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Old 2020-06-14, 17:32   #1
Uncwilly
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Default How many cofactors have been shown prime by PRP?

On a couple of machines I have been running the PRP on Mersenne numbers with known cofactors (on a low power machine and the other on two cores of a 6 core machine). I was wondering how many of these cofactors have been shown to be prime. Especially, I was think about those that are not likely to be cracked by TF or P-1 anytime soon.

I am running the task to help raise my standings in all of the different tasks (except first time LL or PRP).
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Old 2020-06-14, 18:06   #2
Prime95
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See this long thread: https://mersenneforum.org/showthread.php?t=19407 Each new PRP is announced here.

I bet mersenne.ca has the info too.

Last fiddled with by Prime95 on 2020-06-14 at 18:07
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Old 2020-06-15, 03:13   #3
Uncwilly
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Cool, I didn't realize that.
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Old 2020-06-16, 15:40   #4
LaurV
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Quote:
Originally Posted by Prime95 View Post
I bet mersenne.ca has the info too.
Yep.
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Old 2020-06-16, 16:16   #5
masser
 
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From this link, it appears that the PRP-cofactors "wavefront" is at 10.4M?

Last fiddled with by masser on 2020-06-16 at 16:17
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Old 2020-06-17, 06:09   #6
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Quote:
Originally Posted by masser View Post
From this link, it appears that the PRP-cofactors "wavefront" is at 10.4M?
Yes, and that's what I'm getting assigned in the moment, too. PRP-CF-DC is getting close to 8.5M.
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Old 2020-06-17, 11:55   #7
ATH
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I did a Lucas PRP test in pfgw on 40 of the 42 cofactors with PRP status, and they are all Lucas PRPs which means they are sort of BPSW PRPs, so the chance/risk they are not prime are astronomically small, which it also was before this test, but even more now

I will probably do the last 2 biggest ones, but it takes a long time since it only runs on 1 core.

Code:
Primality testing (2^78737-1)/23714605956035916529/67059801476528402969297162417 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 78577-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^78737-1)/23714605956035916529/67059801476528402969297162417 is Lucas PRP! (58.6418s+0.0154s)

Primality testing (2^82939-1)/867140681119/1018662740943783967 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 82840-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.02%
(2^82939-1)/867140681119/1018662740943783967 is Lucas PRP! (55.6972s+0.0006s)

Primality testing (2^84211-1)/1347377/31358793176711980763958121/3314641676042347824169591561 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 84015-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.05%
(2^84211-1)/1347377/31358793176711980763958121/3314641676042347824169591561 is Lucas PRP! (51.4970s+0.0005s)

Primality testing (2^86137-1)/2584111/7747937967916174363624460881 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 11+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 86024-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.04%
(2^86137-1)/2584111/7747937967916174363624460881 is Lucas PRP! (53.4370s+0.0007s)

Primality testing (2^86371-1)/41681512921035887 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 86316-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.02%
(2^86371-1)/41681512921035887 is Lucas PRP! (70.6683s+0.0006s)

Primality testing (2^87691-1)/500982892169/1610747697738457 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 8K, Pass1=128, Pass2=64, clm=2 on A 87602-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^87691-1)/500982892169/1610747697738457 is Lucas PRP! (69.0134s+0.0006s)

Primality testing (2^106391-1)/286105171290931103 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 10K, Pass1=128, Pass2=80, clm=2 on A 106334-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^106391-1)/286105171290931103 is Lucas PRP! (108.1303s+0.0006s)

Primality testing (2^130439-1)/260879 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 15K, Pass1=320, Pass2=48, clm=2 on A 130422-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.02%
(2^130439-1)/260879 is Lucas PRP! (122.1655s+0.0006s)

Primality testing (2^136883-1)/536581361 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 15K, Pass1=320, Pass2=48, clm=2 on A 136855-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.03%
(2^136883-1)/536581361 is Lucas PRP! (140.2193s+0.0006s)

