openpfgw : Message: Re: [openpfgw] Wagstaff Numbers

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Wagstaff Numbers - Proof for a Primality Test

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Message #1894 of 2071 |

Re: [openpfgw] Wagstaff Numbers - Proof for a Primality Test

--- On Sun, 10/5/08, Anton Vrba <antonvrba@...> wrote:
> Hello fellow group members,
>
> After a long time I rear my head by posting a proof for a
> Wagstaff
> number primality test.

This would be better on the primenumbers list.

> http://www.mersenneforum.org/showpost.php?p=144516&postcount=1

"Consider an element w ... that has no solution w^k == 1"

is meaningless.

Skipping everything before it, (19) seems to be obviously false, as the order
you've specified does not divide the order of the group.

Phil

Sun Oct 5, 2008 9:25 am

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Phil Carmody <thefatphil@...>

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Message #1894 of 2071 |

Expand Messages	Author	Sort by Date
Hello fellow group members, After a long time I rear my head by posting a proof for a Wagstaff number primality test. This test is similar to the well known...	Anton Vrba antonvrba	Oct 5, 2008 9:02 am
... This would be better on the primenumbers list. ... "Consider an element w ... that has no solution w^k == 1" is meaningless. Skipping everything before it,...	Phil Carmody thefatphil	Oct 5, 2008 9:25 am
... 1) As Phil noted, there is horrific garbling of the meaning of "order". 2) The use of "i" for sqrt(-1) is meaningless, since W_p = 3 mod 4. 3) Anton has...	David Broadhurst djbroadhurst	Oct 5, 2008 5:07 pm
... I meant that there is no such "i" in Z_{W_p}. In Z_{W_p}[sqrt(2)], we make take i = 2^((p-1)/2)sqrt(2), so that i^2+1 = 3W_p = 0 mod W_p. David...	David Broadhurst djbroadhurst	Oct 5, 2008 6:28 pm
Thank you Phil and thank you David for pointing out my mistakes I cannot transfer to the other forum as my privallages are not enough to upload files. Instead...	Anton Vrba antonvrba	Oct 7, 2008 7:54 pm
the correct file version is 2.0 ... enough ... of ... equality ... the ... a ... and ... by...	Anton Vrba antonvrba	Oct 8, 2008 12:39 pm
... I append the message that I sent to Anton, showing why Bruce's argument works for Mersenne primes, but not for Wagstaff primes. It seems from ...	David Broadhurst djbroadhurst	Oct 9, 2008 6:13 pm
... Seems is the incorrect word - Has withdrawn is correct I did type an apology to be posted on this forum - It seems I did not hit the send button! best...	Anton Vrba antonvrba	Oct 10, 2008 7:49 am
My oversight, is that my claim to the order of $\alpha$ is wrong. The proof of Bruce works because when he states $\omega^{2^p}=1$ and $\omega^{2^{p-1}}=-1$...	Anton Vrba antonvrba	Oct 10, 2008 7:57 am

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