On 26 Apr 2001, Brian J. Beasley wrote
> On 26 Apr 2001, at 6:34, Hans Riesel wrote:
>
> > Hi everybody,
> >
> > If 2^p-1 is known to be composite with no factor known, then so is
> > 2^(2^p-1)-1.
>
> Much as I hate to nitpick a far better mathematician than myself,
> this is seems to be an overstatement.
(two paragraphs deleted)
> Question (deep) - if we did discover a factor of 2^(2^727-1)-1, would
> that help us to find a factor of 2^727-1 ?
I am skeptical too. Show us how the factors
131009 of M_(M11) = 2^(2^11 - 1) - 1
724639 of M_(M11)
285212639 of M_(M23)
lead to factorizations of M11 and M23. Why don't the factors
231733529 of M_(M17)
62914441 of M_(M19)
lead to similar factorizations of M17 and M19?
With c = 2^727 - 1, 2^751 - 1, 2^809 - 1, 2^997 - 1, 2^1051 - 1,
I looked for factors 2*k*c + 1 of 2^c - 1, but found none
with k <= 20000. I invite those with a special search program
for M_(M127) factors to search these further.
Peter L. Montgomery
[EMAIL PROTECTED]
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