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 ? |
8502 | 3^206977-112756 | 98754 | Enzo Doria | 07/2014 |
8501 | 10^98754-40000000001 | 98754 | Robert Price | 09/2020 |
8503 | 7^116846-50 | 98747 | Lelio R Paula | 08/2016 |
8504 | (19152^23059-1)/19151 | 98740 | Serge Batalov | 06/2022 |
8505 | 23267^17512+17512^23267 | 98730 | Hans Havermann | 04/2020 |
8506 | 2^327967-28635 | 98728 | Lelio R Paula | 08/2016 |
8507 | 707^34642+34642^707 | 98710 | Norbert Schneider | 12/2017 |
8508 | (10771^24481-1)/10770 | 98710 | Serge Batalov | 06/2022 |
8509 | 6^126850-47 | 98709 | Lelio R Paula | 08/2016 |
8510 | (2^327886+2170)/2 | 98704 | Stefano Morozzi | 09/2020 |
8511 | (22*10^98697+47)/3 | 98698 | Robert Price | 06/2021 |
8512 | 8*6^126830-7 | 98694 | Lelio R Paula | 11/2014 |
8513 | 11^94770-270 | 98693 | Enzo Doria | 08/2012 |
8514 | (2^327846+3250)/2 | 98692 | Stefano Morozzi | 01/2021 |
8515 | 2^327832+43 | 98688 | Lelio R Paula | 12/2012 |
8516 | 2^327795+761 | 98677 | Lelio R Paula | 02/2013 |
8517 | (2^327796+1522)/2 | 98677 | Stefano Morozzi | 09/2020 |
8518 | 10^98669+147411 | 98670 | Patrick De Geest | 11/2016 |
8520 | 10^98669-9^(98669-1) | 98669 | Robert Price | 05/2016 |
8519 | 10^98669-105249 | 98669 | Patrick De Geest | 11/2016 |
8521 | (7911^25309-1)/7910 | 98657 | Serge Batalov | 06/2022 |
8522 | 2^327671-109801 | 98639 | Enzo Doria | 04/2014 |
8523 | 24398^11037+11037^24398 | 98638 | Hans Havermann | 10/2019 |
8524 | 5^141090-14 | 98618 | Lelio R Paula | 08/2016 |
8525 | 20^75799+47 | 98617 | Lelio R Paula | 08/2016 |
8526 | (5452^26393-1)/5451 | 98616 | Serge Batalov | 06/2022 |
8527 | 28101^3226+3226^28101 | 98597 | Hans Havermann | 07/2020 |
8528 | 2^327515-1017 | 98592 | Lelio R Paula | 08/2016 |
8529 | 6^126692+97681 | 98586 | Mike Oakes | 04/2011 |
8530 | 2^327467-741 | 98578 | Lelio R Paula | 08/2016 |
8531 | (2947^28411-1)/2946 | 98566 | Serge Batalov | 06/2022 |
8532 | 22713^21800+21800^22713 | 98540 | Hans Havermann | 05/2020 |
8533 | (2^327329+9)/19 | 98535 | Lelio R Paula | 10/2013 |
8534 | 7^116577-66 | 98519 | Lelio R Paula | 08/2016 |
8535 | (3*2^327250+1)/7 | 98512 | Lelio R Paula | 11/2013 |
8536 | 23220^17479+17479^23220 | 98512 | Hans Havermann | 03/2020 |
8537 | (2^327240+3798)/2 | 98509 | Stefano Morozzi | 02/2021 |
8538 | (28514^22111-1)/28513 | 98502 | Serge Batalov | 06/2022 |
8539 | (19*2^327192+1)/275 | 98494 | Lelio R Paula | 11/2013 |
8540 | 2^327162-66945 | 98486 | Lelio R Paula | 08/2016 |
8541 | 30139^1852+1852^30139 | 98484 | Hans Havermann | 02/2020 |
