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Wagstaff Numbers - Proof for a Primality Test   Message List  
Reply | Forward Message #1893 of 2071 |
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 Lucas Lehmer test and aslo
uses the iteration s -> S^2-2. Let p>3 and prime, W_p=(1/3)(2^p+1)
then primality is given if and only if S_p = S_2 for S_0 = 6.

The complete proof in a pdf file is in the file section of this forum
(last entry in the list) or you could pick it up on below URL.
http://www.mersenneforum.org/showpost.php?p=144516&postcount=1

I would appreciate feedback especially from David as I really dipped
deep into theory.

I really hope we can move some entries from Henri Lifchitz's list.

best regards
Anton
Sun Oct 5, 2008 7:23 am

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antonvrba
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Forward 		Message #1893 of 2071 |
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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
Offline Send Email 		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
Offline Send Email 		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
Offline Send Email 		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 = 3*W_p = 0 mod W_p. David...
David Broadhurst
djbroadhurst
Offline Send Email 		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
Offline Send Email 		Oct 7, 2008
7:54 pm

the correct file version is 2.0 ... enough ... of ... equality ... the ... a ... and ... by...
Anton Vrba
antonvrba
Offline Send Email 		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
Offline Send Email 		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
Offline Send Email 		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
Offline Send Email 		Oct 10, 2008
7:57 am
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