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 ? |
6501 | 10^90209-724797 | 90209 | Patrick De Geest | 07/2019 |
6502 | 10^90208+189531 | 90209 | Patrick De Geest | 07/2019 |
6503 | 10^90208-2247 | 90208 | Patrick De Geest | 09/2018 |
6504 | (629^32233-1)/628 | 90207 | Michael Stocker | 05/2020 |
6505 | 116^43693-115 | 90203 | Norbert Schneider | 08/2018 |
6506 | 10^90202+3553 | 90203 | Patrick De Geest | 09/2018 |
6508 | 3^189053+280 | 90202 | Lelio R Paula | 04/2016 |
6507 | 10^90202-67793 | 90202 | Patrick De Geest | 07/2019 |
6509 | 2^299639-187 | 90201 | Lelio R Paula | 10/2012 |
6510 | 10^90199+254031 | 90200 | Patrick De Geest | 07/2019 |
6511 | 10^90199-2891 | 90199 | Patrick De Geest | 09/2018 |
6513 | 2^299631+183 | 90198 | Lelio R Paula | 10/2012 |
6512 | 21567^15212+15212^21567 | 90198 | Hans Havermann | 08/2020 |
6514 | 10^90196+187539 | 90197 | Patrick De Geest | 07/2019 |
6516 | 10^90196-9683 | 90196 | Patrick De Geest | 09/2018 |
6515 | 21708^14287+14287^21708 | 90196 | Hans Havermann | 08/2020 |
6517 | 10^90193+104973 | 90194 | Patrick De Geest | 07/2019 |
6518 | 10^90193-9809 | 90193 | Patrick De Geest | 09/2018 |
6519 | (21*2^299611-1)/29 | 90192 | Lelio R Paula | 02/2014 |
6520 | (2277^26863-1)/2276 | 90186 | Serge Batalov | 08/2020 |
6521 | 2^299567+113 | 90179 | Lelio R Paula | 10/2012 |
6522 | 2^299550+189 | 90174 | Lelio R Paula | 10/2012 |
6523 | 10^90170+376063 | 90171 | Patrick De Geest | 07/2019 |
6524 | 10^90170-6749 | 90170 | Patrick De Geest | 09/2018 |
6525 | (2^299535+3)/29 | 90168 | Lelio R Paula | 01/2013 |
6526 | (2^299521+13)/15 | 90164 | Stefano Morozzi | 03/2020 |
6527 | 22316^10971+10971^22316 | 90163 | Hans Havermann | 08/2020 |
6528 | 10^90160+271947 | 90161 | Patrick De Geest | 07/2019 |
6529 | 10^90160-5613 | 90160 | Patrick De Geest | 09/2018 |
6530 | (97*10^90155-1)/3 | 90157 | Serge Batalov | 12/2014 |
6532 | 3^188938+8680 | 90147 | Lelio R Paula | 04/2016 |
6531 | 10^90146+160209 | 90147 | Patrick De Geest | 07/2019 |
6533 | 10^90146-2027 | 90146 | Patrick De Geest | 09/2018 |
6534 | 6^115840-55 | 90142 | Lelio R Paula | 05/2016 |
6535 | (5*10^90142-473)/9 | 90142 | Robert Price | 12/2017 |
6536 | 8*7^106659+5 | 90139 | Lelio R Paula | 10/2014 |
6539 | 2^299406-16653 | 90131 | Enzo Doria | 05/2013 |
6537 | (317057^16384+1)/2 | 90131 | Richard Fischer | 10/2019 |
6538 | (2^299409+834)/2 | 90131 | Stefano Morozzi | 01/2020 |
6540 | 10^90128+288673 | 90129 | Patrick De Geest | 07/2019 |
6542 | 208049#+(216091#)/(208049#) | 90128 | Makoto Morimoto | 04/2016 |
