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) !!!
Submit your PRPs
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Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
501 | 2^898762-251511 | 270555 | Enzo Doria | 12/2013 |
502 | 2^898589+47 | 270503 | Lelio R Paula | 03/2016 |
503 | 187322*10^270343-187321 | 270349 | Danilo Nitsche | 09/2013 |
504 | 48358*10^270343-48357 | 270348 | Danilo Nitsche | 09/2013 |
505 | (10^270343-1)/9 | 270343 | Maksym Voznyy | 07/2007 |
506 | 2^897867-3217 | 270285 | Yves Minet | 12/2016 |
507 | 2^897849-115273 | 270280 | Enzo Doria | 07/2015 |
508 | 2^896616-114179 | 269909 | Enzo Doria | 12/2014 |
509 | 2^894928+583561 | 269401 | Enzo Doria | 04/2017 |
510 | 2^894673-39343 | 269324 | Enzo Doria | 08/2015 |
511 | F(1285607) | 268676 | Henri Lifchitz | 11/2008 |
512 | 2^892112+187663 | 268553 | Enzo Doria | 08/2016 |
513 | (10^268207+1)/11 | 268206 | Paul Bourdelais | 02/2010 |
514 | 2^890957-69583 | 268205 | Enzo Doria | 12/2015 |
515 | 32841!^2+32840!^2+...+2!^2+1!^2 | 268128 | Serge Batalov | 07/2017 |
516 | 2^890122-351401 | 267954 | Enzo Doria | 07/2015 |
517 | (19^209359-1)/18 | 267718 | Paul Bourdelais | 08/2010 |
518 | (85^138647+1)/86 | 267507 | Paul Bourdelais | 07/2019 |
519 | (485^99523-1)/484 | 267291 | Michael Stocker | 05/2020 |
520 | 2^886324+77791 | 266811 | Enzo Doria | 06/2016 |
521 | 2^884714+1880527 | 266326 | Enzo Doria | 10/2016 |
522 | 11^255426+255426^11 | 265999 | Serge Batalov | 05/2014 |
523 | 2^883462-343421 | 265949 | Enzo Doria | 07/2015 |
524 | 2^883442+1875019 | 265943 | Enzo Doria | 06/2016 |
525 | 2^883333-291583 | 265910 | Enzo Doria | 07/2015 |
526 | 2^880411+1882673 | 265031 | Enzo Doria | 12/2016 |
527 | 2^879530-2788031 | 264765 | Enzo Doria | 12/2015 |
528 | 2^878118+2793079 | 264340 | Enzo Doria | 02/2016 |
529 | (37^168527-1)/36 | 264283 | Paul Bourdelais | 08/2019 |
530 | 2^875748-461129 | 263627 | Enzo Doria | 07/2015 |
531 | 2^875181-2789923 | 263456 | Enzo Doria | 12/2015 |
532 | 2^875101-350083 | 263432 | Enzo Doria | 08/2015 |
533 | 2^874684+1883587 | 263307 | Enzo Doria | 01/2017 |
534 | 2^874616+1872211 | 263286 | Enzo Doria | 05/2016 |
535 | 3^551491+16 | 263129 | Robert Price | 04/2020 |
536 | 2^874073+2792957 | 263123 | Enzo Doria | 02/2016 |
537 | 2^873628+1878751 | 262989 | Enzo Doria | 08/2016 |
538 | 2^873288-269 | 262886 | Yves Minet | 01/2015 |
539 | 2^871146-3173 | 262242 | Yves Minet | 07/2016 |
540 | 2^869601-163 | 261776 | Yves Minet | 01/2015 |
541 | 2^869326+282859 | 261694 | Enzo Doria | 11/2016 |
542 | 2^869035-114181 | 261606 | Enzo Doria | 12/2014 |
543 | 2^865715+80303 | 260607 | Enzo Doria | 07/2016 |
544 | 2^865048+1882411 | 260406 | Enzo Doria | 12/2016 |
545 | 2^864899-113871 | 260361 | Enzo Doria | 10/2014 |
546 | (7*10^260198-61)/9 | 260198 | Erik Branger | 11/2011 |
547 | 2^864298-2788421 | 260180 | Enzo Doria | 12/2015 |
548 | 2^864039-2791357 | 260102 | Enzo Doria | 01/2016 |
