Hi,


I have no idea where to look for, so I'm hoping you can give me some pointers.


I'm interested by numbers of form $p-1$ when $p$ is a prime number. Do they have a name, so that I can google them?


More precisely, I'm interested in their factors. Ok, obviously 2 is a factor, but what about the others? Are there a lot of small factors? Do we know the rate of the growth of its larger factor, is it linear, logarithmic?


Thanks.



Factors of p-1 when p is prime.
Two extremes of this problem are Fermat primes and Sophie Germain primes. If either class had infinitely many members, that would contribute to an answer of your question. There is literature about the distribution of prime factors (cf. Riesel and Knuth), but I do not know the literature regarding the restriction to numbers of the form prime - 1 .


If I had to start anywhere for questions like this, I would choose one or all three of the following:


Richard Guy's Unsolved problems in Number Theory,


Hans Riesel's book on computer methods for primality proving and factorization,


Prime Numbers: a Computational perspective, by Crandall and Pomerance.


Forgive my memory if the titles or authors are missing or incorrectly spelled.


Gerhard "Ask Me About System Design" Paseman, 2010.06.08