6541 | 10^90128-8387 | 90128 | Patrick De Geest | 09/2018 |
6543 | (F(5)^128941-F(4)^128941)/F(3) | 90126 | Wayne Halsdorf | 03/2012 |
6544 | 6^115819-53 | 90125 | Lelio R Paula | 05/2016 |
6545 | 10^90123+6313 | 90124 | Patrick De Geest | 09/2018 |
6547 | 6^115816-16853 | 90123 | Enzo Doria | 02/2013 |
6546 | 10^90123-22617 | 90123 | Patrick De Geest | 07/2019 |
6548 | 6^115813-23 | 90121 | Lelio R Paula | 05/2016 |
6549 | (22*10^90110+161)/3 | 90111 | Robert Price | 02/2017 |
6551 | (2^299330-509203)/69 | 90106 | Lelio R Paula | 01/2013 |
6550 | 10^90105+915759 | 90106 | Patrick De Geest | 07/2019 |
6553 | 10^90105-767 | 90105 | Patrick De Geest | 09/2018 |
6552 | 10^90104+48189 | 90105 | Patrick De Geest | 07/2019 |
6554 | (6050^23827-1)/6049 | 90105 | Serge Batalov | 08/2020 |
6555 | 10^90104-7703 | 90104 | Patrick De Geest | 09/2018 |
6556 | 10^90103+9159 | 90104 | Patrick De Geest | 09/2018 |
6557 | 10^90103-208457 | 90103 | Patrick De Geest | 07/2019 |
6558 | 10^90102+73011 | 90103 | Patrick De Geest | 07/2019 |
6559 | 10^90102-602433 | 90102 | Patrick De Geest | 07/2019 |
6560 | 10^90101+1225537 | 90102 | Patrick De Geest | 07/2019 |
6561 | 10^90101-3207 | 90101 | Patrick De Geest | 09/2018 |
6562 | 21730^14007+14007^21730 | 90101 | Hans Havermann | 08/2020 |
6563 | (29*10^90096-17)/3 | 90097 | Erik Branger | 09/2014 |
6564 | 10^90089+143181 | 90090 | Patrick De Geest | 07/2019 |
6565 | 10^90089-3573 | 90089 | Patrick De Geest | 09/2018 |
6566 | 2^299247+1870529 | 90083 | Enzo Doria | 05/2016 |
6567 | 10^90079+1609 | 90080 | Patrick De Geest | 09/2018 |
6568 | 10^90079-230043 | 90079 | Patrick De Geest | 07/2019 |
6569 | 2^299229-2797783 | 90077 | Enzo Doria | 04/2016 |
6570 | 2^299220-16317 | 90075 | Enzo Doria | 04/2013 |
6571 | 11^86491-1350 | 90072 | Enzo Doria | 12/2012 |
6572 | 10^90071+52333 | 90072 | Patrick De Geest | 07/2019 |
6574 | 10^90071-1233 | 90071 | Patrick De Geest | 09/2018 |
6573 | (314401^16384+1)/2 | 90071 | Richard Fischer | 10/2019 |
6575 | 10^90069+158527 | 90070 | Patrick De Geest | 07/2019 |
6576 | 10^90069-7841 | 90069 | Patrick De Geest | 09/2018 |
6577 | (31*10^90064-1)/3 | 90066 | Robert Price | 03/2017 |
6578 | 10^90060+149431 | 90061 | Patrick De Geest | 07/2019 |
6579 | 10^90060-839 | 90060 | Patrick De Geest | 09/2018 |
6580 | 10^90052+2361 | 90053 | Patrick De Geest | 09/2018 |
6581 | 10^90052-90929 | 90052 | Patrick De Geest | 07/2019 |
6582 | 10^90047+619 | 90048 | Patrick De Geest | 09/2018 |
6583 | 10^90047-151071 | 90047 | Patrick De Geest | 07/2019 |
