Quote:
My best guess is that trying 6 digits on either side is not enough. I think the largest P1 prime factor ever found is something greater than 50 digits (166 bits), so it is plausible that those three factors are some part of the digit sequence for a product of valid prime factors of the Mersenne numbers in question.

The largest factor found with P1 has 47 digits. The largest GIMPS factor found with P1 has 45 digits.
http://www.loria.fr/~zimmerma/records/Pminus1.html
the server only displays factors upto about 31 or 32 digits corectely. So i guess you'll have to add 1 or 2 extra digits in your test.