I have a silly script that tries to predict the challenge keys. I like to toy with this stuff.
If I pass it the sequence of known keys from #1 to #64, this is the prediction for #65:
Prediction: 3.05208467e+19 -> 1A78FD45E05A73800
Now passing it the sequence from #1 to #65:
Prediction: 4.73075146e+19 -> 290860DE1FB9B1000
I found nothing from -1M to +1M for this value.
EDIT:
The space for puzzle 66 is 0x3FFFFFFFFFFFFFFFF-0x20000000000000000 which gives in decimal 36 893 488 147 419 103 231.