## PRP Records

### Probable Primes Top 10000

#### (295756 PRPs in the top)

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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See the Latest PRPs
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 1-250 251-500 501-750 751-1000 1001-1250 1251-1500 1501-1750 1751-2000 2001-2250 2251-2500 2501-2750 2751-3000 3001-3250 3251-3500 3501-3750 3751-4000 4001-4250 4251-4500 4501-4750 4751-5000 5001-5250 5251-5500 5501-5750 5751-6000 6001-6250 6251-6500 6501-6750 6751-7000 7001-7250 7251-7500 7501-7750 7751-8000 8001-8250 8251-8500 8501-8750 8751-9000 9001-9250 9251-9500 9501-9750 9751-10000

 Rank Probable prime Digits (> 50000) Who ? When ? 5501 26603^26888-26888^26603 118978 Norbert Schneider 07/2021 5502 6*10^118964+43 118965 Robert Price 07/2020 5503 (8*10^118960+49)/3 118961 Robert Price 05/2020 5504 31253^6402+6402^31253 118959 Hans Havermann 02/2021 5505 (194*10^118925-17)/3 118927 Robert Price 09/2020 5506 2^395062-109121 118926 Enzo Doria 04/2014 5507 2^395055-4627 118924 Yves Minet 05/2019 5508 (2^395054+702)/2 118923 Stefano Morozzi 09/2020 5509 2^395018-224141 118913 Harrison Mesh 06/2022 5510 (2^395011+2526)/2 118910 Stefano Morozzi 09/2020 5511 (2^394918+78557)/3 118882 Lelio R Paula 01/2015 5512 25771^26948-26948^25771 118872 Frank Doornink 02/2024 5513 (2^394858+1018)/2 118864 Stefano Morozzi 09/2020 5514 (77*10^118862-149)/9 118863 Robert Price 03/2022 5515 (16*10^118852+77)/3 118853 Robert Price 03/2019 5516 fibonacci(568658)-2 118843 Jon Grantham 08/2023 5517 (2^394739+3)/1883 118826 Lelio R Paula 04/2014 5518 10^118772+163599 118773 Patrick De Geest 02/2021 5520 10^118772-40000000001 118772 Robert Price 09/2020 5519 10^118772-207603 118772 Patrick De Geest 02/2021 5521 26842^26577+26577^26842 118763 Hans Havermann 02/2021 5522 (2^394513+2034)/2 118760 Stefano Morozzi 09/2020 5523 (2^394473+2774)/2 118748 Stefano Morozzi 02/2021 5524 27949^17710+17710^27949 118734 Hans Havermann 02/2021 5525 2^394266+71389 118686 Enzo Doria 04/2016 5526 (10^118681-3^118681)/7 118681 Jon Grantham 08/2023 5527 2^394215-51261 118671 Tony Prest / Never Odd Or Even 04/2018 5528 (2^394215-48793)/5/5 118670 Tony Prest / Never Odd Or Even 04/2018 5529 (2^394215-17063)/3/3/5 118669 Tony Prest / Never Odd Or Even 04/2018 5530 (2^394215-24393)/5/5/5/5/5 118668 Tony Prest / Never Odd Or Even 04/2018 5531 (2^394215-35885)/3/71/173 118666 Tony Prest / Never Odd Or Even 04/2018 5532 (2^394215-47925)/353/2269 118665 Tony Prest / Never Odd Or Even 04/2018 5533 29201^11568+11568^29201 118652 Hans Havermann 02/2021 5534 (2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673 118650 Tony Prest / Never Odd Or Even 04/2018 5535 (2^394131+2214)/2 118645 Stefano Morozzi 09/2020 5536 (17*10^118635+13)/3 118636 Robert Price 01/2019 5537 5^169727+2 118635 Lelio R Paula 08/2013 5538 2^394034-3 118617 M. Frind & P. Underwood 09/2002 5539 (7*10^118607+179)/3 118608 Robert Price 09/2018 5540 3^248572-6242 118599 Enzo Doria 05/2014 5541 (3*2^393964-1)/181 118594 Lelio R Paula 04/2014 5542 (49*10^118576-319)/9 118577 Robert Price 