8542 | 23182^17703+17703^23182 | 98479 | Hans Havermann | 01/2020 |
8543 | 4*10^98472-3 | 98473 | Erik Branger | 11/2013 |
8544 | 26167^5794+5794^26167 | 98466 | Hans Havermann | 01/2020 |
8545 | (6883*2^327047-1)/77 | 98453 | Lelio R Paula | 05/2015 |
8546 | (71*10^98446+1)/9 | 98447 | Serge Batalov | 11/2010 |
8547 | (2009^29803-1)/2008 | 98436 | Serge Batalov | 06/2022 |
8548 | 13^88363+94 | 98432 | Lelio R Paula | 08/2016 |
8549 | 48^58543-47^58543 | 98425 | Jean-Louis Charton | 11/2005 |
8550 | 6^126481+41 | 98422 | Lelio R Paula | 08/2016 |
8551 | 78*10^98413-7 | 98415 | Robert Price | 05/2017 |
8552 | 22634^22263+22263^22634 | 98404 | Hans Havermann | 07/2020 |
8553 | (47*10^98386+241)/9 | 98387 | Robert Price | 06/2022 |
8554 | 7^116416+46 | 98383 | Lelio R Paula | 08/2016 |
8555 | 7^116407-24 | 98376 | Lelio R Paula | 07/2016 |
8556 | 439^37228+37228^439 | 98374 | Norbert Schneider | 08/2018 |
8557 | 2^326782-1860671 | 98372 | Enzo Doria | 03/2016 |
8558 | 17^79948+58 | 98372 | Lelio R Paula | 08/2016 |
8559 | 22499^22602-22602^22499 | 98368 | Norbert Schneider | 08/2020 |
8560 | 3^206143-98 | 98356 | Lelio R Paula | 08/2016 |
8561 | 8*5^140705+7 | 98350 | Lelio R Paula | 11/2014 |
8562 | (2^326632+1662)/2 | 98326 | Stefano Morozzi | 09/2020 |
8563 | (638^35053-1)/637 | 98315 | Serge Batalov | 06/2022 |
8564 | 2^326585+11 | 98312 | Lelio R Paula | 12/2012 |
8565 | 2^326582-459161 | 98311 | Enzo Doria | 05/2015 |
8566 | (1266^31687-1)/1265 | 98304 | Serge Batalov | 06/2022 |
8568 | (2^326548+9)/5 | 98301 | Lelio R Paula | 10/2013 |
8567 | (2^326549+18)/10 | 98301 | Stefano Morozzi | 03/2020 |
8569 | 2^326538+71659 | 98298 | Enzo Doria | 04/2016 |
8570 | (2^326520+2082)/2 | 98293 | Stefano Morozzi | 09/2020 |
8571 | (2^326521+1002)/2 | 98293 | Stefano Morozzi | 09/2020 |
8572 | 15^83575-58 | 98292 | Lelio R Paula | 08/2016 |
8573 | 10^98288+3 | 98289 | Robert Price | 03/2011 |
8574 | 10^98288-117017 | 98288 | Patrick De Geest | 11/2011 |
8575 | (44*10^98284-719)/9 | 98285 | Robert Price | 12/2017 |
8576 | (5985^26021-1)/5984 | 98280 | Serge Batalov | 06/2022 |
8577 | 23466^15419+15419^23466 | 98277 | Hans Havermann | 02/2020 |
8578 | 2^326421-2797573 | 98263 | Enzo Doria | 04/2016 |
8579 | 2^326401+16095 | 98257 | Lelio R Paula | 07/2016 |
8580 | (6494^25771-1)/6493 | 98249 | Serge Batalov | 06/2022 |
8581 | 7^116240-116240^7 | 98235 | Norbert Schneider | 05/2017 |
8582 | 17^79826-78 | 98222 | Lelio R Paula | 08/2016 |
8583 | 2^326268-809 | 98217 | Yves Minet | 04/2011 |
