Hoogendoorn, Sander writes:
Torben Schlaqntz wrote:
> It seems to me that this k (in 2kp+1) is never:
> 4,12,20,28,36,46,52,60,68,76,84
> at least for less than M416.947.
> Am I again a fool for a pattern already proved?
It has been proven that k = 1 or 7 mod 8
Careful! It has been proven that _factors_ are of that form, not that
the k's (of 2*k*p + 1 where 2*k*p + 1 is a factor of M(p)) are of that
form. k, in fact, can be 0 mod 4, e.g., since, if a factor is 1 mod 8:
factor = 2*k*p + 1 = 1 (mod 8)
2*k*p = 0 (mod 8)
k*p = 0 (mod 4)
k = 0 (mod 4)
... since p, being prime, is not 0 mod 4. This occurs, e.g., for
M(11), as one of the factors is 89.
Will
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