Message 6995 from Yahoo.Groups.Primeform
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Date: Fri, 24 Feb 2006 22:36:16 -0000
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From: "David Broadhurst" <d.broadhurst@...>
Subject: Re: Primality proof of (34*10^15768-43)/9 - need help!
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--- In primeform@yahoogroups.com, "gchil0" <jgchilders@...> wrote:

> Since F=1 in this case, the search for
> factors congruent to n is unnecessary,

That's not /strictly/ correct.
In principle your target could have
had a factor congruent to n modulo G
and it would have been found.

I think that it is better to say that, with F=1,
the same polynomials which are used
to test for factors congruent to 1 modulo G
are also used to test for factors congruent to n modulo G,
since n = -1 mod G and the CHG method checks for either sign of
x in a possible factor x*G+1. Hence the absence of factors at
negative x certifies the absence of factors congruent to
n modulo G.

I have no idea why John's programme did not stop
when you expected it to stop, since I have
never run his code.

I can confirm that my validation programme
proves the absence of factors in /both/
residue classes, whenever G>1, as here.

David


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