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Old 2013-02-11, 11:48   #4
akruppa's Avatar
Aug 2002

25×7×11 Posts

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. 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.
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