mersenneforum.org - View Single Post - Number of distinct prime factors of a Double Mersenne number

ewmayer · 2012-11-09, 21:16

Any such estimate needs to take into account the special "restricted" form of Mersenne factors, which in general will cause M(p) (and by extension M(M(p) for M(p) prime) to have a lower expected number of factors than a general odd number of similar size. Here is a paper I found via cursory online search - the paper itself is not so much of interest in the present context as are the references, several of which appear to have investigated the question you ask.

2012-11-09, 21:16	#2
ewmayer ∂²ω=0 Sep 2002 República de California 2DD0₁₆ Posts	Any such estimate needs to take into account the special "restricted" form of Mersenne factors, which in general will cause M(p) (and by extension M(M(p) for M(p) prime) to have a lower expected number of factors than a general odd number of similar size. Here is a paper I found via cursory online search - the paper itself is not so much of interest in the present context as are the references, several of which appear to have investigated the question you ask.