000000000000000000000000000001111101001111001110111101111111110111111 101111111111110110111 2584878
1000001000100000000111000000010000000000000                                            4471075643392               11010010110001010101 0000000000000000000000000000000000000110110101111111110111011111110111011011111 111111111011011000111 460364
10000000000000001000010000100100100101000000000000000000000000000000000                1180610218174911086592      11010010110001010101 0000000000000000000000111111100111001101111110111000101011111101111100101100101 010101001001101101011 639556
10000101100101100100000001000000000000                                                 143437860864                11010010110001010101 0000000000000000000000000000000000000001100111101111111111011111101011111011010 111111111011011111111 306764
10000111100100000000110000001001100000000000000000000000000000000                      19536641653416656896        11010010110001010101 0000000000000000000000000100101111101101100010111101100111111011100001111111111 011100110110011100111 545697
1100000000001000000001001001010000010000000000                                         52785167270912              11010010110001010101 0000000000000000000000000000000000010011101111101111100111101100100111111101101 111110111111110111111 521087
1110000001000000100010001000000001000000000000000000000000                             252485399178379264          11010010110001010101 0000000000000000000000000000010111101010101111111001110111110011110110111000011 001110111100111111111 2088597
10000100001000000010000010100100000000000000000                                        72636760719360              11010010110001010101 0000000000000000000000000000000000010111100111111111111110010110101110101111110 111111111111100111100 2993930
10000010000000000000000000000011000100000000000000000000000000000000000                1199038366474748035072      11010010110001010101 0000000000000000000000111111110101010110010110101110111111111111100111001010100 011100110101000110110 3188671
1101000000010000000000000000010011                                                     13962838035                 11010010110001010101 0000000000000000000000000000000000000000100111111111110011111111101111111111110 010111111111101111011 3544993
1001000000110000000000100100000000000000000000000000000000000000000000000000000        340453189689176777293824    11010010110001010101 0000000000000000111101110001111111111011101011011110101101001110000011000001001 101110100111111100000 3706349
10100101000000001010010110010100010000000000000000000000000000000000                   190234961158489505792       11010010110001010101 0000000000000000000000010100011000011100111111110111101111111001011100101101111 100101111101111000110 9665405

11101111101111011101010101111111011111000000000                                        131799304879616             11010010110001010101 0000000000000000000000000000000000011101111101101111101011111110111111011111101 011100111111111110000 171916
111111101101111101011111111111111111100000000000000000000000000000000000000000         300900407024389665587200    11010010110001010101 0000000000000000111001011011001101100100111001011111011001111101111100110110011 011000110100110011010 912410
11111111101111011110110111111010111100000000000000000000000000000000000000000          150963379505513073999872    11010010110001010101 0000000000000000100000110111101111001111110000111001100011110001111100111000011 110011001111110101011 66735
11111111111111010111001111010111111111100000000000000000                               72054793048031232           11010010110001010101 0000000000000000000000000000001011110101100100111011010000111111101100101111111 011111111111111101110 1285381
11110111111111110111111101011111000000000                                              2130286919168               11010010110001010101 0000000000000000000000000000000000000011111111111111110111111101000111101111101 011111011110101101111 2017397
1110111110111111111011111101110111101111000000000                                      527215284182528             11010010110001010101 0000000000000000000000000000000000111010111111110011111011111111111011011010101 100101111101111001111 2074411
111111100111110101111101111111100111110000000000000000000000000000000                  586814457269698166784       11010010110001010101 0000000000000000000000101011011110111011111101000001111110101111110111011101100 101001100101111000101 865171
11110110110111011011110111001111100000000000000000000000000000000                      35577165604173381632        11010010110001010101 0000000000000000000000000110111011011110111001011101101000110111011111110110011 110110110010100111011 1969013
10111101110111111111111111101101111000000000000000000000000000                         3420483897526321152         11010010110001010101 0000000000000000000000000001101011011010111100111001001111011011111100111111011 011100111011010111110 2335793
1111111111111111101111101111101000000000000000000000000000000000000000000000000 0       1208921134182166849126400   11010010110001010101 0000000000000010101100111101011111010111111010000100110010011110001110110010011 100110001110100111110 2737277
110111101111110101101111111100000000000000000000000000000000000000000000               4113439263260321775616      11010010110001010101 0000000000000000000010100000101101101111011001110111000110011111111101011101111 101011011100110110001 2915316
1110111111111010101101100101100000000000000000000000000000000                          2161541776039477248         11010010110001010101 0000000000000000000000000001001111111101011111001101101001111001111011110111100 111101011000111101101 3096661
11110011111010111110111111111111011000                                                 261908856792                11010010110001010101 0000000000000000000000000000000000000001111011111110111011111110111101011011111 110101111100111111111 187237
111111101101011101101101011101101111011000000000000000000000000000000                  587624523626472013824       11010010110001010101 0000000000000000000000101011011111110100010111000111111100011111100111100001011 101110011111100101101 324378
1101110011111111111010111111100000000000000000000000000000000000000000                 1019181200498545917952      11010010110001010101 0000000000000000000000111011111101101011101000010011010010001011010111111110011 101010010111111110111 3195532
111111011010101111101111111100000000000000                                             4358045417472               11010010110001010101 0000000000000000000000000000000000000110101111110111101111111111111011111111110 001011011111011111100 6086716
111110111001011011011001001100000000000000000000000000000                              141632157423501312          11010010110001010101 0000000000000000000000000000001111101111111000011101011001101111111101111111111 101110111101001101000 6186611
1011111111111110011001000000000000000000000000000000000000000000000                    110676840451932160000       11010010110001010101 0000000000000000000000001101111111111010111101110111000011101111111000110110111 110101101010000100011 6374746
111111111101100101111111111000                                                         1073111032                  11010010110001010101 0000000000000000000000000000000000000000001111101101111110111111111111111111111 111111101001101111110 7087942
11110111101111111110011101110000000000000000000                                        136201796845568             11010010110001010101 0000000000000000000000000000000000011101111111111110011111010110001111111111111 111111111100010110001 7247521

