Ryan and P1 and 12
Is it fluke or intentionally chosen B1/B2 that all of Ryan's recent P1 results have a GhzDays ending in .xx12?
14.1712 if B1 and B2 required 6.1412 if found via B1 only. Ryan Propper Manual testing 98454437 FPM1 20191011 14:00 0.3 14.1712 Factor: 124390959709723920942323644574431 / (P1, B1=965000, B2=24125000, E=6) Ryan Propper Manual testing 98433241 FPM1 20191011 14:00 0.3 6.1412 Factor: 102501238638612689076865713323434384005097 / (P1, B1=965000) and about 100 more ending in .xx12 
Fluke. Same B1/B2 and same FFT size = same credit. Stage1only credit matching full pm1 credit is fluke.
I don't think ryanp gives a flying fox about GIMPS credit, let alone gimmicky credits. 
The 337th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2351[/M].
The 55digit most recent factor was found by Ryan Propper and the PRP test was done by Fan Ming. Note that Ryan had found a 52digit factor for the same exponent just six days earlier. [URL="http://factordb.com/index.php?id=1100000001374723506"]FactorDB link[/URL] 
I noticed the proof of the cofactor had still not been done, so I did it and uploaded it just now.
 Will [QUOTE=GP2;528295]The 337th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2351[/M]. The 55digit most recent factor was found by Ryan Propper and the PRP test was done by Fan Ming. Note that Ryan had found a 52digit factor for the same exponent just six days earlier. [URL="http://factordb.com/index.php?id=1100000001374723506"]FactorDB link[/URL][/QUOTE] 
[QUOTE=GP2;528295]The 337th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2351[/M].
The 55digit most recent factor was found by Ryan Propper and the PRP test was done by Fan Ming. Note that Ryan had found a 52digit factor for the same exponent just six days earlier. [URL="http://factordb.com/index.php?id=1100000001374723506"]FactorDB link[/URL][/QUOTE] Looks like Fan Ming sniped the PRP test, as I had the original assignment from the server... 
[QUOTE=mnd9;528319]Looks like Fan Ming sniped the PRP test, as I had the original assignment from the server...[/QUOTE]
For both this exponent and the previous one ([M]M2441[/M]), the factor had already been uploaded to FactorDB, and FactorDB had the cofactor as a PRP. It probably does the test automatically for such small exponents. And for all we know, the factor discoverer may also have quietly run a PRP test. So priority of the PRP discoveries for tiny exponents is problematic. I just mention the person who reported it to Primenet first. 
[QUOTE=mnd9;528319]Looks like Fan Ming sniped the PRP test, as I had the original assignment from the server...[/QUOTE]
I'm really sorry for that. I saw this message just now. Sorry for the poach. I tested this and found the result is PRP, which is unusual, so I submitted the PRP result... 
The 338th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M1723[/M].
The 51digit most recent factor was found by Ryan Propper and the PRP test was done by mnd9. The cofactor is already certified prime. For cofactors this small, FactorDB does the PRP test automatically and certification is done routinely and quickly. The factor had already been submitted to FactorDB, perhaps by Ryan himself. [URL="http://factordb.com/index.php?id=1100000001383185509"]FactorDB link[/URL] 
[QUOTE=GP2;529195]The 338th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M1723[/M].
[/QUOTE] Very nice. It would also be nice if people could factor some on the numbers within the Cunningham numbers instead of only cherry picking relatively untested numbers outside the tables. Yes, the former is a lot harder. "We choose to go to the moon and do the other thing. Not because they are easy, but because they are hard". 
The 339th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M216317[/M].
The most recent factor was found by Niels_Mache_Nextcloud and the PRP test was done by mnd9. This cofactor is too big to be certified prime by Primo. [URL="http://factordb.com/index.php?id=1100000001403622864"]FactorDB link[/URL] This was actually discovered yesterday, but for some reason PrimeNet did not send the usual notification. 
[QUOTE=GP2;531567]This was actually discovered yesterday, but for some reason PrimeNet did not send the usual notification.[/QUOTE]
I got both notifications. Your yahoo address was on the CC list. Spam filter? 
[QUOTE=GP2;531567]The 339th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M216317[/M].
The most recent factor was found by Niels_Mache_Nextcloud and the PRP test was done by mnd9. This exponent is too big to be certified prime by Primo. [URL="http://factordb.com/index.php?id=1100000001403622864"]FactorDB link[/URL] This was actually discovered yesterday, but for some reason PrimeNet did not send the usual notification.[/QUOTE] :toot: [CODE]time echo "print((2^2163171)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551)"  gp q ./lucasPRP  1 2 216317 1 Lucas testing on x^2  3*x + 1 ... Is Lucas PRP! real 0m18.301s user 0m18.344s sys 0m0.012s [/CODE] 
PFGW concurs:
[CODE]Primality testing (2^2163171)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551 [N+1, BrillhartLehmerSelfridge] 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 216076bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^2163171)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551 is [SIZE="4"][B]Lucas PRP![/B][/SIZE] (318.0994s+0.0096s)[/CODE] 
[QUOTE=Prime95;531568]I got both notifications. Your yahoo address was on the CC list. Spam filter?[/QUOTE]
Nope, nothing in the spam folder. Not a problem, unless it's a symptom of email problems that might crop up again the next time a Mersenne prime is found. 
The 340th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3733[/M].
The most recent factor (53 digits) was found by Ryan Propper and the PRP test was done by Yuji Hasegawa. It was the seventh factor for this exponent. The cofactor has already been certified prime by Primo. [URL="http://factordb.com/index.php?id=1100000001408200550"]FactorDB link[/URL] George let me know about it, since PrimeNet once again did not send the usual notification. 
[QUOTE=GP2;532338]George let me know about it, since PrimeNet once again did not send the usual notification.[/QUOTE]
How does one subscribe to these notifications? 
[QUOTE=mathwiz;532339]How does one subscribe to these notifications?[/QUOTE]
By reading this thread :smile: 
[QUOTE=GP2;532338]The 340th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3733[/M].
The most recent factor (53 digits) was found by Ryan Propper and the PRP test was done by Yuji Hasegawa. It was the seventh factor for this exponent. The cofactor has already been certified prime by Primo. [URL="http://factordb.com/index.php?id=1100000001408200550"]FactorDB link[/URL] George let me know about it, since PrimeNet once again did not send the usual notification.[/QUOTE] I didn't think the server emailed out notifications for cofactor PRPs. Anyway... I was going to mark this one as "cofactor proven" in the database, but it's not showing up in the right place yet, probably because the "PRP" result hasn't had a doublecheck yet. I'll check on it later if/when someone submits a verifying run  shouldn't take long I'm sure. 
