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-   -   Mersenne number factored (disbelievers are biting elbows) (https://www.mersenneforum.org/showthread.php?t=19407)

 GP2 2020-02-01 02:17

The 343rd fully-factored or probably-fully-factored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2749[/M].

The most recent factor (65 digits!) was found by Ryan Propper on January 28 and the PRP test was done by Jinyuan Wang.

The cofactor has already been certified prime.

 LaurV 2020-02-01 08:55

[QUOTE=GP2;536354] fully-factored or probably-fully-factored <snip>
The cofactor has already been certified prime.
[/QUOTE]
Then, it is not "probable", but sure :)
Congrats to the finder and all contributors!

 axn 2020-02-01 11:44

[QUOTE=LaurV;536368]Then, it is not "probable", but sure :)[/QUOTE]
The set, of which it is the 343rd, consists of fully-factored and probably-fully-factored numbers.

 xilman 2020-02-01 12:27

[QUOTE=LaurV;536368]Then, it is not "probable", but sure :)
Congrats to the finder and all contributors![/QUOTE]OR.

Not EXOR

 LaurV 2020-02-02 08:28

[QUOTE=axn;536372]fully-factored [U][B]and[/B][/U] probably-fully-factored numbers.[/QUOTE]

[QUOTE=xilman;536376]OR.
Not EXOR[/QUOTE]
Yaarrr :chappy:
Ye nitpickers!

:rofl:

 paulunderwood 2020-02-04 19:54

Least unproven cofactor

What is the least unproven Mersenne cofactor? I would like to ECPP it.

NVM. I found M78,737 on [url]https://www.mersenne.ca/prp.php[/url]

 ATH 2020-06-27 23:41

I did a Lucas PRP test with PFGW on the 42 PRPs here: [url]https://www.mersenne.ca/prp.php[/url]

Not surprisingly they are all Lucas PRP:

[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)

Primality testing (2^7080247-1)/156822217506727/11283326312536321/9632940548330339593 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 5, base 5+sqrt(5)
Generic modular reduction using generic reduction FMA3 FFT length 720K, Pass1=320, Pass2=2304, clm=4 on A 7080084-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^7080247-1)/156822217506727/11283326312536321/9632940548330339593 is Lucas PRP! (493240.3769s+0.0461s)

Primality testing (2^7313983-1)/305492080276193 [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 768K, Pass1=384, Pass2=2K, clm=2 on A 7313935-bit number
Calling Brillhart-Lehmer-Selfridge with factored part 0.00%
(2^7313983-1)/305492080276193 is Lucas PRP! (387269.4697s+0.0243s)

[/CODE]

 GP2 2020-07-09 05:20

[M]M10,443,557[/M] has been reported fully factored.

This would be a new record. The previous record-holder was [M]M7,313,983[/M]

 paulunderwood 2020-07-09 06:59

[QUOTE=GP2;550090][M]M10,443,557[/M] has been reported fully factored.

This would be a new record. The previous record-holder was [M]M7,313,983[/M][/QUOTE]

Congrats! I'll leave it to ATH to do a Lucas test.

 ATH 2020-07-09 12:09

[QUOTE=paulunderwood;550093]Congrats! I'll leave it to ATH to do a Lucas test.[/QUOTE]

You are welcome to run it with your own software. PFGW takes a very long time because it can only use 1 core and because it does a lot of other tests before starting the Lucas test. Last 2 took 4.5 and 5.7 days, this would probably take 8+ days.

 paulunderwood 2020-07-09 12:13

[QUOTE=ATH;550103]You are welcome to run it with your own software. PFGW takes a very long time because it can only use 1 core and because it does a lot of other tests before starting the Lucas test. Last 2 took 4.5 and 5.7 days, this would probably take 8+ days.[/QUOTE]

Will do...

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