10/2021 5543 7^140303-6 118570 Robert Price 11/2014 5544 (2^393864+2686)/2 118565 Stefano Morozzi 09/2020 5545 (2^393862+3150)/2 118564 Stefano Morozzi 09/2020 5546 (2^393849+3762)/2 118561 Stefano Morozzi 01/2021 5547 (529*10^118554-7)/9 118556 Robert Price 08/2021 5548 26712^26777-26777^26712 118534 Norbert Schneider 07/2021 5549 (2^393661+2666)/2 118504 Stefano Morozzi 09/2020 5550 (2^393650+1614)/2 118501 Stefano Morozzi 09/2020 5551 27655^19264+19264^27655 118495 Hans Havermann 02/2021 5552 10^118485+469413 118486 Patrick De Geest 05/2021 5553 10^118485-50001 118485 Robert Price 08/2020 5554 (2^393528+1030)/2 118464 Stefano Morozzi 09/2020 5555 2^393427+75683 118434 Enzo Doria 04/2016 5556 2^393376-114749 118418 Enzo Doria 04/2015 5557 (65*10^118417+493)/9 118418 Robert Price 08/2021 5558 30960^6671+6671^30960 118397 Hans Havermann 02/2021 5559 (2^393234+2010)/2 118375 Stefano Morozzi 09/2020 5560 (2^393205+3030)/2 118367 Stefano Morozzi 09/2020 5561 (2^393191+2174)/2 118362 Stefano Morozzi 09/2020 5562 2^393180+73 118359 Lelio R Paula 04/2013 5563 3*2^393125+5 118343 Jon Grantham 07/2023 5564 27546^19771+19771^27546 118339 Hans Havermann 02/2021 5565 p(23881)#/2+256 118328 Robert Price 05/2017 5566 (10^118324+359)/9 118324 Serge Batalov 12/2014 5567 (2^393048+570)/2 118319 Stefano Morozzi 09/2020 5568 p(23879)#/2+64 118317 Robert Price 03/2017 5569 2^393033+20147 118315 Enzo Doria 08/2023 5570 8*10^118308+59 118309 Robert Price 11/2021 5571 9*10^118282+29 118283 Robert Price 03/2022 5572 (238*10^118265-1)/3 118267 Robert Price 04/2020 5574 (53*10^118216+1)/9 118217 Serge Batalov 11/2010 5573 (2^392707+1710)/2 118217 Stefano Morozzi 09/2020 5575 (7*2^392697+1)/15 118214 Renaud Lifchitz 03/2011 5576 (157^53819-1)/156 118179 Alexander Zhirkov 06/2016 5577 (2^392567+2750)/2 118175 Stefano Morozzi 01/2021 5578 55*10^118172+3 118174 Robert Price 07/2022 5579 (19*2^392551+1)/3 118171 Lelio R Paula 04/2014 5580 27185^22222+22222^27185 118168 Hans Havermann 01/2021 5581 2^392516-29219 118160 Enzo Doria 07/2015 5582 66*10^118155+7 118157 Robert Price 07/2020 5583 Phi(177231,10) 118152 Maksym Voznyy 09/2015 5584 2^392413-112123 118129 Enzo Doria 06/2014 5585 27491^19798+19798^27491 118119 Hans Havermann 02/2021 5586 (49*10^118109-319)/9 118110 Robert Price 10/2021 5587 (2^392342+5)/27 118106 Lelio R Paula 04/2014 5588 (2^392333+1782)/2 118104 Stefano Morozzi 01/2021 5589 2^392300-1841429 118095 Enzo Doria 06/2015 5590 3*2^392260-5 118083 Jon Grantham 07/2023 5591 2^392220+75241 118070 Enzo Doria 04/2016 5592 27836^17409+17409^27836 118047 Hans Havermann 02/2021 5593 10^118009+664447 118010 Patrick De Geest 07/2018 5594 10^118009-20001 118009 Robert Price 01/2018 5595 (14*10^117991+61)/3 117992 Robert Price 12/2018 5596 2^391933+5897 117984 Yves Minet 02/2011 5597 2^391912-1849259 117978 Enzo Doria 08/2015 5598 (2*34^77029+1043)/11 117968 Eric Chen 08/2023 5599 5*2^391836-3 117956 Jon Grantham 07/2023 5600 28357^14440+14440^28357 117953 Hans Havermann 02/2021 5601 (2^391812+5)/14181 117944 Lelio R Paula 04/2014 5602 (7*10^117930-79)/9 117930 Robert Price 01/2021 