Another one factored by Ryan Propper and tested by mrh: [url]https://mersenne.org/M3467[/url]
[url]https://mersenneforum.org/showthread.php?t=24989[/url] 
The 341st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M3467[/M].
The most recent factor (55 digits) was found by Ryan Propper and the PRP test was done by mrh. The cofactor has already been certified prime by Primo. [URL="http://factordb.com/index.php?id=1100000001409480260"]FactorDB link[/URL] 
The 342nd fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2887[/M].
The most recent factor (56 digits) was found by Ryan Propper and the PRP test was done by Niels_Mache_Nextcloud. The cofactor has already been certified prime. [URL="http://factordb.com/index.php?id=1100000001435182860"]FactorDB link[/URL] 
The 343rd fullyfactored or probablyfullyfactored 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. [URL="http://factordb.com/index.php?id=1100000001440761806"]FactorDB link[/URL] 
[QUOTE=GP2;536354] fullyfactored or probablyfullyfactored <snip>
The cofactor has already been certified prime. [/QUOTE] Then, it is not "probable", but sure :) Congrats to the finder and all contributors! 
[QUOTE=LaurV;536368]Then, it is not "probable", but sure :)[/QUOTE]
The set, of which it is the 343rd, consists of fullyfactored and probablyfullyfactored numbers. 
[QUOTE=LaurV;536368]Then, it is not "probable", but sure :)
Congrats to the finder and all contributors![/QUOTE]OR. Not EXOR 
[QUOTE=axn;536372]fullyfactored [U][B]and[/B][/U] probablyfullyfactored numbers.[/QUOTE]
[QUOTE=xilman;536376]OR. Not EXOR[/QUOTE] Yaarrr :chappy: Ye nitpickers! :rofl: 
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] 
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 (2^787371)/23714605956035916529/67059801476528402969297162417 [N+1, BrillhartLehmerSelfridge] 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 78577bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^787371)/23714605956035916529/67059801476528402969297162417 is Lucas PRP! (58.6418s+0.0154s) Primality testing (2^829391)/867140681119/1018662740943783967 [N+1, BrillhartLehmerSelfridge] 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 82840bit number Calling BrillhartLehmerSelfridge with factored part 0.02% (2^829391)/867140681119/1018662740943783967 is Lucas PRP! (55.6972s+0.0006s) Primality testing (2^842111)/1347377/31358793176711980763958121/3314641676042347824169591561 [N+1, BrillhartLehmerSelfridge] 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 84015bit number Calling BrillhartLehmerSelfridge with factored part 0.05% (2^842111)/1347377/31358793176711980763958121/3314641676042347824169591561 is Lucas PRP! (51.4970s+0.0005s) Primality testing (2^861371)/2584111/7747937967916174363624460881 [N+1, BrillhartLehmerSelfridge] 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 86024bit number Calling BrillhartLehmerSelfridge with factored part 0.04% (2^861371)/2584111/7747937967916174363624460881 is Lucas PRP! (53.4370s+0.0007s) Primality testing (2^863711)/41681512921035887 [N+1, BrillhartLehmerSelfridge] 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 86316bit number Calling BrillhartLehmerSelfridge with factored part 0.02% (2^863711)/41681512921035887 is Lucas PRP! (70.6683s+0.0006s) Primality testing (2^876911)/500982892169/1610747697738457 [N+1, BrillhartLehmerSelfridge] 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 87602bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^876911)/500982892169/1610747697738457 is Lucas PRP! (69.0134s+0.0006s) Primality testing (2^1063911)/286105171290931103 [N+1, BrillhartLehmerSelfridge] 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 106334bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^1063911)/286105171290931103 is Lucas PRP! (108.1303s+0.0006s) Primality testing (2^1304391)/260879 [N+1, BrillhartLehmerSelfridge] 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 130422bit number Calling BrillhartLehmerSelfridge with factored part 0.02% (2^1304391)/260879 is Lucas PRP! (122.1655s+0.0006s) Primality testing (2^1368831)/536581361 [N+1, BrillhartLehmerSelfridge] 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 136855bit number Calling BrillhartLehmerSelfridge with factored part 0.03% (2^1368831)/536581361 is Lucas PRP! (140.2193s+0.0006s) Primality testing (2^1510131)/61157791169561859593299975690769 [N+1, BrillhartLehmerSelfridge] 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 150908bit number Calling BrillhartLehmerSelfridge with factored part 0.03% (2^1510131)/61157791169561859593299975690769 is Lucas PRP! (163.7675s+0.0006s) Primality testing (2^1574571)/4612545359/358012521626153 [N+1, BrillhartLehmerSelfridge] 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 157377bit number Calling BrillhartLehmerSelfridge with factored part 0.02% (2^1574571)/4612545359/358012521626153 is Lucas PRP! (205.8268s+0.0016s) Primality testing (2^1738671)/52536637502689 [N+1, BrillhartLehmerSelfridge] 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 173822bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^1738671)/52536637502689 is Lucas PRP! (207.3193s+0.0007s) Primality testing (2^1745331)/193594572654550537/91917886778031629891960890057 [N+1, BrillhartLehmerSelfridge] 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 174380bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^1745331)/193594572654550537/91917886778031629891960890057 is Lucas PRP! (282.0728s+0.0006s) Primality testing (2^1756311)/92733169/330463093135534238072561 [N+1, BrillhartLehmerSelfridge] 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 175527bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^1756311)/92733169/330463093135534238072561 is Lucas PRP! (229.2851s+0.0053s) Primality testing (2^2163171)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551 [N+1, BrillhartLehmerSelfridge] 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 216076bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^2163171)/9551099878153/42354904941257/1528559546583299567/6527839497610595205744558551 is Lucas PRP! (318.0994s+0.0096s) Primality testing (2^2215091)/292391881 [N+1, BrillhartLehmerSelfridge] 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 221481bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^2215091)/292391881 is Lucas PRP! (378.0034s+0.0006s) Primality testing (2^2700591)/540119/6481417/7124976157756725967 [N+1, BrillhartLehmerSelfridge] 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 269955bit number Calling BrillhartLehmerSelfridge with factored part 0.02% (2^2700591)/540119/6481417/7124976157756725967 is Lucas PRP! (545.4598s+0.0007s) Primality testing (2^2712111)/613961495159 [N+1, BrillhartLehmerSelfridge] 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 271172bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^2712111)/613961495159 is Lucas PRP! (532.5829s+0.0012s) Primality testing (2^2715491)/238749682487 [N+1, BrillhartLehmerSelfridge] 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 271512bit number Calling BrillhartLehmerSelfridge with factored part 0.03% (2^2715491)/238749682487 is Lucas