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Old 2021-09-21, 15:08   #6
alpertron's Avatar
Aug 2002
Buenos Aires, Argentina

5·277 Posts

Originally Posted by Dr Sardonicus View Post
At present, the smallest Mersenne number which is known to be composite, but for which no factors are known, is M1277, or 21277 - 1, which is a lot smaller than any RSA 2048. It's a 385 decimal digit composite number.
Furthermore, completely factor a Mersenne number (if it cannot be done with trial factoring, P-1 or ECM) requires SNFS which runs a lot faster than GNFS. So factoring a n-bit Mersenne number is far easier than a n-bit RSA candidate.
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