10000000000000000000000000000000000000000                                              1099511627776
1111111111111111111111111111111111111111                                               1099511627776(-1)


1000000000000000000000000000000000000000000000000000000000000000000000000000000 00       1208925819614629174706176
1111111111111111111111111111111111111111111111111111111111111111111111111111111 1        1208925819614629174706176(-1)

1000001100010010000010000100000010100000 0000000000                                     576453884411904             11010010110001010101
1000011000100111000001000000000000000000 000000000000000                                18880272506290176           11010010110001010101
1000000000001101000001110000000000000000 0000                                           8799590023168               11010010110001010101
1001010000000000100100000000000010000000 00000000000000000000000000000000000            21841269246843326300160     11010010110001010101
1000000011110001000001000000000000000000 00000000000000000000                           580700744018034688          11010010110001010101
1000000000000010010000101100000000001000 000000000000000000000000                       9224008379343568896         11010010110001010101
1010000100000100000000000000000001000000 000                                            5532454748672               11010010110001010101
1000101000011000000010010000000000000000 0000000000                                     607343339372544             11010010110001010101
1010000000001001110010000000100000000000 00000000000000000000000                        5765984128772079616         11010010110001010101
1011100000000010011010001100100110000000 000000000                                      404640974962688             11010010110001010101
1010100010000010010000010100000000000000 0000000                                        92638696964096              11010010110001010101
100000000000000101001010010010000000000                                                 274888729600                11010010110001010101
1000001000100000000111000000010000000000 000                                            4471075643392               11010010110001010101
1000000000000000100001000010010010010100 0000000000000000000000000000000                1180610218174911086592      11010010110001010101
10000101100101100100000001000000000000                                                  143437860864                11010010110001010101
1000011110010000000011000000100110000000 0000000000000000000000000                      19536641653416656896        11010010110001010101
1100000000001000000001001001010000010000 000000                                         52785167270912              11010010110001010101
1110000001000000100010001000000001000000 000000000000000000                             252485399178379264          11010010110001010101

10000000000000000000000000000000000000000                                               1099511627776
1111111111111111111111111111111111111111                                                1099511627776(-1)