PRP! (544.3375s+0.0006s) Primality testing (2^4065831)/813167 [N+1, BrillhartLehmerSelfridge] 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 406564bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^4065831)/813167 is Lucas PRP! (1213.9665s+0.0006s) Primality testing (2^4324571)/1672739247834685086279697 [N+1, BrillhartLehmerSelfridge] 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 432377bit number Calling BrillhartLehmerSelfridge with factored part 0.02% (2^4324571)/1672739247834685086279697 is Lucas PRP! (1514.2660s+0.0007s) Primality testing (2^4403991)/880799/31518475633/16210820281161978209 [N+1, BrillhartLehmerSelfridge] 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 440281bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^4403991)/880799/31518475633/16210820281161978209 is Lucas PRP! (1616.8335s+0.0009s) Primality testing (2^4884411)/61543567/30051203516986199 [N+1, BrillhartLehmerSelfridge] 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 488361bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^4884411)/61543567/30051203516986199 is Lucas PRP! (1886.7971s+0.0007s) Primality testing (2^5765511)/4612409/64758208321/242584327930759 [N+1, BrillhartLehmerSelfridge] 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 576446bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^5765511)/4612409/64758208321/242584327930759 is Lucas PRP! (2427.9374s+0.0085s) Primality testing (2^6119991)/18464214225958267477777390354183 [N+1, BrillhartLehmerSelfridge] 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 611896bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^6119991)/18464214225958267477777390354183 is Lucas PRP! (2210.3935s+0.0012s) Primality testing (2^6759771)/1686378749257/7171117283326998925471 [N+1, BrillhartLehmerSelfridge] 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 675864bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^6759771)/1686378749257/7171117283326998925471 is Lucas PRP! (3419.3362s+0.0007s) Primality testing (2^6841271)/23765203727 [N+1, BrillhartLehmerSelfridge] 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 684093bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^6841271)/23765203727 is Lucas PRP! (3200.8319s+0.0044s) Primality testing (2^6963431)/11141489/36009913139329 [N+1, BrillhartLehmerSelfridge] 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 696275bit number Calling BrillhartLehmerSelfridge with factored part 0.01% (2^6963431)/11141489/36009913139329 is Lucas PRP! (3238.8290s+0.0046s) Primality testing (2^7501511)/429934042631/7590093831289/397764574647511/8361437834787151/17383638888678527263 [N+1, BrillhartLehmerSelfridge] 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 749905bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^7501511)/429934042631/7590093831289/397764574647511/8361437834787151/17383638888678527263 is Lucas PRP! (4287.7923s+0.0043s) Primality testing (2^8229711)/6583769/28211445881/21255852651726486149207 [N+1, BrillhartLehmerSelfridge] 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 822840bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^8229711)/6583769/28211445881/21255852651726486149207 is Lucas PRP! (5668.1033s+0.0034s) Primality testing (2^10106231)/12602017578957977 [N+1, BrillhartLehmerSelfridge] 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 1010570bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^10106231)/12602017578957977 is Lucas PRP! (6651.6134s+0.0039s) Primality testing (2^11681831)/54763676838381762583 [N+1, BrillhartLehmerSelfridge] 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 1168118bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^11681831)/54763676838381762583 is Lucas PRP! (11847.6134s+0.0027s) Primality testing (2^13049831)/52199321 [N+1, BrillhartLehmerSelfridge] 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 1304958bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^13049831)/52199321 is Lucas PRP! (11420.8682s+0.0034s) Primality testing (2^16294691)/644908484660139264379223 [N+1, BrillhartLehmerSelfridge] 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 1629390bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^16294691)/644908484660139264379223 is Lucas PRP! (25361.2088s+0.0496s) Primality testing (2^17907431)/146840927/158358984977/3835546416767873/20752172271489035681 [N+1, BrillhartLehmerSelfridge] 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 1790563bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^17907431)/146840927/158358984977/3835546416767873/20752172271489035681 is Lucas PRP! (26036.0751s+0.0050s) Primality testing (2^23274171)/23915387348002001 [N+1, BrillhartLehmerSelfridge] 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 2327363bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^23274171)/23915387348002001 is Lucas PRP! (38071.2133s+0.0098s) Primality testing (2^34644731)/604874508299177 [N+1, BrillhartLehmerSelfridge] 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 3464424bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^34644731)/604874508299177 is Lucas PRP! (107647.0818s+0.0132s) Primality testing (2^41872511)/72234342371519 [N+1, BrillhartLehmerSelfridge] 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 4187205bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^41872511)/72234342371519 is Lucas PRP! (159196.3674s+0.0201s) Primality testing (2^48348911)/1701881633/70659688575577 [N+1, BrillhartLehmerSelfridge] 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 4834815bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^48348911)/1701881633/70659688575577 is Lucas PRP! (240488.3063s+0.0189s) Primality testing (2^52407071)/75392810903 [N+1, BrillhartLehmerSelfridge] 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 5240671bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^52407071)/75392810903 is Lucas PRP! (260942.1577s+0.0389s) Primality testing (2^70802471)/156822217506727/11283326312536321/9632940548330339593 [N+1, BrillhartLehmerSelfridge] 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 7080084bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^70802471)/156822217506727/11283326312536321/9632940548330339593 is Lucas PRP! (493240.3769s+0.0461s) Primality testing (2^73139831)/305492080276193 [N+1, BrillhartLehmerSelfridge] 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 7313935bit number Calling BrillhartLehmerSelfridge with factored part 0.00% (2^73139831)/305492080276193 is Lucas PRP! (387269.4697s+0.0243s) [/CODE] 
[M]M10,443,557[/M] has been reported fully factored.
This would be a new record. The previous recordholder was [M]M7,313,983[/M] 
[QUOTE=GP2;550090][M]M10,443,557[/M] has been reported fully factored.
This would be a new record. The previous recordholder was [M]M7,313,983[/M][/QUOTE] Congrats! I'll leave it to ATH to do a Lucas test. 
[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. 
[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... 
[QUOTE=GP2;550090][M]M10,443,557[/M] has been reported fully factored.[/QUOTE]I tried to get a PRPCFD assignment of this via the manual assignment page. PrimeNet didn't want to give it to me.