6584 | L(430949)/861899/1440387561539 | 90045 | Serge Batalov | 07/2017 |
6585 | 22996^8233+8233^22996 | 90043 | Hans Havermann | 08/2020 |
6586 | 2^299112+73951 | 90042 | Enzo Doria | 04/2016 |
6587 | 8^99702+7^(99702-1) | 90040 | Robert Price | 02/2016 |
6588 | 10^90038+157803 | 90039 | Patrick De Geest | 07/2019 |
6589 | 10^90038-9687 | 90038 | Patrick De Geest | 09/2018 |
6591 | 5*10^90033+3 | 90034 | Dmitry Domanov | 11/2010 |
6590 | (17574^21211-1)/17573 | 90034 | Serge Batalov | 08/2020 |
6592 | 10^90030+225813 | 90031 | Patrick De Geest | 07/2019 |
6593 | 10^90030-1461 | 90030 | Patrick De Geest | 09/2018 |
6594 | 243^37738+37738^243 | 90029 | Norbert Schneider | 01/2015 |
6595 | 10^90025+70569 | 90026 | Patrick De Geest | 07/2019 |
6596 | 10^90025-8703 | 90025 | Patrick De Geest | 09/2018 |
6597 | 2^299048-113297 | 90023 | Enzo Doria | 07/2014 |
6598 | 10^90015+849 | 90016 | Patrick De Geest | 09/2018 |
6599 | 10^90015-228387 | 90015 | Patrick De Geest | 07/2019 |
6600 | 10^90010+6811 | 90011 | Patrick De Geest | 09/2018 |
6601 | 10^90010-183597 | 90010 | Patrick De Geest | 11/2018 |
6602 | 10^90009+58321 | 90010 | Patrick De Geest | 11/2018 |
6603 | 10^90008+847 | 90009 | Patrick De Geest | 09/2018 |
6604 | 10^90009-356013 | 90009 | Patrick De Geest | 11/2018 |
6605 | 25696^3183+3183^25696 | 90009 | Hans Havermann | 08/2020 |
6607 | 3^188648+92 | 90008 | Lelio R Paula | 12/2015 |
6606 | 10^90008-706049 | 90008 | Patrick De Geest | 11/2018 |
6608 | 5*2^298991+7 | 90006 | Lelio R Paula | 08/2014 |
6609 | (25*2^298997+1)/3267 | 90005 | Lelio R Paula | 01/2013 |
6610 | 10^90000+8869 | 90001 | Patrick De Geest | 12/2009 |
6612 | 10^89999+82939 | 90000 | Dirk Augustin | 04/2007 |
6611 | 10^90000-140343 | 90000 | Patrick De Geest | 12/2009 |
6613 | 10^89999-194891 | 89999 | Patrick De Geest | 11/2009 |
6614 | (2^298918+1798)/2 | 89983 | Stefano Morozzi | 01/2020 |
6615 | 19^70365-78 | 89980 | Lelio R Paula | 12/2015 |
6616 | NaturalLogarithmOf2(89973) | 89973 | Eric W. Weisstein | 10/2015 |
6617 | 2^298852-64875 | 89964 | Lelio R Paula | 11/2013 |
6618 | (2^298825+1010)/2 | 89955 | Stefano Morozzi | 01/2020 |
6619 | 18^71659+37 | 89952 | Lelio R Paula | 12/2015 |
6620 | (2908*29^61501-3)/7 | 89942 | Curtis Bright | 05/2015 |
6621 | (2^298769+1202)/2 | 89939 | Stefano Morozzi | 01/2020 |
6622 | (5941^23827-1)/5940 | 89916 | Serge Batalov | 08/2020 |
6623 | 17^73067+20 | 89906 | Lelio R Paula | 11/2015 |
6624 | 2^298637-99 | 89899 | Lelio R Paula | 10/2012 |
