What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
6251 | 10^90960-610659 | 90960 | Patrick De Geest | 07/2019 |
6252 | 10^90959-275213 | 90959 | Patrick De Geest | 07/2019 |
6253 | (2^302129+3110)/2 | 90950 | Stefano Morozzi | 09/2020 |
6255 | 10^90948+9867 | 90949 | Patrick De Geest | 01/2019 |
6254 | 21665^15774+15774^21665 | 90949 | Hans Havermann | 04/2020 |
6256 | 10^90948-109239 | 90948 | Patrick De Geest | 07/2019 |
6257 | 2^302113+74105 | 90946 | Enzo Doria | 04/2016 |
6258 | 2^302102-6555 | 90942 | Lelio R Paula | 02/2016 |
6259 | 10^90930+95223 | 90931 | Patrick De Geest | 07/2019 |
6260 | 10^90930-3623 | 90930 | Patrick De Geest | 01/2019 |
6261 | 156*(10^(4*22731)-1)/101-1 | 90925 | Robert Price | 05/2014 |
6262 | 3^190568+38 | 90925 | Lelio R Paula | 04/2016 |
6263 | 10^90917+179863 | 90918 | Patrick De Geest | 07/2019 |
6264 | 10^90917-6693 | 90917 | Patrick De Geest | 01/2019 |
6265 | 2^302009-16449 | 90914 | Enzo Doria | 04/2013 |
6266 | 10^90908+3181 | 90909 | Patrick De Geest | 01/2019 |
6267 | 10^90908-139511 | 90908 | Patrick De Geest | 07/2019 |
6268 | 10^90904+106947 | 90905 | Patrick De Geest | 07/2019 |
6269 | 10^90904-5169 | 90904 | Patrick De Geest | 01/2019 |
6270 | 10^90903+120963 | 90904 | Patrick De Geest | 07/2019 |
6271 | 10^90902+2613 | 90903 | Patrick De Geest | 01/2019 |
6272 | 10^90903-190737 | 90903 | Patrick De Geest | 07/2019 |
6273 | 25174^4083+4083^25174 | 90903 | Hans Havermann | 08/2020 |
6274 | 10^90902-952329 | 90902 | Patrick De Geest | 07/2019 |
6275 | (17*2^301951-1)/165 | 90896 | Lelio R Paula | 02/2014 |
6276 | 3^190497+74 | 90891 | Lelio R Paula | 04/2016 |
6277 | (24737*2^301896+1)/399 | 90882 | Lelio R Paula | 06/2014 |
6278 | 10^90880+5707 | 90881 | Patrick De Geest | 01/2019 |
6279 | 10^90880-152993 | 90880 | Patrick De Geest | 07/2019 |
6280 | 18^72397+89 | 90878 | Lelio R Paula | 06/2016 |
6281 | (2^301876+762)/2 | 90874 | Stefano Morozzi | 09/2020 |
6282 | 134^42719-133 | 90868 | Norbert Schneider | 03/2019 |
6283 | 6^116769-47 | 90864 | Lelio R Paula | 05/2016 |
6284 | 10^90858+233433 | 90859 | Patrick De Geest | 07/2019 |
6285 | 10^90858-8301 | 90858 | Patrick De Geest | 01/2019 |
6286 | 24298^5483+5483^24298 | 90851 | Hans Havermann | 08/2020 |
6287 | 10^90849+40141 | 90850 | Patrick De Geest | 07/2019 |
6288 | 10^90849-4721 | 90849 | Patrick De Geest | 01/2019 |
6289 | 2^301712-465 | 90825 | Lelio R Paula | 02/2016 |
6290 | 2^301693-69 | 90819 | Lelio R Paula | 11/2012 |
6291 | 2^301683-301683^2 | 90816 | Henri Lifchitz | 05/2005 |
6292 | 10^90807+7279 | 90808 | Patrick De Geest | 01/2019 |
6293 | 10^90807-162263 | 90807 | Patrick De Geest | 07/2019 |
6294 | 6*10^90803+79 | 90804 | Robert Price | 09/2020 |
6295 | 10^90800-6453 | 90800 | Patrick De Geest | 11/2018 |
6296 | 11^87187-1710 | 90796 | Enzo Doria | 12/2012 |
6297 | 5*10^90793+21 | 90794 | Robert Price | 01/2017 |
6298 | (22*10^90792-13)/9 | 90793 | Robert Price | 03/2015 |
6299 | 2^301591-1615 | 90788 | Lelio R Paula | 02/2016 |