[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]
[CODE]time ./pfgw64 f0 od q"(2^104435571)/37289325994807"  ../../coding/gwnum/lucasPRP  1 2 10443557 1 PFGW Version 4.0.0.64BIT.20190528.x86_Dev [GWNUM 29.8] No factoring at all, not even trivial division Lucas testing on x^2  3*x + 1 ... Is Lucas PRP! real 411m8.299s user 1571m46.737s sys 15m10.377s [/CODE] :toot: 
I took liberty to let Lifchitz [URL="http://www.primenumbers.net/prptop/prptop.php"]PRP Top site[/URL] know.
It is in position #3 now. [c](2^104435571)/37289325994807 is Fermat, Lucas and Frobenius PRP! (P = 5, Q = 3, D = 13) Time : 80331.237 sec.[/c] 
[QUOTE=GP2;550090][M]M10,443,557[/M] has been reported fully factored.
This would be a new record. The previous recordholder was [M]M7,313,983[/M][/QUOTE] [M]M10,443,557[/M] was 344th. 345th is [M]M3307[/M], as reported [URL="https://www.mersenneforum.org/showthread.php?p=551249#post551249"]here[/URL] and [URL="https://www.mersenneforum.org/showthread.php?p=551258&#post551258"]here[/URL] The cofactor was certified in factordb on July 19th. 
Yay! :party:

