Discussion thread here: https://bitcointalk.org/index.php?topic=1306983.msg64526037#... Bitcoin puzzles are private keys with just a few unknown bits so that anyone can bruteforce them to collect a reward. Puzzle 66 contained 66 unknown bits and had 6.6 BTC deposited into it by the initial puzzle creator. The private key was 0x000000000000000000000000000000000000000000000002832ed74f2b5e35ee or 256 bits with mostly ze…
I'm also unclear on where you got the 'multiple of 5' bit about. It seems the keys corresponding to numbers divisible by 5 were used in a spend transaction by the puzzle creator. Using those addresses in spend transactions reveals the public key and saves compute that would be wasted hashing. It also enables direct attacks using Pollard's rho (which someone already posted a link for above).
Src: https://bitcointalk.org/index.php?topic=1306983.msg51466379#... https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm_for_...
Another interesting discussion on bitcointalk about using Pollard's kangaroo: https://bitcointalk.org/index.php?topic=5244940.0