1111111111111111111111111111111111111111 1099511627775
 
1011110111011111111111111110110111100000 815506910688    /1048576 777727,995574951171875
1011111111111110011001000000000000000000 824606720000    /1048576 786406,25
1101110011111111111010111111100000000000 949186459648    /1048576 905214,748046875
1101111011111101011011111111000000000000 957734711296    /1048576 913366,99609375
1110111110111101110101010111111101111100 1029682069372   /1048576 981981,343624114990234375
1110111110111111111011111101110111101111 1029717351919   /1048576 982014,99168300628662109375
1110111111111010101101100101100000000000 1030703437824   /1048576 982955,396484375
11110011111010111110111111111111011000   261908856792    /1048576 249775,74996185302734375
1111011011011101101111011100111110000000 1060282158976   /1048576 1011163,8631591796875
1111011110111111111001110111000000000000 1064076537856   /1048576 1014782,46484375
1111011111111111011111110101111100000000 1065143459584   /1048576 1015799,960693359375
1111101110010110110110010011000000000000 1080567607296   /1048576 1030509,57421875
1111110110101011111011111111000000000000 1089511354368   /1048576 1039038,99609375
1111111001111101011111011111111001111100 1093027102332   /1048576 1042391,874629974365234375
1111111011010111011011010111011011110110 1094535968502   /1048576 1043830,8415431976318359375
1111111011011111010111111111111111111000 1094669303800   /1048576 1043957,99999237060546875
1111111110111101111011011111101011110000 1098403150576   /1048576 1047518,8737640380859375
111111111101100101111111111000           1073111032      /1048576 1023,39842987060546875
1111111111111101011100111101011111111110 1099468888062   /1048576 1048535,2402324676513671875
1111111111111111101111101111101000000000 1099507366400   /1048576 1048571,93603515625

1000000000000000100001000010010010010100 549764474004    /1048576 524296,258930206298828125      7
100000000000000101001010010010000000000  274888729600    /1048576 262154,3212890625              6
1000000000000010010000101100000000001000 549793742856    /1048576 524324,17188262939453125       6
1000000000001101000001110000000000000000 549974376448    /1048576 524496,4375                    6
1000000011110001000001000000000000000000 553799385088    /1048576 528144,25                      6
1000001000000000000000000000001100010000 558345749264    /1048576 532480,0007476806640625        4
1000001000100000000111000000010000000000 558884455424    /1048576 532993,7509765625              6
1000001100010010000010000100000010100000 562943246496    /1048576 536864,515777587890625         8
1000010000100000001000001010010000000000 567474693120    /1048576 541186,0400390625              6
10000101100101100100000001000000000000   143437860864    /1048576 136793,00390625                8
1000011000100111000001000000000000000000 576180191232    /1048576 549488,25                      7
1000011110010000000011000000100110000000 582237292928    /1048576 555264,7523193359375           10
1000101000011000000010010000000000000000 593108729856    /1048576 565632,5625                    6
1001000000110000000000100100000000000000 619280744448    /1048576 590592,140625                  5
1001010000000000100100000000000010000000 635664597120    /1048576 606217,0001220703125           5
1010000000001001110010000000100000000000 687358871552    /1048576 655516,501953125               7
1010000100000100000000000000000001000000 691556843584    /1048576 659520,00006103515625          4
1010010100000000101001011001010001000000 708680455232    /1048576 675850,34869384765625          11
1010100010000010010000010100000000000000 723739820032    /1048576 690212,078125                  7
1011100000000010011010001100100110000000 790314404224    /1048576 753702,5491943359375           12
1100000000001000000001001001010000010000 824768238608    /1048576 786560,2861480712890625        7
1101000000010000000000000000010011       13962838035     /1048576 13316,00001811981201171875     6
1110000001000000100010001000000001000000 963155361856    /1048576 918536,53131103515625          7

40!/39!/1!  40
40!/38!/2!  780
40!/37!/3!  9880
40!/36!/4!  91390
40!/35!/5!  658008
40!/34!/6!  3838380
40!/33!/7!  18643560
40!/32!/8!  76904685
40!/31!/9!  273438880
40!/30!/10! 847660528
40!/29!/11! 2311801440
40!/28!/12! 5586853480

3838380/2^20 3,660564422607421875


1000000000000000000000000000000000000000 549755813888
549755813888/1048576 524288

