Quote:
Originally Posted by axn

Post #30 in that thread has a table of p1 and p+1 factorizations for all but the latest Mprime exponent.
Quote:
Originally Posted by akruppa
We pondered this observation before, see axn's link and a few other threads here. The tentative title is "extended crank P minus one smoothness hypothesis", "ECPMOSH", or something like that... I forgot.

Ahem ... it's eCPM1SH
^{TM}. Use it. Live it. Embrace it with every fiber of your wholegraindosed semicolon, or something.
Quote:
At any rate, if the smoothness of p1 has an effect on the probability of Mp being prime, then I'm fairly certain it is due to the smoothness of p1 affecting the probability that Mp has small prime factors, and thus after trial division, the survivors should be practically equally good candidates for primes again.

Indeed  if someone manages to find a deeper reason for *why* this [alleged] statistical factornumber correlation should occur, we may be able to remove the 'C' from the above trademarked initialism.