8584 | 22659^21590+21590^22659 | 98210 | Hans Havermann | 10/2019 |
8585 | 22268^22587-22587^22268 | 98202 | Norbert Schneider | 08/2020 |
8586 | (418*10^98199+23)/9 | 98201 | Robert Price | 08/2017 |
8587 | 12*10^98198-7 | 98200 | Robert Price | 11/2017 |
8588 | 15^83496-76 | 98199 | Lelio R Paula | 08/2016 |
8589 | (10223*2^326179+1)/6125 | 98190 | Lelio R Paula | 07/2014 |
8590 | 9*5^140471-4 | 98186 | Lelio R Paula | 11/2014 |
8591 | (35103^21601-1)/35102 | 98180 | Serge Batalov | 06/2022 |
8593 | 22774^20455+20455^22774 | 98175 | Hans Havermann | 07/2020 |
8592 | (4516^26863-1)/4515 | 98175 | Serge Batalov | 06/2022 |
8594 | 2^326069-2383 | 98157 | Yves Minet | 10/2013 |
8595 | (9661^24631-1)/9660 | 98152 | Serge Batalov | 06/2022 |
8596 | (4175^27109-1)/4174 | 98149 | Serge Batalov | 06/2022 |
8597 | (57801^20611-1)/57800 | 98144 | Serge Batalov | 06/2022 |
8598 | 2^325973+1185 | 98128 | Lelio R Paula | 07/2016 |
8599 | (25*2^325949-1)/17 | 98121 | Lelio R Paula | 02/2014 |
8600 | 2^325945-1847269 | 98120 | Enzo Doria | 07/2015 |
8601 | 8*10^98111-67 | 98112 | Robert Price | 10/2017 |
8602 | (2^325902+1138)/2 | 98106 | Stefano Morozzi | 09/2020 |
8603 | (215^42061-1)/214 | 98103 | Serge Batalov | 06/2022 |
8604 | (6775^25609-1)/6774 | 98102 | Serge Batalov | 06/2022 |
8605 | (6718^25633-1)/6717 | 98100 | Serge Batalov | 06/2022 |
8606 | 2^325866+15 | 98096 | Lelio R Paula | 12/2012 |
8607 | 22591^21952+21952^22591 | 98079 | Hans Havermann | 02/2020 |
8608 | 2^325765+1974305 | 98066 | Enzo Doria | 06/2016 |
8609 | 2^325733-58695 | 98056 | Lelio R Paula | 07/2016 |
8610 | (7*10^98055-529)/9 | 98055 | Robert Price | 08/2021 |
8611 | 2^325717-3645 | 98051 | Lelio R Paula | 07/2016 |
8612 | (2^325704+718)/2 | 98047 | Stefano Morozzi | 09/2020 |
8613 | (15679^23371-1)/15678 | 98045 | Serge Batalov | 06/2022 |
8614 | (23342^22441-1)/23341 | 98022 | Serge Batalov | 06/2022 |
8615 | 23968^12293+12293^23968 | 98021 | Hans Havermann | 11/2019 |
8616 | (23*2^325583-1)/21 | 98011 | Lelio R Paula | 02/2014 |
8617 | (7*10^98007-13)/3 | 98008 | Robert Price | 06/2016 |
8618 | (2^325544+1110)/2 | 97999 | Stefano Morozzi | 09/2020 |
8619 | 2^325512-459959 | 97989 | Enzo Doria | 05/2015 |
8620 | (2^325492+682)/2 | 97983 | Stefano Morozzi | 09/2020 |
8621 | (3^205354-8)/17 | 97978 | Lelio R Paula | 09/2013 |
8622 | 2^325433+76817 | 97966 | Enzo Doria | 05/2016 |
8623 | 5*10^97963+81 | 97964 | Robert Price | 08/2017 |
8624 | (13208^23773-1)/13207 | 97961 | Serge Batalov | 06/2022 |
8625 | 2^325390-109061 | 97953 | Enzo Doria | 04/2014 |
