I have a BSGS that solves puzzle 60 in 3 seconds.
The problem is that we don't have public keys.

We're rounding circles again... I have a Kangaroo precomputed DB that can solve any puzzle up to 75 bits in less than one second. It contains close to 3 billion DP points so far. Takes less than 50 GB of disk space.
The problem is that we don't have public keys.

Maybe we should go in the shrinking ranges direction...
Let's take 68: 80000000000000000:fffffffffffffffff
What would be the point to scan a sub range of it like 80000000000000000 to 8000fffffffffffff when we can bet that the private key beginning isn't 8000 ? (or 9999, aaaa , bbbb , cccc , dddd , eeee, ffff)