5603 27531^19168+19168^27531 117904 Hans Havermann 02/2021 5604 (46*10^117902+683)/9 117903 Robert Price 03/2019 5605 26349^26668-26668^26349 117893 Frank Doornink 03/2024 5606 27670^18189+18189^27670 117869 Hans Havermann 02/2021 5607 (7*2^391521+1)/285 117858 Lelio R Paula 04/2014 5608 (56*10^117856+583)/9 117857 Robert Price 08/2021 5609 32169^4606+4606^32169 117846 Hans Havermann 02/2021 5610 (71*10^117803-143)/9 117804 Robert Price 10/2021 5611 2^391324+90901 117801 Yves Minet 02/2011 5612 2^391301-1859923 117794 Enzo Doria 03/2016 5613 2^391261-4131 117782 Yves Minet 02/2018 5614 (2^391211+554)/2 117766 Stefano Morozzi 09/2020 5615 38434^1157+1157^38434 117737 Hans Havermann 01/2021 5616 (2^391115-7)/11791 117734 Lelio R Paula 04/2014 5617 (85*10^117719+473)/9 117720 Robert Price 01/2020 5618 (2^391049+582)/2 117718 Stefano Morozzi 09/2020 5619 (21*23^86445-197)/22 117715 Eric Chen 08/2023 5620 31083^6122+6122^31083 117709 Hans Havermann 02/2021 5621 2^390960+1880881 117691 Enzo Doria 11/2016 5622 (71*10^117685+91)/9 117686 Robert Price 04/2022 5624 2^390897-1860553 117672 Enzo Doria 11/2015 5623 (61*10^117671+47)/9 117672 Robert Price 07/2022 5625 2^390889-115003 117670 Enzo Doria 06/2015 5626 12^109010+35 117642 Riley Fisher 08/2023 5627 2^390779-30337 117637 Paul Bourdelais 02/2012 5628 (2^390735+378)/2 117623 Stefano Morozzi 02/2021 5629 11^112916-780 117590 Enzo Doria 12/2012 5630 27641^17916+17916^27641 117564 Hans Havermann 02/2021 5631 27906^16321+16321^27906 117561 Hans Havermann 02/2021 5632 27294^20275+20275^27294 117555 Hans Havermann 02/2021 5633 (2^390473+1002)/2 117544 Stefano Morozzi 09/2020 5634 35912^1875+1875^35912 117541 Hans Havermann 02/2021 5635 (16^97613-5^97613)/11 117537 Robert Price 07/2013 5636 (2^390438+1774)/2 117534 Stefano Morozzi 01/2021 5637 (2^390418+1722)/2 117528 Stefano Morozzi 09/2020 5638 (2^390403+654)/2 117523 Stefano Morozzi 09/2020 5639 (2^390343+2246)/2 117505 Stefano Morozzi 01/2021 5640 28043^15478+15478^28043 117493 Hans Havermann 02/2021 5641 (17*2^390272+1)/1983 117482 Lelio R Paula 04/2014 5642 37077^1474+1474^37077 117479 Hans Havermann 01/2021 5643 31^78759-30 117459 Theodore Burton 02/2007 5644 (2^390176+1222)/2 117455 Stefano Morozzi 09/2020 5645 (2^390133+1242)/2 117442 Stefano Morozzi 09/2020 5646 (2^390013+2634)/2 117406 Stefano Morozzi 09/2020 5647 3*10^117402+61 117403 Robert Price 09/2020 5648 2^389998+37 117402 Lelio R Paula 03/2013 5649 (2^389977+314)/2 117395 Stefano Morozzi 09/2020 5650 (2^389921+342)/2 117378 Stefano Morozzi 01/2021 5651 71830^43+43^71830 117333 Hans Havermann 01/2021 5652 (2^389768+1582)/2 117332 Stefano Morozzi 09/2020 5653 33802^2951+2951^33802 117292 Hans Havermann 02/2021 5654 26789^23866+23866^26789 117277 Hans Havermann 02/2021 5655 29^80192-1*80192^29 117273 Dylan Delgado 12/2019 5656 (101*10^117260+7)/9 117262 Robert Price 02/2022 5657 (13*10^117249+161)/3 117250 Robert Price 11/2018 5658 2^389478+43 117245 Lelio R Paula 03/2013 5659 (298*10^117229-7)/3 117231 Robert Price 06/2020 5660 (2^389416+342)/2 117226 Stefano Morozzi 01/2021 5661 (29*2^389351-1)/9 