6300 | (52^52901+1)/53 | 90777 | Paul Bourdelais | 08/2017 |
6301 | 2^301546-109037 | 90775 | Enzo Doria | 04/2014 |
6302 | 10^90772+4029 | 90773 | Patrick De Geest | 11/2018 |
6303 | 10^90772-36627 | 90772 | Patrick De Geest | 07/2019 |
6304 | 10^90771+67737 | 90772 | Patrick De Geest | 07/2019 |
6305 | 10^90771-441003 | 90771 | Patrick De Geest | 07/2019 |
6306 | 10^90770+28941 | 90771 | Patrick De Geest | 07/2019 |
6307 | 10^90770-431 | 90770 | Patrick De Geest | 11/2018 |
6308 | 14^79195-3 | 90768 | Lelio R Paula | 06/2016 |
6309 | 10^90766+877 | 90767 | Patrick De Geest | 11/2018 |
6312 | 2^301517-1861693 | 90766 | Enzo Doria | 11/2015 |
6310 | 10^90766-109241 | 90766 | Patrick De Geest | 07/2019 |
6311 | 10^90765+485361 | 90766 | Patrick De Geest | 07/2019 |
6313 | 10^90765-4797 | 90765 | Patrick De Geest | 11/2018 |
6314 | 10^90757+7573 | 90758 | Patrick De Geest | 11/2018 |
6315 | 10^90757-554979 | 90757 | Patrick De Geest | 07/2019 |
6316 | 10^90756+438109 | 90757 | Patrick De Geest | 07/2019 |
6317 | 10^90756-8727 | 90756 | Patrick De Geest | 11/2018 |
6318 | 10^90749+823 | 90750 | Patrick De Geest | 11/2018 |
6321 | 2^301460-173 | 90749 | Lelio R Paula | 11/2012 |
6319 | 10^90748+4213 | 90749 | Patrick De Geest | 11/2018 |
6320 | 10^90749-130413 | 90749 | Patrick De Geest | 07/2019 |
6322 | 10^90748-75411 | 90748 | Patrick De Geest | 07/2019 |
6323 | 10^90747+438471 | 90748 | Patrick De Geest | 07/2019 |
6324 | 10^90747-9279 | 90747 | Patrick De Geest | 11/2018 |
6325 | (85*10^90745-103)/9 | 90746 | Robert Price | 10/2017 |
6326 | (2^301439+1206)/2 | 90742 | Stefano Morozzi | 09/2020 |
6327 | 10^90726+4077 | 90727 | Patrick De Geest | 11/2018 |
6328 | 10^90726-504951 | 90726 | Patrick De Geest | 07/2019 |
6329 | 10^90721+181 | 90722 | Patrick De Geest | 11/2018 |
6330 | (2^301372+2722)/2 | 90722 | Stefano Morozzi | 09/2020 |
6331 | 10^90721-177149 | 90721 | Patrick De Geest | 07/2019 |
6332 | (2^301317+1146)/2 | 90706 | Stefano Morozzi | 09/2020 |
6333 | 2^301312-89 | 90704 | Lelio R Paula | 11/2012 |
6334 | 10^90696+6349 | 90697 | Patrick De Geest | 11/2018 |
6336 | 2^301285-129 | 90696 | Lelio R Paula | 11/2012 |
6335 | 10^90696-635049 | 90696 | Patrick De Geest | 07/2019 |
6337 | 2^301282-109991 | 90695 | Enzo Doria | 04/2014 |
6338 | 10^90690+8877 | 90691 | Patrick De Geest | 11/2018 |
6339 | 10^90690-227433 | 90690 | Patrick De Geest | 07/2019 |
6340 | 10^90683+61411 | 90684 | Patrick De Geest | 07/2019 |
6341 | (2^301244+1738)/2 | 90684 | Stefano Morozzi | 09/2020 |
6342 | 10^90683-2577 | 90683 | Patrick De Geest | 11/2018 |
6343 | 2^301228-1854269 | 90679 | Enzo Doria | 09/2015 |
6345 | (151*10^90669-1)/3 | 90671 | Robert Price | 04/2017 |
6344 | (2^301201+2046)/2 | 90671 | Stefano Morozzi | 09/2020 |
6346 | (32*10^90669+13)/9 | 90670 | Robert Price | 04/2015 |
6347 | 10^90669+9793 | 90670 | Patrick De Geest | 11/2018 |
6348 | 10^90669-223931 | 90669 | Patrick De Geest | 07/2019 |
6349 | (2^301191+2510)/2 | 90668 | Stefano Morozzi | 09/2020 |