The 346th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is M1999.
The most recent factor (49 digits) was found by Ryan Propper on September 02 and the cofactor was certified to be prime by anonymous and verfied by FactorDB. [URL="http://factordb.com/index.php?query=2%5E19991"]FactorDB link.[/URL] 
The 347th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M2029[/M].
The most recent factor (58 digits) was found by Ryan Propper on September 04 and the cofactor is certified prime. [URL="http://factordb.com/index.php?id=1000000000000002029"]FactorDB link[/URL]. 
Gelly has proved the [URL="https://primes.utm.edu/primes/page.php?id=131278"]M84,211 cofactor[/URL]. The page [url]https://www.mersenne.ca/prp.php[/url] needs to be updated.

Impressive. How long did that take?

[QUOTE=Prime95;558075]Impressive. How long did that take?[/QUOTE]
[URL="https://mersenneforum.org/showpost.php?p=557830&postcount=17"]4132590s (47.8 days)[/URL] on Gelly's 32 core AMD Threadripper 
[QUOTE=paulunderwood;558073]Gelly has proved the [URL="https://primes.utm.edu/primes/page.php?id=131278"]M84,211 cofactor[/URL]. The page [url]https://www.mersenne.ca/prp.php[/url] needs to be updated.[/QUOTE]I've added it to the fullyfactored list, thanks.

The 348th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M4349[/M].
The most recent factor (41 digits) was found by Ryan Propper on September 30 and the PRP test was done by mnd9. [URL="http://factordb.com/index.php?id=1100000001579350367"]FactorDB link[/URL]. 
[QUOTE=GP2;558515][URL="http://factordb.com/index.php?id=1100000001579350367"]FactorDB link[/URL].[/QUOTE]
As of this writing, this hasn't got a certification. FactorDB did not assign one automatically, the exponent must be too big. Edit: now it's certified. 
The 349th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M1489[/M].
The most recent factor (60 digits) was found by nordi on December 17 (UTC) and the PRP test was also done by nordi. There are 7 factors in all, plus the cofactor. [URL="http://factordb.com/index.php?id=1100000002332264431"]FactorDB link[/URL]. 
[QUOTE=GP2;566411]or probablyfullyfactored[/QUOTE]
Do you mean we don't know if the ~235 digits cofactor is definitively prime or not? :razz: Congrats for the very nice ECM hit! :party: 
[QUOTE=LaurV;566424]Do you mean we don't know if the ~235 digits cofactor is definitively prime or not? :razz:[/QUOTE]
Please reread posts 508511 :judge: :whack: 
[QUOTE=axn;566431]Please reread posts 508511 :judge: :whack:[/QUOTE]
Yes Sir! :blush: (now, I am worrying... I am fxcking getting older and stupider! I could not remember that discussion, before rereading it!) Edit: hey Mike/Serge! (only you can touch posts without letting fingerprints). I remember for sure that my "size approximations" (mental calculation) was like "~300 digits" which I wrote there, and for sure I didn't make it so accurate, haha. If I would have done it so accurate, by either computing the cofactor or looking for it, then the "~" sign ("about") would have had no sense. The cofactor is indeed 235 digits (just checked FDB). So, one of you decided to fix my approximation, or I am getting nuts for real? 
[QUOTE=LaurV;566432]I am fxcking getting older and stupider! [/QUOTE]
No doubt :missingteeth: :razz: 
[QUOTE=LaurV;566432](now, I am worrying... I am fxcking getting older and stupider! I could not remember that discussion, before rereading it!)[/QUOTE]There is a Pennsylvania Dutch proverb, "We grow too soon old, and too late smart."
As to getting older, you simply have to live with it. You can [i]not[/i] live with the alternative. As to "stupider," that's not the right adjective. "More forgetful," particularly of things in the near past, almost certainly. :paul: Back in the days of the Usenet, when I suddenly realized I simply wasn't remembering things in the way I had long taken for granted, I posted to the effect that "The thing I forget that gets me in the most trouble is, I keep forgetting that my memory isn't as good as it used to be."[sup]†[/sup] I got a very gratifying response: "It's not nice to make people spray coffee all over their monitors." If only I remembered recent things that well... [sup]†[/sup]For the edification of younger denizens of the Forum, who have yet to experience what I'm talking about, what I meant by this was that, I often still counted on my memory being as good as it had been, even though it wasn't, and that I consequently failed to do things because I had forgotten them, whereas previously I would have remembered. I had to learn to compensate for this distressing change in circumstances. In the context of online discussions, it meant that it was a good idea to scan earlier posts on a given topic before :deadhorse: Nowadays, it is almost second nature to make out a shopping list before heading out on a shopping trip. This really helps, except for when (a) I get to my first stop, and realize I left the list at home, or (b) I bring the list, but forget to consult it. 
[QUOTE=Dr Sardonicus;566442]Nowadays, it is almost second nature to make out a shopping list before heading out on a shopping trip. This really helps, except for when (a) I get to my first stop, and realize I left the list at home, or (b) I bring the list, but forget to consult it.[/QUOTE]... or (c) you forgot where the shops are and where your house is and spend the rest of your life sleeping on the park bench wondering who you are. :davar55:

[QUOTE=retina;566443]... or (c) you forgot where the shops are and where your house is and spend the rest of your life sleeping on the park bench wondering who you are. :davar55:[/QUOTE]Speak for yourself.
It occurs to me that this would be a [i]great[/i] way to put off inquiries as to the location of your evil lair: "I've forgotten!" 
[QUOTE=Dr Sardonicus;566449]It occurs to me that this would be a [i]great[/i] way to put off inquiries as to the location of your evil lair: "I've forgotten!"[/QUOTE]I know where it is (at least within a 840km radius circle.)

