Message 6769 from Yahoo.Groups.Primeform
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Date: Wed, 28 Dec 2005 11:49:41 -0000
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From: "p_jobling" <Paul.Jobling@...>
Subject: Re: Paul Jobling's record palindrome
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>> what sieving program are you using (is it NewPGen) ?
> I am pretty sure this is a custom siever.

It is indeed (though since I used the nuts and bolts of NewPGen for
the functionality, it was easiest to actually put it in the product).
It is not too tricky:

10^(2n+6)+10^n*P7+1 = 0 (mod p)

> P7 = -(10^(2n+6)+1).10^(-n) (mod p)

(P7 a 7 digit palindrome).

We can find 10^(2n+6) mod p using RTL exponentiation, and 10^(-n) by
finding 10^(-1) mod p then more RTL. I couldn't find any more
shortcuts though, such as any Aurifeuillian-like factorization for
certain P7 values.

> With my best wishes for a happy new year with many new prime
> discoveries.

I would second that. A question for the group: what would be top of
your feasible wishlist this year?

Regards,

Paul.


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