6350 | 10^90665+10989 | 90666 | Patrick De Geest | 07/2019 |
6351 | 10^90665-3087 | 90665 | Patrick De Geest | 11/2018 |
6352 | 10^90662+89637 | 90663 | Patrick De Geest | 07/2019 |
6353 | 10^90662-9519 | 90662 | Patrick De Geest | 11/2018 |
6354 | 10^90661+2373 | 90662 | Patrick De Geest | 11/2018 |
6355 | 10^90661-194781 | 90661 | Patrick De Geest | 07/2019 |
6356 | 3*5^129698+8 | 90656 | Lelio R Paula | 10/2014 |
6357 | F(433781) | 90655 | Henri Lifchitz | 09/2003 |
6358 | 19^70891+82 | 90653 | Lelio R Paula | 06/2016 |
6359 | (29*2^301124-1)/13 | 90648 | Lelio R Paula | 02/2014 |
6360 | 10^90636+64159 | 90637 | Patrick De Geest | 07/2019 |
6361 | 10^90636-3101 | 90636 | Patrick De Geest | 11/2018 |
6362 | 7*3^189953-8 | 90632 | Lelio R Paula | 08/2014 |
6363 | 10^90626+339289 | 90627 | Patrick De Geest | 07/2019 |
6364 | 10^90626-1131 | 90626 | Patrick De Geest | 11/2018 |
6365 | 11^87022-1800 | 90625 | Enzo Doria | 12/2012 |
6366 | 10^90623+861 | 90624 | Patrick De Geest | 11/2018 |
6367 | 10^90623-305841 | 90623 | Patrick De Geest | 07/2019 |
6368 | (2^301042+47)/12036969 | 90616 | Lelio R Paula | 06/2013 |
6370 | 2^301004-2786939 | 90612 | Enzo Doria | 03/2016 |
6369 | 10^90611+169977 | 90612 | Patrick De Geest | 07/2019 |
6371 | 10^90611-9737 | 90611 | Patrick De Geest | 11/2018 |
6372 | 10^90610+36747 | 90611 | Patrick De Geest | 07/2019 |
6374 | 10^90609+6823 | 90610 | Patrick De Geest | 11/2018 |
6373 | 10^90610-26573 | 90610 | Patrick De Geest | 07/2019 |
6375 | 10^90609-228173 | 90609 | Patrick De Geest | 07/2019 |
6376 | 2^300980-27 | 90605 | Lelio R Paula | 11/2012 |
6377 | 2*10^90597-7 | 90598 | Dmitry Domanov | 11/2010 |
6378 | 197^39485+2 | 90597 | Lelio R Paula | 06/2013 |
6379 | 7^107198+48 | 90593 | Lelio R Paula | 04/2016 |
6380 | (86*10^90588+121)/9 | 90589 | Robert Price | 03/2017 |
6381 | 2^300923+53 | 90587 | Lelio R Paula | 11/2012 |
6382 | 2^300874+7 | 90573 | Lelio R Paula | 10/2012 |
6383 | 10^90567+9489 | 90568 | Patrick De Geest | 11/2018 |
6384 | 10^90567-231353 | 90567 | Patrick De Geest | 07/2019 |
6385 | (2^300857+2214)/2 | 90567 | Stefano Morozzi | 01/2020 |
6386 | 5^129568-56 | 90565 | Lelio R Paula | 04/2016 |
6387 | 2^300847-112831 | 90564 | Enzo Doria | 06/2014 |
6388 | 10^90562+790197 | 90563 | Patrick De Geest | 07/2019 |
6389 | 10^90562-2981 | 90562 | Patrick De Geest | 11/2018 |
6390 | (7796^23269-1)/7795 | 90557 | Serge Batalov | 08/2020 |
6391 | 10^90549+3811 | 90550 | Patrick De Geest | 11/2018 |
6392 | 10^90549-630303 | 90549 | Patrick De Geest | 07/2019 |
6393 | 2^300790-4541 | 90547 | Yves Minet | 03/2019 |
6394 | 10^90532+8169 | 90533 | Patrick De Geest | 11/2018 |
6395 | 10^90531+9831 | 90532 | Patrick De Geest | 11/2018 |
6396 | 10^90532-154889 | 90532 | Patrick De Geest | 07/2019 |
6397 | 10^90531-1060589 | 90531 | Patrick De Geest | 07/2019 |
6399 | 2^300718+255255 | 90526 | Lelio R Paula | 02/2016 |
6398 | (2^300719+938)/2 | 90526 | Stefano Morozzi | 01/2020 |
6400 | 10^90516+215917 | 90517 | Patrick De Geest | 07/2019 |