524288 549755813888/1048576
524296
524324
524496

18446744073709551616
1844674407

1111111111111111111111111111111111011011111110101111111111111101111111111101111 1110111111111111111111111110111111111111111011010000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000000000000000000 00000000000000000000
1000000000000000000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000 170141183460469231731687303715884105728
170141183460469231731687303715884105728/18446744073709551616 9223372036854775808

9223372036854775808 170141183460469231731687303715884105728/18446744073709551616

128!/127!/1!  128
128!/126!/2!  8128
128!/125!/3!  341376
128!/124!/4!  10668000
128!/123!/5!  264566400
128!/122!/6!  5423611200
128!/121!/7!  94525795200
128!/120!/8!  1429702652400
128!/119!/9!  19062702032000
128!/118!/10! 226846154180800
128!/117!/11! 2433440563030400
128!/116!/12! 23726045489546400
128!/115!/13! 211709328983644800
128!/114!/14! 1739040916651368000

faster "bit" there is a library from "ice" https://github.com/iceland2k14/secp256k1 there it is necessary to throw its libraries into the folder with the script.

***

and read (with a translator) https://istina.msu.ru/profile/FilatovOV/ , https://vk.com/@fil_post-eta-statya-rvet-vse-predstavleniya-o-veroyatnostyah , https://disk.yandex.ru/i/LsEWmhs3ArM7Tw

not yet, there is too much to think about 

***

It can be stuck in this shit for the rest of your life.

All this madness is described by the formula Ralph Hartley (I = K log2(N)) or easier log2(x)=

there should be a lot in the folder

dc.py
fb.py
gb.py
hb.py
...
run.cmd

***

algorithm from here Answer #4: https://www.py4u.net/discuss/207582 because this one is slower https://combi.readthedocs.io/en/stable/intro.html

then the last option is to look for luck. who have 64-core processors.

different 2 symbols for seed give different results

pz 20 example...

step 1100006 seed 000000111011001011000011111101 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 1532829 seed 000001001101100011010111111001 bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1129134 seed AAAAAAaaaAaaaaAAaaAaaAaAAaaaAA bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...

step 494992 seed BBBBBBbBBBBbBbbbBbbbbbBbBbbBbb bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 548744 seed BBBBBBbBBbBbbbBBbbBBbbbbbbBBbb bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 896722 seed BBBBBBbbBbBBbBbbBbbbBbbBbbBBbb bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1325957 seed SSSSSsSSSSsSssssSsSSsssssSsssS bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 5492813 seed RRRRrrRRrRrRRrrRrrrRRRrRRrrrrr bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 6988942 seed RRRRrrrRrrrrRRrrrRRrrRRRrRRRrr bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 7290958 seed RRRRrrrrRrrRRRrrrRRRrrRrrRRrrR bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 7721483 seed RRRRrrrrrrrrrRrrRrrRRrRRRRrRRR bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 8730248 seed RRRrRRrRRrrrrRrRrrrRrRrRrRRRrr bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1811954 seed OOOOOoOoOooooOoOOOooooooooOOOO bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 1873426 seed VVVVVvVvvVVvvvVvvVvVvVVvVvvvvV bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 430546 seed WWWWWWWwwwwWwWwWWwwWwWwwWWwwww bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 3821040 seed XXXXxXXxxXXxXxxxXxxxXXxxxXXxXx bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 2652540 seed JJJJJjjjJJJjJjjjjjJjjjJJJJjjjJ bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 2777464 seed JJJJJjjjJjJJjjjjJjJJjjjjJJJJjj bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...
step 765336 seed FFFFFFfFfffFfffffFffFFFFffFffF bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
step 2367636 seed FFFFFffFfFFfffFFFffFffffffFfFF bit 11010010110001010101 dec 863317 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum
...

it turns out for different 2 seed symbols we have 200-300 collisions

22 sym len
6892620648693261354600   76!/38!/38!
1000000000000000000000 =
5892620648693261354600 / 2^64 319,4396054473088187643 collision

that is, there are already 1000-1500 collisions on 5 different 2-sign seeds

200 Aa
200 Bb
200 Cc
200 Dd
200 Ff

5 1000 collisions

10 2000 collisions

15 3000 collisions

20 4000 collisions

25 5000 collisions

30 6000 collisions

35 7000 collisions

40 8000 collisions

45 9000 collisions

50 10000 collisions

100 20000 collisions

500 100000 collisions

It was misleading. I was delighted and did not notice the catch. "collisions" are simply out of range.

