I made some computations. Used Python 3. I was curious if the next puzzle can be ax+b=y.
d1, d2, d3 are corresponding private keys from puzzle. Needed to compute a and b.
First script for puzzle 66:
#!/usr/bin/env python3
import math
d1=0x0000000000000000000000000000000000000000000000007cce5efdaccf6808
d2=0x000000000000000000000000000000000000000000000000f7051f27b09112d4
d3=0x000000000000000000000000000000000000000000000001a838b13505b26867
asqr=(d2-(d2/d1))/d1
a=math.sqrt(asqr)
print("a =",a)
b=d2/(a*d1)
print("b =",b)
d4=a*d3+b
print("next =",hex(int(d4)))
Second script for puzzle 120:
#!/usr/bin/env python3
import math
d1=0x000000000000000000000000000000000000016f14fc2054cd87ee6396b33df3
d2=0x00000000000000000000000000000000000035c0d7234df7deb0f20cf7062444
d3=0x0000000000000000000000000000000000060f4d11574f5deee49961d9609ac6
asqr=(d2-(d2/d1))/d1
a=math.sqrt(asqr)
print("a =",a)
b=d2/(a*d1)
print("b =",b)
d4=a*d3+b
print("next =",hex(int(d4)))
The output is however strange, because a=b!
This means the next puzzle is multiplied and added to it the same value, I mean the multiplicator and later adding a number are the same.
First script gives:
a = 1.4068509690560507
b = 1.4068509690560507
next = 0x254d0fd348f800000
Second script gives:
a = 6.122671382779787
b = 6.122671382779785
next = 0x251a1b44dd0e160000000000000000
What can mean that just raising the value(s) of a and b can give next puzzle private key!