549 | 2^863621-113833 | 259976 | Enzo Doria | 10/2014 |
550 | 2^862837+75767 | 259740 | Enzo Doria | 05/2016 |
551 | 2^862637-31 | 259680 | Jorge Menendez | 05/2019 |
552 | 2^862088+1874941 | 259515 | Enzo Doria | 06/2016 |
553 | 2^861987-134557 | 259484 | Hans Havermann | 10/2018 |
554 | 2^861516-1854029 | 259343 | Enzo Doria | 09/2015 |
555 | 2^860975-1853977 | 259180 | Enzo Doria | 09/2015 |
556 | 3^543128+16 | 259138 | Robert Price | 04/2020 |
557 | 2^860625-1858843 | 259074 | Enzo Doria | 10/2015 |
558 | 2^860110+77689 | 258919 | Enzo Doria | 05/2016 |
559 | 2^859600+1880371 | 258766 | Enzo Doria | 10/2016 |
560 | 2^859433+494711 | 258716 | Makoto Morimoto | 10/2013 |
561 | (2^859433-44)/(2^2*3) | 258715 | Makoto Morimoto | 08/2019 |
562 | (2^859433+39899)/(73*3907*46301) | 258705 | Makoto Morimoto | 10/2016 |
563 | 2^859240+1875271 | 258658 | Enzo Doria | 06/2016 |
564 | Tau(971^15738) | 258571 | Nik Lygeros / Olivier Rozier | 05/2015 |
565 | (144^119671+1)/145 | 258292 | Paul Bourdelais | 08/2019 |
566 | (11*2^857159-13)/15 | 258031 | Renaud Lifchitz | 08/2011 |
567 | 2^857016-633113 | 257988 | Enzo Doria | 12/2013 |
568 | 2^855732-113969 | 257602 | Enzo Doria | 10/2014 |
569 | 2^853682-3911 | 256984 | Enzo Doria | 05/2014 |
570 | 11^246668-90 | 256879 | Enzo Doria | 12/2012 |
571 | 2^851904-113939 | 256449 | Enzo Doria | 10/2014 |
572 | 2^851725-851725^2 | 256395 | Henri Lifchitz | 03/2019 |
573 | 11^246167-90 | 256357 | Enzo Doria | 12/2012 |
574 | 2^850700-569049 | 256087 | Enzo Doria | 11/2013 |
575 | 21^193601-20^193601 | 255983 | Jean-Louis Charton | 02/2015 |
576 | (37^163193+1)/38 | 255918 | Paul Bourdelais | 07/2019 |
577 | 2^849177-114025 | 255628 | Enzo Doria | 12/2014 |
578 | 2^848502-3173 | 255425 | Yves Minet | 07/2016 |
579 | 2^848178-140291 | 255328 | Enzo Doria | 01/2014 |
580 | 2^847622-2441 | 255160 | Yves Minet | 02/2016 |
581 | 2^847291+182843 | 255061 | Enzo Doria | 11/2016 |
582 | 2^847174+1879429 | 255025 | Enzo Doria | 09/2016 |
583 | 24*29^174239+13361 | 254809 | Curtis Bright | 04/2015 |
584 | 2^845610-1868591 | 254554 | Enzo Doria | 04/2016 |
585 | 2^845484+81931 | 254517 | Enzo Doria | 08/2016 |
586 | 2^845402-114761 | 254492 | Enzo Doria | 05/2015 |
587 | 2^844334-2792441 | 254170 | Enzo Doria | 02/2016 |
588 | 11^243796-90 | 253888 | Enzo Doria | 12/2012 |
589 | 30^171733-29^171733 | 253671 | Jean-Louis Charton | 10/2018 |
590 | 2^842209+1876037 | 253531 | Enzo Doria | 07/2016 |
591 | 2^842123-59197 | 253505 | Enzo Doria | 10/2015 |
592 | 2^840797-3 | 253106 | Paul Bourdelais | 06/2019 |
593 | 2^840716-2969 | 253081 | Yves Minet | 05/2016 |
594 | 2^840358-462491 | 252973 | Enzo Doria | 08/2015 |
595 | 2^840310+1878379 | 252959 | Enzo Doria | 08/2016 |
596 | 11^242579-60 | 252620 | Enzo Doria | 10/2012 |
597 | 45^152659+2 | 252378 | Robert Price | 09/2015 |
598 | (95^127583+1)/96 | 252322 | Paul Bourdelais | 07/2019 |
599 | 2^837725+1869377 | 252181 | Enzo Doria | 05/2016 |