6401 | 10^90516-6783 | 90516 | Patrick De Geest | 11/2018 |
6402 | 10^90511+30177 | 90512 | Patrick De Geest | 07/2019 |
6403 | 10^90511-6977 | 90511 | Patrick De Geest | 11/2018 |
6404 | (8573^23011-1)/8572 | 90502 | Serge Batalov | 08/2020 |
6405 | 2^300637+95 | 90501 | Lelio R Paula | 11/2012 |
6407 | 7^107087-24 | 90500 | Lelio R Paula | 04/2016 |
6406 | 10^90499+191547 | 90500 | Patrick De Geest | 07/2019 |
6408 | 10^90499-5823 | 90499 | Patrick De Geest | 11/2018 |
6410 | (10^90499+3^90499)/13 | 90498 | Robert Price | 01/2013 |
6409 | 13^81241+90 | 90498 | Lelio R Paula | 06/2016 |
6411 | (2^300600+1222)/2 | 90490 | Stefano Morozzi | 01/2020 |
6412 | 10^90480+5131 | 90481 | Patrick De Geest | 11/2018 |
6413 | 10^90480-85721 | 90480 | Patrick De Geest | 07/2019 |
6414 | 6^116273-85 | 90478 | Lelio R Paula | 05/2016 |
6415 | 10^90473+3139 | 90474 | Patrick De Geest | 11/2018 |
6416 | 10^90473-150599 | 90473 | Patrick De Geest | 07/2019 |
6417 | 10^90470+2319 | 90471 | Patrick De Geest | 11/2018 |
6418 | 10^90470-71637 | 90470 | Patrick De Geest | 07/2019 |
6419 | 6^116256-17573 | 90465 | Enzo Doria | 02/2013 |
6420 | 2^300502+54615 | 90461 | Lelio R Paula | 02/2016 |
6421 | (13*2^300487+1)/45 | 90456 | Lelio R Paula | 09/2013 |
6422 | 10^90453+141843 | 90454 | Patrick De Geest | 07/2019 |
6423 | 10^90453-3969 | 90453 | Patrick De Geest | 11/2018 |
6424 | 10^90440+1359 | 90441 | Patrick De Geest | 11/2018 |
6425 | 10^90440-18821 | 90440 | Patrick De Geest | 07/2019 |
6426 | (3^189545-8)/5 | 90436 | Lelio R Paula | 01/2013 |
6427 | (7*2^300406-1)/3 | 90432 | Lelio R Paula | 02/2014 |
6428 | 10^90430+3339 | 90431 | Patrick De Geest | 11/2018 |
6429 | 10^90430-63477 | 90430 | Patrick De Geest | 07/2019 |
6430 | (5408^24223-1)/5407 | 90422 | Serge Batalov | 08/2020 |
6431 | 10^90414+229593 | 90415 | Patrick De Geest | 07/2019 |
6432 | 10^90414-1547 | 90414 | Patrick De Geest | 11/2018 |
6433 | 10^90404+47041 | 90405 | Patrick De Geest | 07/2019 |
6434 | 10^90404-6429 | 90404 | Patrick De Geest | 11/2018 |
6435 | 10^90401+2077 | 90402 | Patrick De Geest | 11/2018 |
6437 | 10^90401-368637 | 90401 | Patrick De Geest | 07/2019 |
6436 | 24900^4271+4271^24900 | 90401 | Hans Havermann | 08/2020 |
6438 | 4*5^129332+3 | 90400 | Lelio R Paula | 10/2014 |
6439 | 10^90397+19783 | 90398 | Patrick De Geest | 07/2019 |
6440 | 23380^7353+7353^23380 | 90398 | Hans Havermann | 08/2020 |
6442 | 10^90397-323 | 90397 | Patrick De Geest | 11/2018 |
6441 | (2^300293+2762)/2 | 90397 | Stefano Morozzi | 01/2020 |
6443 | 24058^5719+5719^24058 | 90394 | Hans Havermann | 08/2020 |
6444 | 2^300249-16245 | 90384 | Enzo Doria | 04/2013 |
6445 | 24414^5035+5035^24414 | 90381 | Hans Havermann | 08/2020 |
6446 | (7*10^90371-313)/9 | 90371 | Robert Price | 11/2016 |
6447 | 10^90363+58677 | 90364 | Patrick De Geest | 07/2019 |
6448 | 10^90363-3557 | 90363 | Patrick De Geest | 11/2018 |
6449 | 10^90358+104641 | 90359 | Patrick De Geest | 07/2019 |
6452 | 2*6^116118+7 | 90358 | Lelio R Paula | 10/2014 |