As I get older I notice 2 things starting to happen:
1. I repeat myself 2. I repeat myself 
[QUOTE=Dr Sardonicus;566442]"It's not nice to make people spray coffee all over their monitors."[/QUOTE]Aka CN>K
Or have you forgotten that too? 
[QUOTE=xilman;566457]Aka CN>K
Or have you forgotten that too?[/QUOTE] I have never seen that before. Therefore I have not forgotten it. 
The 350th fullyfactored or probablyfullyfactored Mersenne number with prime exponent
The 350th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [URL="https://www.mersenne.org/M1399"]M1399[/URL].
The most recent factor (61 digits) was found by Ryan Propper on December 19 (UTC) and the PRP test was done by mikr and myself. There are 3 factors in all, plus the cofactor. 
[QUOTE=Maciej Kmieciak;566781]The 350th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [URL="https://www.mersenne.org/M1399"]M1399[/URL].
The most recent factor (61 digits) was found by Ryan Propper on December 19 (UTC) and the PRP test was done by mikr and myself. There are 3 factors in all, plus the cofactor.[/QUOTE]FWIW, I ran PariGP's isprime() on this PRP308 with the following result: [code]? n=(2^13991)/28875361/4320651071020341609502042221583629017824960697/9729831901051958663829453004687723271026191923786080297556081; ? isprime(n) %2 = 1[/code] It didn't take very long. The manual entry says[quote]3.4.31 isprime(x, {flag = 0}): true (1) if x is a (proven) prime number, false (0) otherwise. This can be very slow when x is indeed prime and has more than 1000 digits, say. Use ispseudoprime to quickly check for pseudo primality. See also factor. If flag = 0, use a combination of BailliePSW pseudo primality test (see ispseudoprime), Selfridge "p − 1" test if x − 1 is smooth enough, and AdlemanPomeranceRumelyCohenLenstra (APRCL) for general x.[/quote] 
@James,
[URL="https://primes.utm.edu/primes/page.php?id=132049"]M82939 cofactor[/URL] is certified prime 
Congrats for this nice result!
[QUOTE=paulunderwood;572397]@James,
[URL="https://primes.utm.edu/primes/page.php?id=132049"]M82939 cofactor[/URL] is certified prime[/QUOTE] Many congrats, Paul! Jean P.S. : How did you do the PRP test before the certification using Primo ? 
Thanks, Jean.
I merely got the candidate from [url]www.mersenne.ca[/url]. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path. 
[QUOTE=paulunderwood;572410]Thanks, Jean.
I merely got the candidate from [url]www.mersenne.ca[/url]. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path.[/QUOTE] Thank you for this detail! Jean 
[QUOTE=paulunderwood;572397][URL="https://primes.utm.edu/primes/page.php?id=132049"]M82939 cofactor[/URL] is certified prime[/QUOTE]I have updated [url=https://www.mersenne.ca/prp.php?show=2&min_exponent=82000&max_exponent=83000#M82939]my PRP list[/url], thanks.

[QUOTE=Jean Penné;572405]
P.S. : How did you do the PRP test before the certification using Primo ?[/QUOTE] [QUOTE=paulunderwood;572410]Thanks, Jean. I merely got the candidate from [url]www.mersenne.ca[/url]. I might have run a 3PRP to be sureish. Anyway, Primo does a quick Fermat+Lucas à la BPSW before embarking on a lengthy ECPP path.[/QUOTE] We had already a Prpcf test on this: [url]https://www.mersenne.org/report_exponent/?exp_lo=82939&exp_hi=&full=1[/url] Notice that for N=(k*2^n+c)/d we're using a Fermat test using base^d as base, then (base^d)^N=base^d mod N should hold for a prp number. So base^(k*2^n+c)==base^d mod N, to help a lot we're using reduction mod (d*N)=mod (k*2^n+c). Then do only one big division at the end of the test, in real life d is "small", at most ~1000 bits. And you can build in a strong check in the routine like for the normal prp test for k*2^n+c numbers. There is only a very small slow down at error check, because here our base is "large". ps. so actually p95 has done a Fermat test using 3^d as base, and not 3. The reason is that we have a check only for 3^d [or base^d]. 
The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M].
The most recent factor (47 digits) was found by Bruno Victal on 20210320 and the PRP test was done by user "mikr". [URL="http://factordb.com/index.php?id=1100000002528023613"]FactorDB link[/URL] 
[QUOTE=GP2;574238]The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M][/QUOTE]Pardon my ignorance, but what is the "type" of a PRP test? I can't remember the last time I saw an exponent status page in which the type of a PRP test was anything but 1. I noticed that this one had a PRP test of "type" 5 rather than 1.