600 | 2^837536-311039 | 252124 | Enzo Doria | 06/2015 |
601 | 21^190632-2 | 252058 | Robert Price | 07/2015 |
602 | 2^837242+1873297 | 252035 | Enzo Doria | 06/2016 |
603 | 2^836656-2787929 | 251859 | Enzo Doria | 11/2015 |
604 | 2^836380+1875541 | 251776 | Enzo Doria | 07/2016 |
605 | (359^98327-1)/358 | 251233 | Alexander Zhirkov | 11/2017 |
606 | tau(41^28288) | 250924 | Nik Lygeros / Olivier Rozier | 10/2013 |
607 | 2^832511-461197 | 250611 | Enzo Doria | 07/2015 |
608 | 2^832505+1881137 | 250609 | Enzo Doria | 11/2016 |
609 | 2^832363+583295 | 250567 | Enzo Doria | 12/2016 |
610 | 2^832244-403635 | 250531 | Enzo Doria | 01/2014 |
611 | 2^831157+1880657 | 250204 | Enzo Doria | 11/2016 |
612 | 2^831088-7200899 | 250183 | Enzo Doria | 01/2015 |
613 | 2^830956-1349 | 250143 | Yves Minet | 07/2015 |
614 | 2^830037+282317 | 249867 | Enzo Doria | 09/2016 |
615 | 2^829589-113653 | 249732 | Enzo Doria | 09/2014 |
616 | 2^828281-3193 | 249338 | Yves Minet | 08/2016 |
617 | 2^828064-2785619 | 249273 | Enzo Doria | 10/2015 |
618 | 2^827602+60409 | 249134 | Enzo Doria | 03/2016 |
619 | 10^249010+348861 | 249011 | Patrick De Geest | 04/2016 |
620 | 10^249010-21 | 249010 | Serge Batalov | 12/2014 |
621 | 2^826733+1882907 | 248872 | Enzo Doria | 12/2016 |
622 | 2^825682+1876549 | 248556 | Enzo Doria | 07/2016 |
623 | 2^824991-114121 | 248348 | Enzo Doria | 12/2014 |
624 | 2^824642-362727 | 248242 | Enzo Doria | 12/2013 |
625 | 2^824565-114265 | 248219 | Enzo Doria | 01/2015 |
626 | (73*10^248145-1)/9 | 248146 | Robert Price | 01/2015 |
627 | (2^823337+1)/(3*362268281) | 247841 | Gord Palameta | 08/2018 |
628 | (2^822971-1)/6583769/28211445881/21255852651726486149207 | 247700 | Robert Kinser | 09/2016 |
629 | 2^822296+76501 | 247536 | Enzo Doria | 05/2016 |
630 | 2^821590-114167 | 247324 | Enzo Doria | 12/2014 |
631 | 2^821512-2790659 | 247300 | Enzo Doria | 12/2015 |
632 | 2^820077+382847 | 246868 | Enzo Doria | 11/2016 |
633 | 2^820001+81269 | 246845 | Enzo Doria | 07/2016 |
634 | 2^819463-59197 | 246683 | Enzo Doria | 10/2015 |
635 | 2^819296+80581 | 246633 | Enzo Doria | 07/2016 |
636 | 2^817160-350369 | 245990 | Enzo Doria | 06/2015 |
637 | 88093#+(653879#)/(88093#) | 245374 | Makoto Morimoto | 11/2017 |
638 | 2^815111-113857 | 245373 | Enzo Doria | 10/2014 |
639 | 2^814914-4001 | 245314 | Yves Minet | 05/2017 |
640 | 846^83761-845^83761 | 245200 | Jean-Louis Charton | 12/2012 |
641 | 2^814356-2790449 | 245146 | Enzo Doria | 12/2015 |
642 | 2^814276-459029 | 245122 | Enzo Doria | 04/2015 |
643 | 2^814023+180923 | 245046 | Enzo Doria | 07/2016 |
644 | (3^513059-2^513059)/(1026119*5430216457) | 244776 | Mike Oakes | 03/2017 |
645 | 3^513007+16 | 244767 | Robert Price | 04/2020 |
646 | 2^811842-113675 | 244389 | Enzo Doria | 09/2014 |
647 | 2^811132-2787929 | 244176 | Enzo Doria | 11/2015 |
648 | 2^809746-2790971 | 243758 | Enzo Doria | 01/2016 |
649 | 2^808767-3295 | 243464 | Yves Minet | 12/2016 |