6451 | 10^90358-4979 | 90358 | Patrick De Geest | 11/2018 |
6450 | 10^90357+112837 | 90358 | Patrick De Geest | 07/2019 |
6453 | 10^90357-189593 | 90357 | Patrick De Geest | 07/2019 |
6454 | 10^90356+53113 | 90357 | Patrick De Geest | 07/2019 |
6455 | 10^90356-7197 | 90356 | Patrick De Geest | 11/2018 |
6456 | 10^90353+603211 | 90354 | Patrick De Geest | 07/2019 |
6457 | 10^90353-1089 | 90353 | Patrick De Geest | 11/2018 |
6458 | (24737*2^300101+1)/25 | 90343 | Lelio R Paula | 06/2014 |
6459 | 4*10^90334-21 | 90335 | Robert Price | 04/2016 |
6460 | (4546^24697-1)/4545 | 90329 | Serge Batalov | 08/2020 |
6461 | 10^90322+137691 | 90323 | Patrick De Geest | 07/2019 |
6462 | 10^90322-9551 | 90322 | Patrick De Geest | 11/2018 |
6463 | 10^90316+9991 | 90317 | Patrick De Geest | 11/2018 |
6464 | (4550^24691-1)/4549 | 90317 | Serge Batalov | 08/2020 |
6465 | 10^90316-45627 | 90316 | Patrick De Geest | 07/2019 |
6466 | 10^90315+32889 | 90316 | Patrick De Geest | 07/2019 |
6468 | 2^300019-110335 | 90315 | Enzo Doria | 05/2014 |
6467 | 10^90315-8561 | 90315 | Patrick De Geest | 11/2018 |
6469 | FAB2(300001,5032) | 90310 | Robert Price | 05/2019 |
6470 | FAB2(300001,29405) | 90310 | Robert Price | 05/2019 |
6471 | (2^299965+2774)/2 | 90299 | Stefano Morozzi | 01/2020 |
6472 | 23679^6506+6506^23679 | 90296 | Hans Havermann | 08/2020 |
6473 | 2^299949-1005 | 90294 | Lelio R Paula | 11/2013 |
6474 | (2^299947+2054)/2 | 90293 | Stefano Morozzi | 01/2020 |
6475 | 21740^14229+14229^21740 | 90291 | Hans Havermann | 08/2020 |
6476 | 10^90279+62457 | 90280 | Patrick De Geest | 07/2019 |
6477 | 10^90279-1551 | 90279 | Patrick De Geest | 09/2018 |
6478 | (2^299892+1986)/2 | 90277 | Stefano Morozzi | 01/2020 |
6479 | (2^299893+3866)/2 | 90277 | Stefano Morozzi | 01/2020 |
6480 | 2^299868-109613 | 90270 | Enzo Doria | 04/2014 |
6481 | 10^90259+359299 | 90260 | Patrick De Geest | 07/2019 |
6482 | 10^90259-9443 | 90259 | Patrick De Geest | 09/2018 |
6483 | (2^299831+3786)/2 | 90258 | Stefano Morozzi | 01/2020 |
6484 | 10^90252+102873 | 90253 | Patrick De Geest | 07/2019 |
6485 | 10^90252-8103 | 90252 | Patrick De Geest | 09/2018 |
6487 | 5*2^299799-3 | 90250 | Lelio R Paula | 08/2014 |
6486 | (2^299803+3326)/2 | 90250 | Stefano Morozzi | 01/2020 |
6488 | 13^81008-2 | 90239 | Lelio R Paula | 09/2013 |
6489 | 80697!4-256 | 90234 | Robert Price | 11/2019 |
6491 | 64^49957-63^49957 | 90232 | Robert Price | 07/2013 |
6490 | (2^299745+2994)/2 | 90232 | Stefano Morozzi | 01/2020 |
6492 | 10^90227+56281 | 90228 | Patrick De Geest | 06/2016 |
6495 | 2^299725+315 | 90227 | Lelio R Paula | 11/2013 |
6493 | 10^90227-1000000001 | 90227 | Robert Price | 05/2016 |
6494 | 10^90227-68763 | 90227 | Patrick De Geest | 06/2016 |
6496 | 5^129082+48 | 90225 | Lelio R Paula | 03/2016 |
6497 | 2^299699+195 | 90219 | Lelio R Paula | 10/2012 |
6498 | (55*10^90211-1)/9 | 90212 | Ray Chandler | 02/2012 |
6499 | 22131^11918+11918^22131 | 90211 | Hans Havermann | 08/2020 |
6500 | 10^90209+8971 | 90210 | Patrick De Geest | 09/2018 |