[QUOTE=Dr Sardonicus;574249]what is the "type" of a PRP test? I can't remember the last time I saw an exponent status page in which the type of a PRP test was anything but 1. I noticed that this one had a PRP test of "type" 5 rather than 1.[/QUOTE]From the undoc.txt of prime95 zip file:[CODE]PRP supports 5 types of residues for compatibility with other PRP programs. If
a is the PRP base and N is the number being tested, then the residue types are: 1 = 64bit residue of a^(N1), a traditional Fermat PRP test used by most other programs 2 = 64bit residue of a^((N1)/2) 3 = 64bit residue of a^(N+1), only available if b=2 4 = 64bit residue of a^((N+1)/2), only available if b=2 5 = 64bit residue of a^(N*known_factors1), same as type 1 if there are no known factors [/CODE]Gpuowl has implemented type 1 mostly, type 4 in some versions. In gpuowl V5.0, simultaneous P1 and PRP was implemented IIRC as a "type 0" using a large base related to P1 B1, IIRC. [URL]https://www.mersenneforum.org/showpost.php?p=510732&postcount=8[/URL] [URL]https://mersenneforum.org/showpost.php?p=519902&postcount=1255[/URL] [URL]https://www.mersenneforum.org/showpost.php?p=519603&postcount=15[/URL] I think Mlucas does type 1. Type 1 is standard for PRP primality test of noknownfactor Mersenne numbers. Type 5 is standard for PRPCF. 
[QUOTE=GP2;574238]The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M].
The most recent factor (47 digits) was found by Bruno Victal on 20210320 and the PRP test was done by user "mikr". [URL="http://factordb.com/index.php?id=1100000002528023613"]FactorDB link[/URL][/QUOTE] I've seen this one as I got it immediately assigned for DC :lol: (still in queue, it will be done tomorrow or the day after). I could move it to the front, but as I have no doubt that is PRP, let it be. Congrats to the finder(s) ! 
[QUOTE=GP2;574238]The 351st fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M8233[/M].[/QUOTE]
The cofactor is now certified prime: [URL="http://factordb.com/index.php?id=1100000002528023613"]http://factordb.com/index.php?id=1100000002528023613[/URL]. 
The 352nd fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7669[/M].
The most recent factor (47 digits) was found by Ryan Propper on 20210326 and the PRP test was done by user "mikr". [URL="http://factordb.com/index.php?id=1100000002531548425"]FactorDB link[/URL] The cofactor is already certified prime. 
The 353rd fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M7013[/M].
The most recent factor (49 digits) was found by Ryan Propper on 20210327 and the PRP test was done by user "riccardo uberti". [URL="http://factordb.com/index.php?id=1100000002534390416"]FactorDB link[/URL] The cofactor is already certified prime. 
That's 3 in a week. Noice!

The 354th fullyfactored or probablyfullyfactored Mersenne number with prime exponent (not including the Mersenne primes themselves) is [M]M5393[/M].
The most recent factor (58 digits) was found by Ryan Propper on 20210407 and the PRP test was done by user "mnd9". Ryan also found a 54digit factor last October. The only other factor has 5 digits (32359). [URL="http://factordb.com/index.php?id=1100000002545348837"]FactorDB link[/URL] The cofactor is already certified prime. 
There are now 355 known Mersenne numbers with prime exponent that are composite and either fully factored or probably fully factored.
The most recent is [M]M4507[/M]. Its final factor (53 digits) was found by Ryan Propper on 20210418 and the PRP test was done by user "ThomRuley". [URL="http://factordb.com/index.php?id=1100000002558891770"]FactorDB link[/URL] The cofactor is already certified prime. 
Ryan Propper found another factor and another PRP #356: M[M]3917[/M]

[QUOTE=ATH;577168]Ryan Propper found another factor and another PRP #356: M[M]3917[/M][/QUOTE]I'm curious. Usually when a cofactor tests as a PRP, the residue is listed as
PRP_PRP_PRP_PRP_ But here, although the history says the remaining cofactor is a probable prime, the PRP cofactor residue is a hex value with, I presume, the last few digits obscured pending confirmation... 
[QUOTE=Dr Sardonicus;577172]I'm curious. Usually when a cofactor tests as a PRP, the residue is listed as
PRP_PRP_PRP_PRP_ But here, although the history says the remaining cofactor is a probable prime, the PRP cofactor residue is a hex value with, I presume, the last few digits obscured pending confirmation...[/QUOTE] Yeah, that is strange I had not noticed, since it was spamming my results.txt with PRP. It was on an AWS instance, and I only noticed it by coincidence, because I was upgrading it to 30.6b4. Now I ran it again and unintentionally double checked my own result, now it shows as PRP. But PRPCF usually do not have hidden or fake residues? I'm not sure why it used type 1 PRP test, here in the 2nd manual test I specifically told it to do a type 5 test. Someone else please double check it as well. 
[QUOTE=ATH;577176]Someone else please double check it as well.[/QUOTE]
Like Ryan's other recent factor discoveries, the factor got reported almost immediately to FactorDB (by Ryan himself?), and the cofactor is usually already certified prime there before the first PRP test completes on PrimeNet. [URL="http://factordb.com/index.php?id=1100000002567981077"]FactorDB link[/URL] 
Wow, 61 digits? That's a beast! Congrats Ryan! :party:

