The Numbers Guy has provided a clear and informative explanation of the recent factorization of the 1039th Mersenne number. I've add just a few comments on his recent blog entry, which I've said is otherwise "faultless" (continuing an earthquake metaphor introduced at the conclusion of his post):
- Mersenne numbers, because of their special form, are especially shaky. They fall much more quickly to factoring methods than the "tested and approved" counterparts of the same length used in cryptography - which is the reason that Mersenne numbers are often targeted in factoring research.