8626 | (55*10^97940+323)/9 | 97941 | Robert Price | 10/2021 |
8627 | 13^87921+24 | 97940 | Lelio R Paula | 08/2016 |
8628 | 10^97930+188277 | 97931 | Patrick De Geest | 09/2022 |
8630 | 10^97930-7000001 | 97930 | Robert Price | 06/2021 |
8629 | 10^97930-66951 | 97930 | Patrick De Geest | 09/2022 |
8631 | 961^32831-960^32831 | 97926 | Jean-Louis Charton | 02/2011 |
8632 | (17968^23017-1)/17967 | 97922 | Serge Batalov | 06/2022 |
8633 | (3337^27793-1)/3336 | 97922 | Serge Batalov | 06/2022 |
8635 | 22600^21499+21499^22600 | 97913 | Hans Havermann | 05/2020 |
8634 | (18703^22921-1)/18702 | 97913 | Serge Batalov | 06/2022 |
8636 | 2^325215+12909 | 97900 | Lelio R Paula | 07/2016 |
8637 | 22619^21286+21286^22619 | 97898 | Hans Havermann | 04/2020 |
8638 | (85*10^97876-49)/9 | 97877 | Robert Price | 12/2020 |
8639 | 7*10^97874-69 | 97875 | Robert Price | 01/2017 |
8640 | 5*10^97869-63 | 97870 | Robert Price | 04/2021 |
8642 | (17^79537+5^79537)/22 | 97865 | Robert Price | 06/2013 |
8641 | 15^83212+22 | 97865 | Lelio R Paula | 08/2016 |
8643 | 2^325087-109057 | 97861 | Enzo Doria | 04/2014 |
8644 | 2^325074+1870657 | 97858 | Enzo Doria | 05/2016 |
8646 | 2^325066-2111 | 97855 | Yves Minet | 08/2013 |
8645 | CopelandErdos(97855) | 97855 | Eric W. Weisstein | 10/2015 |
8647 | (8694^24841-1)/8693 | 97851 | Serge Batalov | 06/2022 |
8648 | (21159^22621-1)/21158 | 97843 | Serge Batalov | 06/2022 |
8649 | 26660^4677+4677^26660 | 97842 | Hans Havermann | 12/2019 |
8650 | 18^77944-89 | 97841 | Lelio R Paula | 07/2016 |
8651 | 119^47136+118 | 97833 | Norbert Schneider | 09/2018 |
8652 | 6^125720-17663 | 97830 | Enzo Doria | 02/2013 |
8653 | (73640^20101-1)/73639 | 97829 | Serge Batalov | 06/2022 |
8654 | 2^324972-2069 | 97827 | Yves Minet | 05/2013 |
8655 | 2^324958-4691 | 97823 | Yves Minet | 05/2019 |
8656 | (8087^25033-1)/8086 | 97820 | Serge Batalov | 06/2022 |
8657 | 2^324944-2788319 | 97818 | Enzo Doria | 03/2016 |
8658 | 22845^19112+19112^22845 | 97807 | Hans Havermann | 10/2019 |
8659 | (2^324898+1270)/2 | 97804 | Stefano Morozzi | 09/2020 |
8661 | 4*10^97799-9 | 97800 | Erik Branger | 11/2013 |
8660 | 2^324882+577294575 | 97800 | Lelio R Paula | 09/2016 |
8662 | 2^324863-1867921 | 97794 | Enzo Doria | 04/2016 |
8663 | 6^125662-18473 | 97785 | Enzo Doria | 03/2013 |
8664 | 12^90604+11 | 97779 | Lelio R Paula | 07/2016 |
8665 | (29*10^97751+49)/3 | 97752 | Robert Price | 09/2021 |
8666 | (37108^21391-1)/37107 | 97741 | Serge Batalov | 06/2022 |
8667 | 5^139830+24 | 97737 | Lelio R Paula | 04/2016 |