6625 | 25513^3336+3336^25513 | 89889 | Hans Havermann | 08/2020 |
6626 | 29748^1051+1051^29748 | 89887 | Hans Havermann | 08/2020 |
6627 | 9^94188+3*8^94188-2*4^94188-3*2^94188 | 89879 | Mike Oakes | 01/2011 |
6628 | (2^298558+3654)/2 | 89875 | Stefano Morozzi | 01/2020 |
6629 | 9*10^89858+19 | 89859 | Robert Price | 05/2016 |
6630 | 2^298501+1870067 | 89858 | Enzo Doria | 05/2016 |
6631 | (286*10^89852-1)/3 | 89854 | Robert Price | 11/2020 |
6632 | 11^86280-98 | 89852 | Lelio R Paula | 11/2015 |
6633 | 2^298473-110059 | 89850 | Enzo Doria | 04/2014 |
6634 | 19^70263-32 | 89850 | Lelio R Paula | 12/2015 |
6635 | 21208^17221+17221^21208 | 89839 | Hans Havermann | 08/2020 |
6636 | (299*10^89836-17)/3 | 89838 | Robert Price | 01/2017 |
6637 | 3^188286+14 | 89836 | Robert Price | 09/2013 |
6638 | (2^298408+450)/2 | 89830 | Stefano Morozzi | 01/2020 |
6639 | gcd(V(1091095),5*F(218219)*(F(218219)+1)+1) | 89822 | Serge Batalov | 04/2015 |
6640 | 2^298367+58905 | 89818 | Lelio R Paula | 11/2013 |
6641 | 21966^12269+12269^21966 | 89815 | Hans Havermann | 08/2020 |
6642 | (2^298333+3126)/2 | 89807 | Stefano Morozzi | 01/2020 |
6643 | 2^298319-109657 | 89803 | Enzo Doria | 04/2014 |
6644 | 8*10^89800+81 | 89801 | Robert Price | 05/2017 |
6645 | 21354^16037+16037^21354 | 89797 | Hans Havermann | 08/2020 |
6646 | (2^298249+714)/2 | 89782 | Stefano Morozzi | 01/2020 |
6647 | 21227^16954+16954^21227 | 89775 | Hans Havermann | 08/2020 |
6648 | (733^31333-1)/732 | 89770 | Serge Batalov | 08/2020 |
6651 | 18^71505-91 | 89759 | Lelio R Paula | 12/2015 |
6649 | (2^298171+1586)/2 | 89759 | Stefano Morozzi | 01/2020 |
6650 | (4788^24391-1)/4787 | 89759 | Serge Batalov | 08/2020 |
6652 | (2^298161+3530)/2 | 89756 | Stefano Morozzi | 01/2020 |
6653 | (7^106187+1)/8 | 89738 | Paul Bourdelais | 04/2008 |
6654 | 2^298079-109531 | 89731 | Enzo Doria | 04/2014 |
6655 | (9255^22621-1)/9254 | 89720 | Serge Batalov | 08/2020 |
6656 | 117^43380+116 | 89718 | Norbert Schneider | 08/2018 |
6657 | (22699*2^298016+1)/385 | 89714 | Lelio R Paula | 06/2014 |
6658 | 156*(10^(4*22427)-1)/101-1 | 89709 | Robert Price | 05/2014 |
6659 | 2^298003-66945 | 89708 | Lelio R Paula | 11/2013 |
6660 | (23*10^89705-83)/3 | 89706 | Robert Price | 09/2017 |
6661 | 17^72900-54 | 89700 | Lelio R Paula | 11/2015 |
6662 | (2^297968+2482)/2 | 89698 | Stefano Morozzi | 01/2020 |
6663 | 3*2^297956+5 | 89695 | Lelio R Paula | 08/2014 |
6664 | (2^297952+3558)/2 | 89693 | Stefano Morozzi | 01/2020 |
6665 | (3992^24907-1)/3991 | 89692 | Serge Batalov | 08/2020 |
6666 | 20^68938-11 | 89691 | Lelio R Paula | 01/2016 |
