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Old 2013-02-12, 00:05   #6
ewmayer
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Sep 2002
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Quote:
Originally Posted by axn View Post
Post #30 in that thread has a table of p-1 and p+1 factorizations for all but the latest M-prime exponent.


Quote:
Originally Posted by akruppa View Post
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 eCPM1SHTM. Use it. Live it. Embrace it with every fiber of your whole-grain-dosed semicolon, or something.

Quote:
At any rate, if the smoothness of p-1 has an effect on the probability of Mp being prime, then I'm fairly certain it is due to the smoothness of p-1 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 factor-number correlation should occur, we may be able to remove the 'C' from the above trademarked initialism.
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