650 | 2^808621-113809 | 243420 | Enzo Doria | 09/2014 |
651 | 2^807724+1879621 | 243150 | Enzo Doria | 09/2016 |
652 | 20^186554-3 | 242713 | Paul Bourdelais | 12/2020 |
653 | 2^805843-113611 | 242583 | Enzo Doria | 08/2014 |
654 | 2^805745-459763 | 242554 | Enzo Doria | 05/2015 |
655 | 2^805353+782687 | 242436 | Enzo Doria | 11/2016 |
656 | 2^804277-417933 | 242112 | Enzo Doria | 01/2014 |
657 | 2^803468-269039 | 241868 | Enzo Doria | 10/2013 |
658 | 2^803172+80851 | 241779 | Enzo Doria | 07/2016 |
659 | 3^506233-2 | 241535 | Robert Price | 11/2013 |
660 | 2^802025-25999 | 241434 | Enzo Doria | 10/2013 |
661 | (3^505823+3^252912+1)/7 | 241339 | Serge Batalov | 03/2014 |
662 | 2^801303+1872923 | 241217 | Enzo Doria | 05/2016 |
663 | 2^800579-1862947 | 240999 | Enzo Doria | 12/2015 |
664 | 3^504206+2 | 240568 | Luke W. Richards | 03/2018 |
665 | 2^798973-26283 | 240515 | Enzo Doria | 10/2013 |
666 | 2^798671-69487 | 240424 | Enzo Doria | 12/2015 |
667 | 2^797220+79831 | 239988 | Enzo Doria | 06/2016 |
668 | 2^796910-26001 | 239894 | Enzo Doria | 10/2013 |
669 | 2^796598+653119 | 239800 | Enzo Doria | 12/2016 |
670 | 2^796432-1859729 | 239750 | Enzo Doria | 11/2015 |
671 | 2^796002-1852211 | 239621 | Enzo Doria | 08/2015 |
672 | 2^795709+75767 | 239533 | Enzo Doria | 04/2016 |
673 | 2^795708+81721 | 239532 | Enzo Doria | 08/2016 |
674 | 2^795468-2786249 | 239460 | Enzo Doria | 10/2015 |
675 | 2^795442+80779 | 239452 | Enzo Doria | 07/2016 |
676 | 2^795075-1852057 | 239342 | Enzo Doria | 08/2015 |
677 | (86^123677+1)/87 | 239252 | Paul Bourdelais | 01/2019 |
678 | 2^794043+1875023 | 239031 | Enzo Doria | 06/2016 |
679 | 2^793347-69577 | 238822 | Enzo Doria | 01/2016 |
680 | 2^792988-344429 | 238714 | Enzo Doria | 08/2015 |
681 | 2^792700-2786369 | 238627 | Enzo Doria | 11/2015 |
682 | 2^792663-1844797 | 238616 | Enzo Doria | 06/2015 |
683 | 2^792605-291943 | 238598 | Enzo Doria | 07/2015 |
684 | (2^792061-2^396031+1)/5 | 238434 | Thomas Ritschel | 03/2014 |
685 | 2^789373+1869377 | 237625 | Enzo Doria | 05/2016 |
686 | ((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961 | 237544 | Serge Batalov | 04/2015 |
687 | 2^788942+1866409 | 237496 | Enzo Doria | 02/2016 |
688 | 2^788844-114329 | 237466 | Enzo Doria | 01/2015 |
689 | 2^788705-1859713 | 237424 | Enzo Doria | 11/2015 |
690 | 2^786180+1871971 | 236664 | Enzo Doria | 05/2016 |
691 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
692 | 2^785260+1866361 | 236387 | Enzo Doria | 02/2016 |
693 | 2^785220+1880611 | 236375 | Enzo Doria | 10/2016 |
694 | 19^184650-2 | 236122 | Robert Price | 10/2014 |
695 | 10^236059+216513 | 236060 | Patrick De Geest | 04/2016 |
696 | 10^236059-20909 | 236059 | Robert Price | 09/2015 |
697 | (87^121487-1)/86 | 235625 | Paul Bourdelais | 12/2018 |
698 | 2^782634-113981 | 235597 | Enzo Doria | 11/2014 |
699 | 2^782423+1879733 | 235533 | Enzo Doria | 09/2016 |
700 | 2^781682-2789543 | 235310 | Enzo Doria | 12/2015 |