6667 | 89*10^89687-7 | 89689 | Robert Price | 03/2017 |
6668 | (6882^23371-1)/6881 | 89688 | Serge Batalov | 08/2020 |
6669 | (297847^16384+1)/2 | 89686 | Richard Fischer | 08/2019 |
6670 | 2^297923+77783 | 89684 | Enzo Doria | 05/2016 |
6671 | (2^297893+1694)/2 | 89675 | Stefano Morozzi | 01/2020 |
6672 | 11^86107-24576000 | 89672 | Enzo Doria | 02/2013 |
6673 | 2^297878-111911 | 89671 | Enzo Doria | 05/2014 |
6674 | 20823^20236+20236^20823 | 89667 | Hans Havermann | 08/2020 |
6675 | 25708^3075+3075^25708 | 89666 | Hans Havermann | 08/2020 |
6676 | 21002^18585+18585^21002 | 89661 | Hans Havermann | 08/2020 |
6677 | (2^297830+3670)/2 | 89656 | Stefano Morozzi | 01/2020 |
6678 | 7^106084+40 | 89652 | Lelio R Paula | 10/2015 |
6679 | (2^297815+618)/2 | 89651 | Stefano Morozzi | 01/2020 |
6680 | 21223^16752+16752^21223 | 89648 | Hans Havermann | 08/2020 |
6682 | (86*10^89640-311)/9 | 89641 | Robert Price | 10/2017 |
6681 | (2^297781+2094)/2 | 89641 | Stefano Morozzi | 01/2020 |
6683 | (2^297741+3326)/2 | 89629 | Stefano Morozzi | 01/2020 |
6684 | (2^297724+3606)/2 | 89624 | Stefano Morozzi | 01/2020 |
6685 | 3*10^89608-59 | 89609 | Robert Price | 10/2017 |
6686 | (2^297650+3250)/2 | 89602 | Stefano Morozzi | 01/2020 |
6687 | 3^187780-11038 | 89594 | Enzo Doria | 05/2014 |
6688 | (13*2^297560-1)/49151787 | 89568 | Lelio R Paula | 02/2014 |
6689 | 5^128141-36 | 89567 | Lelio R Paula | 10/2015 |
6690 | 4*7^105951+9 | 89540 | Lelio R Paula | 10/2014 |
6691 | (7*10^89539-439)/9 | 89539 | Robert Price | 09/2017 |
6692 | (9772^22441-1)/9771 | 89536 | Serge Batalov | 08/2020 |
6693 | 22823^8374+8374^22823 | 89534 | Hans Havermann | 08/2020 |
6694 | (2^297401+2954)/2 | 89527 | Stefano Morozzi | 01/2020 |
6695 | (2^297403+1670)/2 | 89527 | Stefano Morozzi | 01/2020 |
6696 | 2^297397+177257 | 89526 | Enzo Doria | 05/2016 |
6698 | 2^297346-16241 | 89511 | Enzo Doria | 04/2013 |
6697 | (5*10^89510+79)/3 | 89511 | Robert Price | 11/2017 |
6699 | 4^148663-3^148663 | 89505 | Jean-Louis Charton | 11/2005 |
6700 | 2^297328-869688105 | 89505 | Lelio R Paula | 07/2016 |
6701 | 2^297325-459043 | 89504 | Enzo Doria | 05/2015 |
6702 | 2^297310-112391 | 89500 | Enzo Doria | 06/2014 |
6703 | 2^297296-112157 | 89496 | Enzo Doria | 06/2014 |
6704 | 57^50966-2 | 89490 | Lelio R Paula | 08/2013 |
6705 | (266*10^89482+1)/3 | 89484 | Robert Price | 02/2016 |
6706 | (14*10^89480-101)/3 | 89481 | Robert Price | 04/2017 |
6707 | 2618^26175+26175^2618 | 89466 | Norbert Schneider | 01/2020 |