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03C3CA0BD8A7D05A949 pz63

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A0705B5714CFEAA29032 pz70

***

The moment of truth or for the first time in history 11/28/2021 real collisions were found in bitcoin. Until I write the address, maybe a person decides to go to the forum himself and write in person. What the Large Bitcoin Collider did not do was 1 person did. And he wrote down his name in the new history.

it works like this.

all permutations ripmd160 in hex format 40 length

from

0000000000000000000000000000000000000000

to

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

for example, puzzle 64 is somewhere there

0000000000000000000000000000000000000000
...
3ee4133d991f52fdf6a25c9834e0745ac74248a0
...
3ee4133d991f52fdf6a25c9834e0745ac74248a1
...
3ee4133d991f52fdf6a25c9834e0745ac74248a2
...
3ee4133d991f52fdf6a25c9834e0745ac74248a3
...
3ee4133d991f52fdf6a25c9834e0745ac74248a4
...
3ee4133d991f52fdf6a25c9834e0745ac74248a5
...
3ee4133d991f52fdf6a25c9834e0745ac74248a6
...
etc
...
3ee4133d991f52fdf6a25c9834e0745ac74248af
...
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

in other words into space

0000000000000000000000000000000000000000
...
FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

there is only 1 such key 3ee4133d991f52fdf6a25c9834e0745ac74248a4 but it is obtained by numbers from space (dec 9223372036854775808-18446744073709551616) and the rest where then are located which end with 0 1 2 3 ... D E F

something this damn shit doesn't want to give up  maybe we can try to get in through ripemd160...



"from Russia with love"

collision test for pz 20

2^20 1048576, 20 1HsMJxNiV7TLxmoF6uJNkydxPFDog4NQum | 863317

(24!/12!/12!)/2^20 2,578884124755859375
1048576 2^20
2704156 step
2 collisions, finds only 1 for some reason

(28!/14!/14!)/2^20 38,25817108154296875
1048576 2^20
40116600 step
38 collisions, look in the script...


for 64 ...

(188!/94!/94!)/2^64 1235956206315626091331338051467874028
18446744073709551616 2^64
22799367824217315491046998779230288685596678611381812000
1235956206315626091331338051467874028 collisions
                                   
(168!/84!/84!)/2^64 1246690648845973918331482456337
18446744073709551616 2^64
22997383338348585032434609379579328145757058837400 168!/84!/84!
1246690648845973918331482456337 collisions
                             
(148!/74!/74!)/2^64 1266470970702566355349691
18446744073709551616 2^64
23362265873332749085315221863910685052043000 148!/74!/74!
1266470970702566355349691 collisions
                       
(128!/64!/64!)/2^64 1298394228608800905,709 collisions
18446744073709551616 2^64
23951146041928082866135587776380551750 128!/64!/64! 
1298394228608800905 collisions
                 
(100!/50!/50!)/2^64 5469330747,064212325444
18446744073709551616 2^64
100891344545564193334812497256 100!/50!/50!
5469330747 collisions
         
(80!/40!/40!)/2^64 5827,977463326783892683
18446744073709551616 2^64
107507208733336176461620 80!/40!/40!
5827 collisions

(70!/35!/35!)/2^64 6,081630306594410506193
18446744073709551616 2^64
112186277816662845432 70!/35!/35!
6 collisions

(68!/34!/34!)/2^64 1,542442469063799766063
18446744073709551616 2^64
28453041475240576740 68!/34!/34!
1 collisions

the best option? (128!/64!/64!)/2^64

because 1 (68!/34!/34!)/2^64 may not exist, how to search 6? (70!/35!/35!)/2^64

112186277816662845432/6 = 18697712969443807572 (~ 2^64)

take the first step randomly and add to it 5 times dec 2^64...

or looking for "mathematical expectation" yeah monkeys are writing a book

it is not clear why because 256 bits can be different

bit to character sampling ratio

1111 11111111 1111111111111111 11111111111111111111111111111111...