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

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Quote:
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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