Primality testing (2^151013-1)/61157791169561859593299975690769 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 13, base 1+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 15K, Pass1=320, Pass2=48, clm=2 on A 150908-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.03%
(2^151013-1)/61157791169561859593299975690769 is Lucas PRP! (163.7675s+0.0006s)

Primality testing (2^157457-1)/4612545359/358012521626153 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 4+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 15K, Pass1=320, Pass2=48, clm=2 on A 157377-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.02%
(2^157457-1)/4612545359/358012521626153 is Lucas PRP! (205.8268s+0.0016s)

Primality testing (2^173867-1)/52536637502689 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on A 173822-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^173867-1)/52536637502689 is Lucas PRP! (207.3193s+0.0007s)

Primality testing (2^174533-1)/193594572654550537/91917886778031629891960890057 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on A 174380-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^174533-1)/193594572654550537/91917886778031629891960890057 is Lucas PRP! (282.0728s+0.0006s)

Primality testing (2^175631-1)/92733169/330463093135534238072561 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 18K, Pass1=384, Pass2=48, clm=2 on A 175527-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^175631-1)/92733169/330463093135534238072561 is Lucas PRP! (229.2851s+0.0053s)

Primality testing (2^216317-1)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 21K, Pass1=448, Pass2=48, clm=2 on A 216076-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^216317-1)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551 is Lucas PRP! (318.0994s+0.0096s)

Primality testing (2^221509-1)/292391881 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 21K, Pass1=448, Pass2=48, clm=2 on A 221481-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^221509-1)/292391881 is Lucas PRP! (378.0034s+0.0006s)

Primality testing (2^270059-1)/540119/6481417/7124976157756725967 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 28K, Pass1=448, Pass2=64, clm=2 on A 269955-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.02%
(2^270059-1)/540119/6481417/7124976157756725967 is Lucas PRP! (545.4598s+0.0007s)

Primality testing (2^271211-1)/613961495159 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 28K, Pass1=448, Pass2=64, clm=2 on A 271172-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^271211-1)/613961495159 is Lucas PRP! (532.5829s+0.0012s)

Primality testing (2^271549-1)/238749682487 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 28K, Pass1=448, Pass2=64, clm=2 on A 271512-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.03%
(2^271549-1)/238749682487 is Lucas PRP! (544.3375s+0.0006s)

Primality testing (2^406583-1)/813167 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 40K, Pass1=640, Pass2=64, clm=2 on A 406564-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^406583-1)/813167 is Lucas PRP! (1213.9665s+0.0006s)

Primality testing (2^432457-1)/1672739247834685086279697 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 1+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 48K, Pass1=768, Pass2=64, clm=2 on A 432377-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.02%
(2^432457-1)/1672739247834685086279697 is Lucas PRP! (1514.2660s+0.0007s)

Primality testing (2^440399-1)/880799/31518475633/16210820281161978209 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 6+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 48K, Pass1=768, Pass2=64, clm=2 on A 440281-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^440399-1)/880799/31518475633/16210820281161978209 is Lucas PRP! (1616.8335s+0.0009s)

Primality testing (2^488441-1)/61543567/30051203516986199 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 48K, Pass1=768, Pass2=64, clm=2 on A 488361-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^488441-1)/61543567/30051203516986199 is Lucas PRP! (1886.7971s+0.0007s)

Primality testing (2^576551-1)/4612409/64758208321/242584327930759 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 60K, Pass1=768, Pass2=80, clm=2 on A 576446-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^576551-1)/4612409/64758208321/242584327930759 is Lucas PRP! (2427.9374s+0.0085s)

Primality testing (2^611999-1)/18464214225958267477777390354183 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 8+sqrt(11)
Generic modular reduction using generic reduction FMA3 FFT length 60K, Pass1=768, Pass2=80, clm=2 on A 611896-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^611999-1)/18464214225958267477777390354183 is Lucas PRP! (2210.3935s+0.0012s)

Primality testing (2^675977-1)/1686378749257/7171117283326998925471 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 4+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192, clm=4 on A 675864-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^675977-1)/1686378749257/7171117283326998925471 is Lucas PRP! (3419.3362s+0.0007s)

