Re: Bitcoin puzzle transaction ~32 BTC prize to who solves it
⭐ Merited by digaran (1)
Someone said that the parity of the target private key does not matter 
This has implications for the choice of divisor.
If the private key is divisible by 2 without a remainder, then the divisor is correct. PrivKey % 2 = 0.
But because the target key is not known, the correct divisor can only be random.
The same applies to public keys, which also have parity.
Example of correct divisors for a test private key:
0x197D95F81F7BA421E829611A8F8BB1204 % 0x15B = 0
It is impossible to find the correct divisor for a public key; you need a private key.
This has implications for the choice of divisor.
If the private key is divisible by 2 without a remainder, then the divisor is correct. PrivKey % 2 = 0.
But because the target key is not known, the correct divisor can only be random.
The same applies to public keys, which also have parity.
Example of correct divisors for a test private key:
0x197D95F81F7BA421E829611A8F8BB1204 % 0x15B = 0
Code:
[i] NB: 0 DIVKey: 1 Inverse DivideKey: 1
[i] 1 TRUE DIVIDER NB: 4 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] 2 TRUE DIVIDER NB: 62 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x7 Result: 0x3A439FEDFED17728EE15703CB5D194DC
[i] 3 TRUE DIVIDER NB: 126 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1 Result: 0x197D95F81F7BA421E829611A8F8BB1204
[i] NB: 200 DIVKey: 10C Inverse DivideKey: 2DD9CA81E9131ABF0B7672A07A44C6AF8899965ECF27C0FF3D1A3724AED80BB
[i] 4 TRUE DIVIDER NB: 329 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] NB: 400 DIVKey: 23C Inverse DivideKey: 51E6EFE35B4CFAA11E6EFE35B4CFAA117EDBBF8316F5AB35212C7A71F936F3C2
[i] 5 TRUE DIVIDER NB: 418 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x15B Result: 0x12CE43D9BA45157E164076DAC9CF14C
[i] 6 TRUE DIVIDER NB: 585 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x4 Result: 0x65F657E07DEE9087A0A5846A3E2EC481
[i] NB: 600 DIVKey: 23E Inverse DivideKey: 4039164CB5F71484039164CB5F71483FE77978885DECC19E99607B9F4FE2CBB
[i] NB: 800 DIVKey: 1C0 Inverse DivideKey: 6D24924924924924924924924924924899E043E4A2BAF6997935B04F767BB3D2
[i] 7 TRUE DIVIDER NB: 809 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x373 Result: 0x763E70ED25521F5892DEADDA978CEC
[i] 8 TRUE DIVIDER NB: 834 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1 Result: 0x197D95F81F7BA421E829611A8F8BB1204
[i] NB: 1000 DIVKey: DE Inverse DivideKey: B9A85C40939A85C40939A85C40939A84D81BA4D0CFD743C5DAAE799D7904C09F
[i] 9 TRUE DIVIDER NB: 1062 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x15B Result: 0x12CE43D9BA45157E164076DAC9CF14C
[i] 10 TRUE DIVIDER NB: 1072 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] 11 TRUE DIVIDER NB: 1127 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x15B Result: 0x12CE43D9BA45157E164076DAC9CF14C
[i] 12 TRUE DIVIDER NB: 1169 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] NB: 1200 DIVKey: 14C Inverse DivideKey: 80C565C87B5F9D4D1BC2503159721ED743AFDC9C2231A3E05E2CE713F071A6FE
[i] 13 TRUE DIVIDER NB: 1337 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1C Result: 0xE90E7FB7FB45DCA3B855C0F2D746537
[i] NB: 1400 DIVKey: 2C0 Inverse DivideKey: A28BA2E8BA2E8BA2E8BA2E8BA2E8BA2DBD141E710462D73192E306F16890FE86
[i] 14 TRUE DIVIDER NB: 1477 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] 15 TRUE DIVIDER NB: 1542 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x4 Result: 0x65F657E07DEE9087A0A5846A3E2EC481
[i] 16 TRUE DIVIDER NB: 1578 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x373 Result: 0x763E70ED25521F5892DEADDA978CEC
[i] NB: 1600 DIVKey: 1EE Inverse DivideKey: 79C8084A9F9C8084A9F9C8084A9F9C7FE9E86E4447FBAEAF98EB545CE5A3A7DA
[i] 17 TRUE DIVIDER NB: 1619 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2B6 Result: 0x96721ECDD228ABF0B203B6D64E78A6
[i] NB: 1800 DIVKey: 346 Inverse DivideKey: 50F46433527B6AEBD67415FEC72DD2C938973869F12AD2BF30BEDBE9EEBFE597
[i] 18 TRUE DIVIDER NB: 1880 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1C Result: 0xE90E7FB7FB45DCA3B855C0F2D746537
