20130910, 02:53  #12  
Jun 2003
Ottawa, Canada
3×17×23 Posts 
Quote:
Jeff. 

20130910, 08:19  #13 
Feb 2004
France
39F_{16} Posts 
Congratulations !
Waowwww ! Two new Wagstaff PRPs !!
That's tremendous, wonderful, extraordinary, etc. I'm missing (english) words ! The sad side of this nice story is that my own Wagstaff PRP now looks quite small... Moreover, Diep, Jeff, and Paul spent a lot of time looking for such a Wagstaff PRP with no luck up to now. I hope that they will have some success some day. They deserve it. So, now we need someone to provide a proof of VrbaReix conjecture ! so that PRPs become true primes ! I hope to see that before I die. Some years ago, I promissed 100€ for such a proof. Now, I would give 200€. Anyone to contribute and add some € or $ to build a reward ? On my side, I'm now making photographs: http://500px.com/Tony_Reix www.tonyfcr.book.fr/ that's fun too ! Regards Tony 
20130910, 18:11  #14 
Bemusing Prompter
"Danny"
Dec 2002
California
11·13·17 Posts 
It looks like Ryan holds the current record for the ECM largest factor and the largest Wagstaff PRP. Really impressive, to say the least. Now all he's missing is a new Mersenne prime. xD
Also, welcome back, Tony! Last fiddled with by ixfd64 on 20130910 at 18:14 
20130910, 18:17  #15 
Einyen
Dec 2003
Denmark
3,257 Posts 
2nd exponent in Prime95:
2^13372531+1/3 is a probable prime! We4: E3ACC173,00000000 
20130910, 18:57  #16 
Sep 2002
Database er0rr
3^{2}×443 Posts 
Serge should be giving some PRP results soon.
I have started a GMP implementation of my test for the new Wagstaffs on a Q6600: (L+2)^(N+1)==5 (mod N, L^2+1) It will take a few weeks 
20130910, 19:08  #17 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
1615_{8} Posts 
Sounds like a race, Paul. I started my machine on SPSP2, ES Lucas, and your Frobenius test yesterday for both numbers. As you say, it will take a long time as they're generic tests using GMP.

20130910, 19:15  #18 
Sep 2002
Database er0rr
3987_{10} Posts 
I have a special version that calculates modulo 2^p+1  so no generic modulo.

20130910, 21:44  #19  
Einyen
Dec 2003
Denmark
3,257 Posts 
Quote:
2^p = 1 (mod 2^p+1) => 2^p = 1 (mod (2^p+1)/3) 

20130911, 04:18  #20 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
1615_{8} Posts 
That is my understanding and I debated whether to start them or not, but I thought it wouldn't hurt and since it should finish first, will give me some idea of when the Lucas and Frobenius tests will be done. It'll be a long wait...

20130911, 16:31  #21 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{5}·3·101 Posts 
Code:
(2^13347311+1)/3 is Base 27  Strong Fermat PRP! Time : 132008.336 sec. (2^13347311+1)/3 is VrbaReix PRP! Time : 131975.246 sec. (2^13372531+1)/3 is Base 27  Strong Fermat PRP! Time : 132322.407 sec. (2^13372531+1)/3 is VrbaReix PRP! Time : 132513.794 sec. (2^13347311+1)/3 is 5PRP! (229303.3908s+398.4266s) (2^13347311+1)/3 is 7PRP! (277072.1587s+419.3222s) (2^13347311+1)/3 is 11PRP! (291376.7357s+419.8591s) (2^13347311+1)/3 is 13PRP! (291281.3062s+418.0968s) (2^13347311+1)/3 is 17PRP! (278100.7506s+382.4561s) (2^13372531+1)/3 is 5PRP! (249353.0860s+421.2026s) (2^13372531+1)/3 is 7PRP! (229612.6239s+399.1560s) (2^13372531+1)/3 is 11PRP! (230611.3771s+399.9541s) (2^13372531+1)/3 is 13PRP! (231212.1002s+401.6447s) (2^13372531+1)/3 is 17PRP! (230925.5544s+399.9358s) # tests for false positives below  (2^13372309+1)/3 is not prime. RES64: 991A9DB47059EE26. OLD64: D0794CB28426C889 Time : 132114.403 sec. (2^13372309+1)/3 is not prime. VrbaReix RES64: FE684FD81D62F060 Time : 132268.574 sec. # b5 (2^13372309+1)/3 is composite: RES64: [E9EDD6FC780DA64D] (225266.1438s+403.6897s) # b3 (2^13372309+1)/3 is composite: RES64: [FA860AF0EE31F99B] (230901.3211s+404.2113s) # b2 (2^13372309+1)/3 is 2PRP! (225516.2154s+403.9142s) Last fiddled with by Batalov on 20130915 at 00:06 Reason: (all queued PFGW tests finished) 
20130919, 22:58  #22  
Einyen
Dec 2003
Denmark
3,257 Posts 
Quote:
Last fiddled with by ATH on 20130919 at 22:59 

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