8668 | (2^324672+1198)/2 | 97736 | Stefano Morozzi | 09/2020 |
8669 | (101*10^97724+7)/9 | 97726 | Robert Price | 02/2022 |
8670 | 2^324612+1155 | 97718 | Lelio R Paula | 07/2016 |
8671 | (2^324597+3542)/2 | 97714 | Stefano Morozzi | 09/2020 |
8672 | 19^76404-44 | 97702 | Lelio R Paula | 07/2016 |
8673 | (5939^25889-1)/5938 | 97694 | Serge Batalov | 06/2022 |
8675 | 2^324505-2983 | 97686 | Yves Minet | 04/2011 |
8674 | (7740^25121-1)/7739 | 97686 | Serge Batalov | 06/2022 |
8676 | (144^45259+1)/145 | 97684 | Paul Bourdelais | 08/2019 |
8677 | (31*2^324496-1)/45 | 97683 | Lelio R Paula | 02/2014 |
8678 | (11234^24109-1)/11233 | 97651 | Serge Batalov | 06/2022 |
8679 | 6^125488-17843 | 97649 | Enzo Doria | 02/2013 |
8680 | (2^324350+3198)/2 | 97639 | Stefano Morozzi | 09/2020 |
8681 | (75638^20011-1)/75637 | 97624 | Serge Batalov | 06/2022 |
8682 | 7^115515-2 | 97622 | Lelio R Paula | 09/2013 |
8683 | (15672^23269-1)/15671 | 97613 | Serge Batalov | 06/2022 |
8684 | (89^50069-1)/88 | 97603 | Paul Bourdelais | 08/2017 |
8685 | 6^125418-5 | 97595 | Lelio R Paula | 11/2014 |
8686 | (2^324193+3522)/2 | 97592 | Stefano Morozzi | 09/2020 |
8687 | (2422^28837-1)/2421 | 97587 | Serge Batalov | 06/2022 |
8688 | (2^324172+666)/2 | 97586 | Stefano Morozzi | 09/2020 |
8689 | 2^324091+111546435 | 97562 | Paul Bourdelais | 10/2021 |
8690 | 2^324076+1155 | 97557 | Lelio R Paula | 07/2016 |
8691 | (2^324074+9)/13 | 97555 | Lelio R Paula | 10/2013 |
8692 | (11*10^97539-71)/3 | 97540 | Robert Price | 04/2022 |
8693 | (55459*2^323993+1)/21 | 97536 | Lelio R Paula | 07/2014 |
8694 | 13^87557-12^87557 | 97534 | Jean-Louis Charton | 12/2008 |
8695 | 2^323946+73939 | 97518 | Enzo Doria | 04/2016 |
8696 | 2^323937+1866947 | 97515 | Enzo Doria | 03/2016 |
8697 | (98339^19531-1)/98338 | 97508 | Serge Batalov | 06/2022 |
8699 | 6^125290-18533 | 97495 | Enzo Doria | 03/2013 |
8698 | (2^323870+1650)/2 | 97495 | Stefano Morozzi | 09/2020 |
8700 | 2^323845+101 | 97488 | Lelio R Paula | 12/2012 |
8701 | 18^77662+65 | 97487 | Lelio R Paula | 07/2016 |
8702 | 22634^20265+20265^22634 | 97479 | Hans Havermann | 04/2020 |
8703 | (5533^26041-1)/5532 | 97467 | Serge Batalov | 06/2022 |
8704 | 2^323772+76771 | 97466 | Enzo Doria | 05/2016 |
8705 | 2^323765-112213 | 97463 | Enzo Doria | 06/2014 |
8706 | 22730^19389+19389^22730 | 97457 | Hans Havermann | 02/2020 |
8707 | 2^323720-6555 | 97450 | Lelio R Paula | 07/2016 |
8708 | 2^323694-1860401 | 97442 | Enzo Doria | 03/2016 |
8709 | 20^74886+3 | 97429 | Lelio R Paula | 06/2016 |
