Quote:
Originally Posted by CRGreathouse
This is similar to my last question here. Where can I look up known factors of (possibly large) Mersenne numbers? For example, I am interested to know if any factors are known for 2^1277  1. I didn't see any on factordb.com but there are probably other resources.
Of course none may be known but I'd like to be a bit more thorough in my checking.

Check out Will Edgington's site:
http://www.garlic.com/~wedgingt/mersenne.html
Download mersdata.zip, and you will see factors of completely factored Mersenne numbers in one file and known factors of incompletely factored Mersenne numbers with exponents up to 200,000 in a second file. (He considers a Mersenne number as 2^n  1 for any n, prime or composite.) It has not been updated in a year, but hopefully should still be useful. Will also has a database of factors for larger exponents, and has responded to inquiries about specific exponents in the past.