The probable primes

[mdettweiler]

Originally Posted by Cybertronic

Hello, can anyone send me a www.sendspace.com link for downloading the latest version of windows-pfgw 3.4.1 ?

http://openpfgw.svn.sourceforge.net/...7.zip?view=log

I have ever trouble with "sourceforge.net".

Thanks !

This thread is enough.

Here you go: http://www.sendspace.com/file/1dmq5y

[Cybertronic]

I believe the original zip-file have bugs ,or ?

-------------

@mdettweiler

Thank you !

[ATH]

LLR now has the option of the BPSW primality test as well as the Frobenius test: http://www.mersenneforum.org/showthread.php?t=15332

http://www.trnicely.net/misc/bpsw.html
http://mathworld.wolfram.com/Baillie...alityTest.html

2^56366+39079 is base 2-Strong Fermat PRP!  Time : 5.705 sec.
2^56366+39079 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -3, D = 13)  Time : 20.933 sec.
2^61792+21661 is base 2-Strong Fermat PRP!  Time : 5.952 sec.
2^61792+21661 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7)  Time : 21.883 sec.
2^73360+10711 is base 2-Strong Fermat PRP!  Time : 7.675 sec.
2^73360+10711 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7)  Time : 29.307 sec.
2^73845+14717 is base 2-Strong Fermat PRP!  Time : 7.968 sec.
2^73845+14717 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -3, D = 13)  Time : 31.113 sec.
2^103766+17659 is base 2-Strong Fermat PRP!  Time : 16.176 sec.
2^103766+17659 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11)  Time : 60.245 sec.
2^104095+7013 is base 2-Strong Fermat PRP!  Time : 17.081 sec.
2^104095+7013 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -7, D = 29)  Time : 64.099 sec.
2^105789+48527 is base 2-Strong Fermat PRP!  Time : 16.764 sec.
2^105789+48527 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -4, D = 17)  Time : 61.494 sec.
2^139964+35461 is base 2-Strong Fermat PRP!  Time : 33.342 sec.
2^139964+35461 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7)  Time : 129.441 sec.
2^148227+60443 is base 2-Strong Fermat PRP!  Time : 33.912 sec.
2^148227+60443 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7)  Time : 130.399 sec.
2^176177+60947 is base 2-Strong Fermat PRP!  Time : 56.482 sec.
2^176177+60947 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 5, D = -19)  Time : 221.824 sec.
2^304015+64133 is base 2-Strong Fermat PRP!  Time : 148.693 sec.
2^304015+64133 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11)  Time : 622.268 sec.
2^308809+37967 is base 2-Strong Fermat PRP!  Time : 147.017 sec.
2^308809+37967 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -7, D = 29)  Time : 618.084 sec.
2^551542+19249 is base 2-Strong Fermat PRP!  Time : 541.642 sec.
2^551542+19249 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = -3, D = 13)  Time : 2477.977 sec.

I'm working on the last 7 prps.

[ATH]

2^983620+60451 is base 2-Strong Fermat PRP! Time : 1765.694 sec.
2^983620+60451 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 9495.456 sec.
2^1191375+8543 is base 2-Strong Fermat PRP! Time : 2585.068 sec.
2^1191375+8543 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 12651.006 sec.
2^1518191+75353 is base 2-Strong Fermat PRP! Time : 4108.723 sec.
2^1518191+75353 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 6, D = -23) Time : 21756.783 sec.

[ATH]

2^2249255+28433 is base 2-Strong Fermat PRP! Time : 9788.623 sec.
2^2249255+28433 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 41861.086 sec.
2^4583176+2131 is base 2-Strong Fermat PRP! Time : 45341.497 sec.
2^4583176+2131 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 263278.015 sec.
2^5146295+41693 is base 2-Strong Fermat PRP! Time : 62297.273 sec.
2^5146295+41693 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 2, D = -7) Time : 327043.150 sec.

Jeff Gilchrist is doing 2^9092392+40291
http://www.mersenneforum.org/showthread.php?t=15242

[Jeff Gilchrist]

2^9092392+40291 is base 2-Strong Fermat PRP! Time : 190718.322 sec.
2^9092392+40291 is strong-Fermat and BPSW PRP, Starting Frobenius test sequence
2^9092392+40291 is strong-Fermat, BPSW and Frobenius PRP! (P = 1, Q = 3, D = -11) Time : 953429.151 sec.

[Dead J. Dona]

How long it takes to test whether 2^56366+39079 is a prime?

And how 2^5146295+41693?

[philmoore]

For 2⁵⁶³⁶⁶+39079, Norman estimated 18 months on a 3.4 GHz Phenom II X4 965. Perhaps with the newer version of Primo and a faster computer, maybe a little less, but who knows? More cores would be better, of course.

On the other hand, I estimated 225 billion years for 2^5146295+41693 via ECPP, maybe only 60 billion years (on a single processor) if we could prove the generalized Riemann hypothesis:
http://www.mersenneforum.org/showthread.php?t=12784

[enderak]

There's a new Primo version, 4.0.0 which is not only 64-bit but uses multiple cores (up to 16). Looks like it runs on Linux only, and is still an alpha version.

I don't have a spare computer with decent specs to install Linux on and test it out, but it looks like it might open the door to proving a few more of the PRP's.

Link: http://www.ellipsa.eu/public/primo/primo.html

[Puzzle-Peter]

OK, I'll bite and try to prove the next two candidates in the list.

[Puzzle-Peter]

I'm taking a 3 week break now. Both tests have eliminated ~3500 bits so far. The smaller one is taking less time per step but the gains per step are smaller and there is more backtracking. So they are nearly equally fast atm.