[i] NB: 2000 DIVKey: 4A Inverse DivideKey: 2CF914C1BACF914C1BACF914C1BACF9112F534A510F48ADA1066AFBECAA1BF5B
[i] Data Saved in file DivideKeys.txt
[i] 1 TRUE DIVIDER NB: 4 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] 2 TRUE DIVIDER NB: 62 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x7 Result: 0x3A439FEDFED17728EE15703CB5D194DC
[i] 3 TRUE DIVIDER NB: 126 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1 Result: 0x197D95F81F7BA421E829611A8F8BB1204
[i] NB: 200 DIVKey: 10C Inverse DivideKey: 2DD9CA81E9131ABF0B7672A07A44C6AF8899965ECF27C0FF3D1A3724AED80BB
[i] 4 TRUE DIVIDER NB: 329 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] NB: 400 DIVKey: 23C Inverse DivideKey: 51E6EFE35B4CFAA11E6EFE35B4CFAA117EDBBF8316F5AB35212C7A71F936F3C2
[i] 5 TRUE DIVIDER NB: 418 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x15B Result: 0x12CE43D9BA45157E164076DAC9CF14C
[i] 6 TRUE DIVIDER NB: 585 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x4 Result: 0x65F657E07DEE9087A0A5846A3E2EC481
[i] NB: 600 DIVKey: 23E Inverse DivideKey: 4039164CB5F71484039164CB5F71483FE77978885DECC19E99607B9F4FE2CBB
[i] NB: 800 DIVKey: 1C0 Inverse DivideKey: 6D24924924924924924924924924924899E043E4A2BAF6997935B04F767BB3D2
[i] 7 TRUE DIVIDER NB: 809 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x373 Result: 0x763E70ED25521F5892DEADDA978CEC
[i] 8 TRUE DIVIDER NB: 834 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1 Result: 0x197D95F81F7BA421E829611A8F8BB1204
[i] NB: 1000 DIVKey: DE Inverse DivideKey: B9A85C40939A85C40939A85C40939A84D81BA4D0CFD743C5DAAE799D7904C09F
[i] 9 TRUE DIVIDER NB: 1062 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x15B Result: 0x12CE43D9BA45157E164076DAC9CF14C
[i] 10 TRUE DIVIDER NB: 1072 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] 11 TRUE DIVIDER NB: 1127 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x15B Result: 0x12CE43D9BA45157E164076DAC9CF14C
[i] 12 TRUE DIVIDER NB: 1169 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] NB: 1200 DIVKey: 14C Inverse DivideKey: 80C565C87B5F9D4D1BC2503159721ED743AFDC9C2231A3E05E2CE713F071A6FE
[i] 13 TRUE DIVIDER NB: 1337 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1C Result: 0xE90E7FB7FB45DCA3B855C0F2D746537
[i] NB: 1400 DIVKey: 2C0 Inverse DivideKey: A28BA2E8BA2E8BA2E8BA2E8BA2E8BA2DBD141E710462D73192E306F16890FE86
[i] 14 TRUE DIVIDER NB: 1477 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2 Result: 0xCBECAFC0FBDD210F414B08D47C5D8902
[i] 15 TRUE DIVIDER NB: 1542 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x4 Result: 0x65F657E07DEE9087A0A5846A3E2EC481
[i] 16 TRUE DIVIDER NB: 1578 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x373 Result: 0x763E70ED25521F5892DEADDA978CEC
[i] NB: 1600 DIVKey: 1EE Inverse DivideKey: 79C8084A9F9C8084A9F9C8084A9F9C7FE9E86E4447FBAEAF98EB545CE5A3A7DA
[i] 17 TRUE DIVIDER NB: 1619 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x2B6 Result: 0x96721ECDD228ABF0B203B6D64E78A6
[i] NB: 1800 DIVKey: 346 Inverse DivideKey: 50F46433527B6AEBD67415FEC72DD2C938973869F12AD2BF30BEDBE9EEBFE597
[i] 18 TRUE DIVIDER NB: 1880 TestKey: 0x197D95F81F7BA421E829611A8F8BB1204 Divider: 0x1C Result: 0xE90E7FB7FB45DCA3B855C0F2D746537
[i] NB: 2000 DIVKey: 4A Inverse DivideKey: 2CF914C1BACF914C1BACF914C1BACF9112F534A510F48ADA1066AFBECAA1BF5B
[i] Data Saved in file DivideKeys.txt
It is impossible to find the correct divisor for a public key; you need a private key.
everything is based on exploring with maths
Code:
x=2000000000000000
t=1185429467683753
A0=x-t
>>814570532316247
A1=t/5
>>237085893536750.6
A2=A0/5
>>162914106463249.4
A3=t-A1
>>948343574147002.4
A4= A0-A2
>>651656425852997.6
A5=A4-A1
>>785429467683753
A6=A3-A2
>>414570532316247
t=1185429467683753
A0=x-t
>>814570532316247
A1=t/5
>>237085893536750.6
A2=A0/5
>>162914106463249.4
A3=t-A1
>>948343574147002.4
A4= A0-A2
>>651656425852997.6
A5=A4-A1
>>785429467683753
A6=A3-A2
>>414570532316247
Even from divisions with results with fractions (floats), you can obtain integers with certainty.
If you use mathematics correctly.