8710 | 24476^9561+9561^24476 | 97427 | Hans Havermann | 01/2020 |
8711 | (2^323623+1766)/2 | 97420 | Stefano Morozzi | 09/2020 |
8712 | (3250^27739-1)/3249 | 97413 | Serge Batalov | 06/2022 |
8714 | 3*10^97399+73 | 97400 | Robert Price | 04/2016 |
8713 | 7^115252-50 | 97400 | Lelio R Paula | 07/2016 |
8715 | (4715^26513-1)/4714 | 97392 | Serge Batalov | 06/2022 |
8716 | 224737#+393581 | 97389 | Nicolas PALAU | 12/2016 |
8717 | (2^323468+3186)/2 | 97374 | Stefano Morozzi | 09/2020 |
8718 | (2^323456+538)/2 | 97370 | Stefano Morozzi | 09/2020 |
8719 | 23277^15236+15236^23277 | 97365 | Hans Havermann | 07/2020 |
8721 | (26*10^97353+31)/3 | 97354 | Robert Price | 07/2016 |
8720 | (2^323403+3510)/2 | 97354 | Stefano Morozzi | 09/2020 |
8722 | 23756^12519+12519^23756 | 97342 | Hans Havermann | 07/2020 |
8723 | 10^97335+271641 | 97336 | Patrick De Geest | 09/2022 |
8725 | 10^97335-4000001 | 97335 | Robert Price | 07/2021 |
8724 | 10^97335-98193 | 97335 | Patrick De Geest | 09/2022 |
8726 | (637*10^97331+11)/9 | 97333 | Robert Price | 10/2021 |
8727 | 23991^11402+11402^23991 | 97332 | Hans Havermann | 07/2020 |
8728 | 61^54517-60^54517 | 97331 | Jean-Louis Charton | 09/2005 |
8729 | (38*10^97329+187)/9 | 97330 | Robert Price | 11/2017 |
8730 | (31147^21661-1)/31146 | 97328 | Serge Batalov | 06/2022 |
8731 | 86455!4+8 | 97319 | Robert Price | 09/2019 |
8732 | 22591^20310+20310^22591 | 97316 | Hans Havermann | 06/2020 |
8733 | 2^323261-431173 | 97312 | Harrison Mesh | 06/2022 |
8734 | (3996^27017-1)/3995 | 97302 | Serge Batalov | 06/2022 |
8735 | 25101^7520+7520^25101 | 97297 | Hans Havermann | 05/2020 |
8736 | (233*10^97294+7)/3 | 97296 | Robert Price | 03/2022 |
8737 | p(19982)#/2-1024 | 97293 | Robert Price | 09/2017 |
8738 | (65*10^97288+277)/9 | 97289 | Robert Price | 08/2021 |
8739 | 6^125021-85 | 97286 | Lelio R Paula | 08/2016 |
8740 | 2^323164-47355 | 97283 | Lelio R Paula | 07/2016 |
8741 | (3^203902+4)/36051015157 | 97276 | Lelio R Paula | 09/2013 |
8742 | 2^323054-6555 | 97249 | Lelio R Paula | 07/2016 |
8743 | 22822^18247+18247^22822 | 97249 | Hans Havermann | 02/2020 |
8744 | 9*10^97247-29 | 97248 | Robert Price | 05/2017 |
8745 | 24382^9735+9735^24382 | 97244 | Hans Havermann | 02/2020 |
8746 | (31*10^97242+41)/9 | 97243 | Robert Price | 04/2015 |
8747 | GoldenRatioPrime[97241] | 97241 | Eric W. Weisstein | 06/2009 |
8748 | 12^90098-41 | 97233 | Lelio R Paula | 07/2016 |
8749 | 2^322928-216929 | 97212 | Enzo Doria | 05/2014 |
8750 | (16731^23017-1)/16730 | 97209 | Serge Batalov | 06/2022 |