701 | 2^780408-113453 | 234927 | Enzo Doria | 08/2014 |
702 | 2^780368-1864829 | 234915 | Enzo Doria | 01/2016 |
703 | 2^779593-1836559 | 234681 | Enzo Doria | 05/2015 |
704 | (8713#+(549391#)/(8713#))/360295171 | 234487 | Makoto Morimoto | 11/2017 |
705 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
706 | 2^778395-113617 | 234321 | Enzo Doria | 08/2014 |
707 | 2^776245-2792353 | 233674 | Enzo Doria | 02/2016 |
708 | 2^776060-114029 | 233618 | Enzo Doria | 11/2014 |
709 | 2^775987-2789557 | 233596 | Enzo Doria | 12/2015 |
710 | 2^775672+1866721 | 233501 | Enzo Doria | 03/2016 |
711 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
712 | 2^774118+1885789 | 233033 | Enzo Doria | 04/2017 |
713 | 21^176191-20^176191 | 232964 | Jean-Louis Charton | 01/2015 |
714 | 2^773679-113425 | 232901 | Enzo Doria | 08/2014 |
715 | 10^232599+192489 | 232600 | Patrick De Geest | 12/2013 |
716 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
717 | 2^772552-458879 | 232562 | Enzo Doria | 04/2015 |
718 | 2^772214+1874899 | 232460 | Enzo Doria | 06/2016 |
719 | 2^771994-1862771 | 232394 | Enzo Doria | 12/2015 |
720 | 2^771889+1876037 | 232362 | Enzo Doria | 07/2016 |
721 | 2^771660+1866511 | 232293 | Enzo Doria | 02/2016 |
722 | 5^332150-18188 | 232163 | Enzo Doria | 06/2014 |
723 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
724 | 2^770082-114161 | 231818 | Enzo Doria | 01/2015 |
725 | (20^177967+1)/21 | 231540 | Paul Bourdelais | 05/2013 |
726 | 2^767622-9221 | 231078 | Lelio R Paula | 01/2016 |
727 | 2^767344+1880311 | 230994 | Enzo Doria | 09/2016 |
728 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
729 | (10^230706+179)/9 | 230706 | Serge Batalov | 12/2014 |
730 | 2^766309+1875257 | 230682 | Enzo Doria | 06/2016 |
731 | 2^765635+1879883 | 230480 | Enzo Doria | 09/2016 |
732 | 2^764348-113697 | 230092 | Enzo Doria | 09/2014 |
733 | 2^764131+78863 | 230027 | Enzo Doria | 05/2016 |
734 | 2^763701+60197 | 229897 | Enzo Doria | 03/2016 |
735 | 2^762841-25905 | 229639 | Enzo Doria | 10/2013 |
736 | 2^761117-113569 | 229120 | Enzo Doria | 08/2014 |
737 | (98^114859+1)/99 | 228709 | Paul Bourdelais | 12/2018 |
738 | (2^758231+1)/(3*27146942976539*73236839266867) | 228223 | Gord Palameta | 12/2018 |
739 | 2^757985-2790013 | 228177 | Enzo Doria | 12/2015 |
740 | 2^757038-1862081 | 227892 | Enzo Doria | 12/2015 |
741 | 2^756839+95849 | 227832 | Makoto Morimoto | 10/2013 |
742 | (2^756839+6989)/756091 | 227826 | Makoto Morimoto | 09/2016 |
743 | (2^756839-50211)/(137*3203) | 227826 | Makoto Morimoto | 08/2019 |
744 | 2^756773-112723 | 227812 | Enzo Doria | 07/2014 |
745 | 524309#+616367 | 227431 | Makoto Morimoto | 02/2016 |
746 | 2^755097-114193 | 227307 | Enzo Doria | 12/2014 |
747 | 2^754473-2791513 | 227120 | Enzo Doria | 01/2016 |
748 | 2^751426-764321 | 226202 | Enzo Doria | 12/2013 |
749 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
750 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |