Quote:
Originally Posted by Dr Sardonicus
At present, the smallest Mersenne number which is known to be composite, but for which no factors are known, is M_{1277}, or 2^{1277}  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, P1 or ECM) requires SNFS which runs a lot faster than GNFS. So factoring a
nbit Mersenne number is far easier than a
nbit RSA candidate.