[EMAIL PROTECTED] writes:
Both of Chris Nash's remarks are intended for odd p.
Hm; yes, I didn't notice that all the exceptions were for even
exponents.
The factor 3 of 2^2 - 1 is not congruent to 1 modulo 2*2.
"Primitive factors" should be restricted to primitive prime factors.
Well, I was thinking of prime & proper factors, but I didn't say that
explicitly and see your points.
The factor 1057 = 7*151 of 2^15-1 = 7*31*151 does not divide any
M(n) with 1 <= n < 15, yet 1057 is not 1 modulo 15
(however the new prime 151 has this form).
Yup. The ecm3 program of the mers package tries very hard to print
only prime factors that are not also factors of smaller Mersennes, and
this was the situation that I was thinking of.
In fact, ecm3 will print a warning if it's given composite factors. Or
when it's given prime factors of a smaller Mersenne number. My
automatic update scripts use this output to factor the composite
factors and figure out which smaller exponent the others really
"belong" to.
Will
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