Primality testing (2^684127-1)/23765203727 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192, clm=4 on A 684093-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^684127-1)/23765203727 is Lucas PRP! (3200.8319s+0.0044s)

Primality testing (2^696343-1)/11141489/36009913139329 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192, clm=4 on A 696275-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.01%
(2^696343-1)/11141489/36009913139329 is Lucas PRP! (3238.8290s+0.0046s)

Primality testing (2^750151-1)/429934042631/7590093831289/397764574647511/8361437834787151/17383638888678527263 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 72K, Pass1=384, Pass2=192, clm=4 on A 749905-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^750151-1)/429934042631/7590093831289/397764574647511/8361437834787151/17383638888678527263 is Lucas PRP! (4287.7923s+0.0043s)

Primality testing (2^822971-1)/6583769/28211445881/21255852651726486149207 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 80K, Pass1=320, Pass2=256, clm=4 on A 822840-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^822971-1)/6583769/28211445881/21255852651726486149207 is Lucas PRP! (5668.1033s+0.0034s)

Primality testing (2^1010623-1)/12602017578957977 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 100K, Pass1=320, Pass2=320, clm=4 on A 1010570-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1010623-1)/12602017578957977 is Lucas PRP! (6651.6134s+0.0039s)

Primality testing (2^1168183-1)/54763676838381762583 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 7+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 112K, Pass1=448, Pass2=256, clm=2 on A 1168118-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1168183-1)/54763676838381762583 is Lucas PRP! (11847.6134s+0.0027s)

Primality testing (2^1304983-1)/52199321 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 128K, Pass1=512, Pass2=256, clm=2 on A 1304958-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1304983-1)/52199321 is Lucas PRP! (11420.8682s+0.0034s)

Primality testing (2^1629469-1)/644908484660139264379223 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 160K, Pass1=640, Pass2=256, clm=2 on A 1629390-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1629469-1)/644908484660139264379223 is Lucas PRP! (25361.2088s+0.0496s)

Primality testing (2^1790743-1)/146840927/158358984977/3835546416767873/20752172271489035681 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 13, base 10+sqrt(13)
Generic modular reduction using generic reduction FMA3 FFT length 192K, Pass1=768, Pass2=256, clm=2 on A 1790563-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^1790743-1)/146840927/158358984977/3835546416767873/20752172271489035681 is Lucas PRP! (26036.0751s+0.0050s)

Primality testing (2^2327417-1)/23915387348002001 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Generic modular reduction using generic reduction FMA3 FFT length 240K, Pass1=320, Pass2=768, clm=1 on A 2327363-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^2327417-1)/23915387348002001 is Lucas PRP! (38071.2133s+0.0098s)

Primality testing (2^3464473-1)/604874508299177 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 384K, Pass1=384, Pass2=1K, clm=4 on A 3464424-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^3464473-1)/604874508299177 is Lucas PRP! (107647.0818s+0.0132s)

Primality testing (2^4187251-1)/72234342371519 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 448K, Pass1=448, Pass2=1K, clm=4 on A 4187205-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^4187251-1)/72234342371519 is Lucas PRP! (159196.3674s+0.0201s)

Primality testing (2^4834891-1)/1701881633/70659688575577 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 1+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 480K, Pass1=384, Pass2=1280, clm=4 on A 4834815-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^4834891-1)/1701881633/70659688575577 is Lucas PRP! (240488.3063s+0.0189s)

Primality testing (2^5240707-1)/75392810903 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 3, base 3+sqrt(3)
Generic modular reduction using generic reduction FMA3 FFT length 560K, Pass1=448, Pass2=1280, clm=4 on A 5240671-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^5240707-1)/75392810903 is Lucas PRP! (260942.1577s+0.0389s)

Last fiddled with by ATH on 2020-06-17 at 12:06
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Old 2020-06-17, 15:41   #8
masser
 
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I would think some of those smaller ones are provably prime by ECPP.

Last fiddled with by masser on 2020-06-17 at 15:43 Reason: Doh! Should have read the companion thread. Paul is on the case!
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