A 61 decimal digit factor winkled out. Amazing!
Whatever the problem was with the PRP cofactor residue, it's been fixed. Two tests show a residue of PRP_PRP_PRP_PRP_ And, as previously noted, the cofactor is already certified prime. Another fullyfactored Mersenne composite! 
There are now 357 known Mersenne numbers with prime exponent that are composite and either fully factored or probably fully factored.
The most recent is [M]M4021[/M]. Its final factor (66 digits) was found by Ryan Propper on 20210519 and the PRP test was done by user "mnd9". [URL="http://factordb.com/index.php?id=1100000002586440192"]FactorDB link[/URL] The cofactor was already certified prime yesterday on FactorDB. 
Just finished the PRPCF of M[M]3769231[/M] and M[M]5078387[/M], looks like Ben Delo will certify both exponents like last time.
Wondering whether anyone has a PPRP cofactor with the exponent size over 1M on the record? 
[QUOTE=tuckerkao;592598]Just finished the PRPCF of M[M]3769231[/M] and M[M]5078387[/M], looks like Ben Delo will certify both exponents like last time.
Wondering whether anyone has a PPRP cofactor with the exponent size over 1M on the record?[/QUOTE] See post 519 of this thread. 
[QUOTE=masser;592607]See post 519 of this thread.[/QUOTE]That would be [url=https://mersenneforum.org/showpost.php?p=550126&postcount=519]this post[/url].
See also the next post to the thread, [url=https://mersenneforum.org/showpost.php?p=550133&postcount=520]this post[/url]. (The PRP cofactor (2^104435571)/37289325994807 has since been pushed down to position #8 in the Probable Primes Top 10000 site) 
[QUOTE=Dr Sardonicus;592610]That would be [url=https://mersenneforum.org/showpost.php?p=550126&postcount=519]this post[/url].
See also the next post to the thread, [url=https://mersenneforum.org/showpost.php?p=550133&postcount=520]this post[/url]. (The PRP cofactor (2^104435571)/37289325994807 has since been pushed down to position #8 in the Probable Primes Top 10000 site)[/QUOTE] I would like young Tucker to do some of the legwork himself. 
[QUOTE=Dr Sardonicus;592610](The PRP cofactor (2^104435571)/37289325994807 has since been pushed down to position #8 in the Probable Primes Top 10000 site)[/QUOTE]
What test will be needed to confirm the probable prime from the cofactor of M[M]10443557[/M]? Is there 1 doable test like LL to the regular PRP? 
[QUOTE=tuckerkao;592627]What test will be needed to confirm the probable prime from the cofactor of M[M]10443557[/M]? Is there 1 doable test like LL to the regular PRP?[/QUOTE]
The short answer is "no!". See [url]https://primes.utm.edu/prove/[/url] :smile: 
[QUOTE=masser;592613]I would like young Tucker to do some of the legwork himself.[/QUOTE]So would I. But if he were willing to do legwork himself, he would not have posted his query. I posted the links for the benefit of others. Back when I was a new user, I was advised to use "show single post" in referring to previous posts. Locating the page with a given post number in a long thread can be tedious.
But, just for fun, I will mention that two smaller p > 1000000 for which M[sub]p[/sub] has a large PRP cofactor are mentioned on this Forum, [i]somewhere[/i] in [url=https://www.mersenneforum.org/showthread.php?t=19157]this thread[/url], which is a predecessor to the present one. That thread is much shorter than this one. 
[QUOTE=Dr Sardonicus;592632]But, just for fun, I will mention that two smaller p > 1000000 for which M[sub]p[/sub] has a large PRP cofactor are mentioned on this Forum, [i]somewhere[/i] in [url=https://www.mersenneforum.org/showthread.php?t=19157]this thread[/url], which is a predecessor to the present one. That thread is much shorter than this one.[/QUOTE]
I saw 4 of them inside that thread: M[M]4187251[/M], M[M]4834891[/M], M[M]5240707[/M], M[M]7080247[/M]. Those are the 4 predecessors of M[M]10443557[/M] which is the current largest known PPRPCF. I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage. The total quantity is scarce enough that qualifies to be the Mersenne treasures of the discoverers. 
[QUOTE=tuckerkao;592633]I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.[/QUOTE]
That sounds like it would be better under the Wiki. Why don't you step up, and curate that? Might reduce the noise here on the Forum. Just asking... 
[QUOTE=tuckerkao;592633]I wish there can be a new specialized page for Known Cofactor Probable Primes or Fully factored Mersenne Numbers that are not Mersenne Primes under Current Progress menu of the GIMPS homepage.[/QUOTE]
[url]https://www.mersenne.ca/prp.php[/url] 
Congrats to Gelly (Robert Gelhar) for proving prime the [URL="http://factordb.com/index.php?id=1100000000013690992"]cofactor of 2^1063911[/URL]

Congrats to Ryan for proving the cofactor of M78737 using FastECPP.

M86137 cofactor has been certified prime by yours truly. :smile:

Congrats for proving a now P25924 prime. :smile:

M[M]245107[/M] is a probable semiprime.
Factor found by Sid & Andy. Test by user SRJ2877. 
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