6708 | (2^297150+3922)/2 | 89451 | Stefano Morozzi | 01/2020 |
6709 | (2^297141+1842)/2 | 89449 | Stefano Morozzi | 01/2020 |
6710 | (2^297140+1458)/2 | 89448 | Stefano Morozzi | 01/2020 |
6711 | (2^297129+726)/2 | 89445 | Stefano Morozzi | 01/2020 |
6712 | 2^297122+99 | 89443 | Lelio R Paula | 10/2012 |
6713 | (3^187435-5)/1286 | 89427 | Lelio R Paula | 01/2013 |
6714 | (28*10^89425+101)/3 | 89426 | Robert Price | 09/2020 |
6715 | (2^297037+3522)/2 | 89417 | Stefano Morozzi | 01/2020 |
6716 | (25*10^89413+161)/3 | 89414 | Robert Price | 01/2017 |
6717 | 29080^1187+1187^29080 | 89406 | Hans Havermann | 08/2020 |
6718 | 2^296990+1870699 | 89403 | Enzo Doria | 05/2016 |
6719 | 2^296972-1017 | 89398 | Lelio R Paula | 11/2013 |
6720 | (7*10^89383+167)/3 | 89384 | Robert Kinser | 10/2017 |
6721 | (85*10^89375-31)/9 | 89376 | Robert Price | 11/2015 |
6722 | 9*2^296870+7 | 89368 | Lelio R Paula | 08/2014 |
6723 | 100^44683-99^44683 | 89366 | Robert Price | 07/2013 |
6724 | 2^296810+76519 | 89349 | Enzo Doria | 05/2016 |
6725 | (2747^25981-1)/2746 | 89342 | Serge Batalov | 08/2020 |
6726 | 8^98928+7^(98928+1) | 89341 | Robert Price | 06/2016 |
6728 | (3^187247+4)/1027 | 89337 | Lelio R Paula | 01/2013 |
6727 | 21832^12359+12359^21832 | 89337 | Hans Havermann | 08/2020 |
6729 | (3^187235-2)/2045 | 89331 | Lelio R Paula | 01/2013 |
6730 | 2^296736-432149 | 89327 | Paul Bourdelais | 05/2013 |
6731 | 2^296737-112519 | 89327 | Enzo Doria | 06/2014 |
6732 | 2^296718-3645 | 89322 | Lelio R Paula | 11/2013 |
6733 | (2^296702+2338)/2 | 89316 | Stefano Morozzi | 01/2020 |
6734 | 2^296681-16221 | 89310 | Enzo Doria | 04/2013 |
6735 | 2^296669-16513 | 89307 | Enzo Doria | 04/2013 |
6736 | (2^296626+1282)/2 | 89294 | Stefano Morozzi | 01/2020 |
6737 | 2^296619-16357 | 89292 | Enzo Doria | 04/2013 |
6738 | 2^296614-110051 | 89290 | Enzo Doria | 04/2014 |
6739 | (2^296601+1730)/2 | 89286 | Stefano Morozzi | 01/2020 |
6740 | (3^187138+8)/83147 | 89283 | Lelio R Paula | 01/2013 |
6741 | (2*10^89279+457)/9 | 89279 | Robert Price | 01/2017 |
6742 | (2^296568+1222)/2 | 89276 | Stefano Morozzi | 01/2020 |
6743 | 15^75907-28 | 89274 | Lelio R Paula | 11/2015 |
6744 | 2^296547-37 | 89270 | Yves Minet | 01/2012 |
6745 | 2^296485+191 | 89251 | Lelio R Paula | 10/2012 |
6746 | 2^296467-75 | 89246 | Lelio R Paula | 10/2012 |
6747 | (2^296462+1674)/2 | 89244 | Stefano Morozzi | 01/2020 |
6748 | 2^296416-109535 | 89231 | Enzo Doria | 04/2014 |
6749 | (23*2^296406+1)/3 | 89228 | Lelio R Paula | 01/2013 |
6750 | 66^49037-65 | 89225 | Norbert Schneider | 11/2014 |