New Wagstaff PRP exponents

[Jeff Gilchrist]

Originally Posted by ryanp

Yes, I am indebted to Jeff's prior work here as well. For my part, I started with the first 25,000 prime exponents from each of q=10e6, 11e6, 12e6 and 13e6. A large fraction of these were weeded out by a very basic program I wrote to do simple trial factoring up to d=1000, then many more by PFGW's own trial factoring. I'll have to do a bit of work to determine exactly how many exponents were fully tested by PFGW.

Your part? Are you part of a larger group of people working on this? Has anyone worked on anything less than 10e6? What ranges are you actively working on now and how much CPU power are you throwing at this?

Jeff.

[T.Rex]

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 Vrba-Reix 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

[ixfd64]

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!

[ATH]

2nd exponent in Prime95:

2^13372531+1/3 is a probable prime! We4: E3ACC173,00000000

[paulunderwood]

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

[danaj]

Sounds like a race, Paul. I started my machine on SPSP-2, 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.

[paulunderwood]

I have a special version that calculates modulo 2^p+1 -- so no generic modulo.

[ATH]

Originally Posted by danaj

Sounds like a race, Paul. I started my machine on SPSP-2, 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.

SPSP-2 will always pass for Wagstaff numbers?

2^p = -1 (mod 2^p+1) => 2^p = -1 (mod (2^p+1)/3)

[danaj]

Originally Posted by ATH

SPSP-2 will always pass for Wagstaff numbers?

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...

[Batalov]

(2^13347311+1)/3 is Base 27 - Strong Fermat PRP!  Time : 132008.336 sec.
(2^13347311+1)/3 is Vrba-Reix PRP!  Time : 131975.246 sec.
(2^13372531+1)/3 is Base 27 - Strong Fermat PRP!  Time : 132322.407 sec.
(2^13372531+1)/3 is Vrba-Reix PRP!  Time : 132513.794 sec.

(2^13347311+1)/3 is 5-PRP! (229303.3908s+398.4266s)
(2^13347311+1)/3 is 7-PRP! (277072.1587s+419.3222s)
(2^13347311+1)/3 is 11-PRP! (291376.7357s+419.8591s)
(2^13347311+1)/3 is 13-PRP! (291281.3062s+418.0968s)
(2^13347311+1)/3 is 17-PRP! (278100.7506s+382.4561s)

(2^13372531+1)/3 is 5-PRP! (249353.0860s+421.2026s)
(2^13372531+1)/3 is 7-PRP! (229612.6239s+399.1560s)
(2^13372531+1)/3 is 11-PRP! (230611.3771s+399.9541s)
(2^13372531+1)/3 is 13-PRP! (231212.1002s+401.6447s)
(2^13372531+1)/3 is 17-PRP! (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.  Vrba-Reix 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 2-PRP! (225516.2154s+403.9142s)

[ATH]

Running N+1 test using discriminant 2, base 1+sqrt(2)

Generic modular reduction using all-complex AVX FFT length 768K, Pass1=256, Pass
2=3K on (2^13372531+1)/3
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^13372531+1)/3 is Lucas PRP! (851290.8327s+0.0578s)

I lost the other test on (2^13347311+1)/3 on the way, 10 days is a long time without any intermediate savefiles. Several other people seems to have these test running on faster computers than mine though, so I didn't restart it.