tepan@MacBook-Pro %

result :

RANGE 49

1000000000000:1ffffffffffff

start = 281474976710656
end = 562949953421311

k = 79985852346388

319943409385552 = 122FCA143C050 #1
337535595429968 = 132FCA143C050 #2

399929261731940 = 16BBBC994B064 #1
417521447776356 = 17BBBC994B064 #2

479915114078328 = 1B47AF1E5A078 #1
497507300122744 = 1C47AF1E5A078 #2


key = 174176B015F4D <- answer

RANGE 53

10000000000000:1fffffffffffff

start = 4503599627370496
end = 9007199254740991

k = 1636475620130100

5190901837100956 = 1271190410779C #1
6827377457231056 = 184176B015F4D0 #2

8463853077361156 = 1E11D45C1B7204 #1
8745328054071812 = 1F11D45C1B7204 #2

key = 180788E47E326C <- answer


i just play around with math, by using simple decimal multiplications combined with logarithmic insights, you can systematically determine key values within a numerical range.

fun fact the unique thing is that the key is indeed located right in the area that has been measured using mathematics, I am using 2 pieces of evidence for now.

for now i'm just doing this thing work, thanks for read and respect my post about puzzle.