117207 Lelio R Paula 04/2014 5662 5*10^117205+23 117206 Robert Price 03/2019 5663 (2^389341-7)/3865 117200 Lelio R Paula 03/2014 5664 27272^19827+19827^27272 117195 Hans Havermann 01/2021 5665 (2^389276+2650)/2 117184 Stefano Morozzi 09/2020 5666 (844*10^117175-7)/9 117177 Robert Price 05/2021 5667 10^117142+209223 117143 Patrick De Geest 04/2018 5669 10^117142-1000000001 117142 Robert Price 03/2018 5668 10^117142-966057 117142 Patrick De Geest 04/2018 5670 10^117135+360577 117136 Patrick De Geest 07/2018 5671 10^117135-401 117135 Robert Price 01/2018 5672 26415^26488-26488^26415 117126 Norbert Schneider 05/2021 5673 4*10^117123+79 117124 Robert Price 08/2018 5674 2^389033-12797413 117111 Enzo Doria 04/2016 5675 (2^388987+2634)/2 117097 Stefano Morozzi 09/2020 5676 2^388960-109505 117089 Enzo Doria 04/2014 5677 7*10^117082-57 117083 Robert Price 06/2020 5678 (2^388928-5)/569 117077 Lelio R Paula 03/2014 5679 2^388888-1529 117067 Yves Minet 01/2013 5680 10^117059+28879 117060 Patrick De Geest 05/2016 5681 (10^117059-71)/1 117059 Serge Batalov 12/2014 5682 (2^388854+3630)/2 117057 Stefano Morozzi 09/2020 5683 (2^388842+2098)/2 117053 Stefano Morozzi 09/2020 5684 (2^388789+3150)/2 117037 Stefano Morozzi 09/2020 5685 (2^388748+378)/2 117025 Stefano Morozzi 02/2021 5686 (693^41189-1)/692 117005 Michael Stocker 05/2020 5687 (26*10^116999-503)/9 117000 Robert Price 07/2018 5688 (2^388609+1554)/2 116983 Stefano Morozzi 09/2020 5689 38496^1093+1093^38496 116975 Hans Havermann 02/2021 5690 3^245154-6256 116969 Enzo Doria 05/2014 5691 5*10^116966-43 116967 Robert Price 01/2019 5692 2^388536-113495 116961 Enzo Doria 08/2014 5693 (2^388512+382)/2 116954 Stefano Morozzi 02/2021 5694 (8*32^77701+271)/31 116952 Eric Chen 11/2023 5695 2^388469-43 116941 Lelio R Paula 03/2013 5696 27417^18416+18416^27417 116939 Hans Havermann 02/2021 5697 (2^388438+1842)/2 116932 Stefano Morozzi 02/2021 5698 (7*2^388372-1)/111 116911 Lelio R Paula 04/2014 5699 (7*2^388335-1)/25 116900 Lelio R Paula 04/2014 5700 2^388180+93 116854 Donovan Johnson 07/2008 5701 (2^388167+2510)/2 116850 Stefano Morozzi 09/2020 5702 (85*10^116842+293)/9 116843 Robert Price 12/2019 5703 35296^2043+2043^35296 116840 Hans Havermann 02/2021 5704 (2^388081+7)/1179 116821 Lelio R Paula 03/2014 5705 38633^1056+1056^38633 116814 Hans Havermann 02/2021 5706 2^387946-113261 116784 Enzo Doria 07/2014 5707 28*36^75009+305 116739 Eric Chen 12/2022 5708 28363^13056+13056^28363 116737 Hans Havermann 02/2021 5709 2^387745+75557 116723 Enzo Doria 04/2016 5710 (29*10^116719+313)/9 116720 Robert Price 04/2021 5711 29622^8699+8699^29622 116695 Hans Havermann 02/2021 5712 (206*10^116687-17)/9 116689 Robert Price 01/2020 5713 (7*10^116684+179)/3 116685 Robert Price 09/2018 5714 2^387554+71455 116666 Enzo Doria 04/2016 5715 (602*10^116647-71)/9 116649 Robert Price 12/2021 5716 3^244461-10 116638 Tyler NeSmith 09/2022 5717 (2^387447+78557)/365 116631 Lelio R Paula 12/2014 5718 (2*10^116620+43)/9 116620 Serge Batalov 11/2022 5719 (19*10^116617+287)/9/12893 116614 Alfred Reich 11/2022 5720 (145*10^116610-1)/9 116612 Serge Batalov 12/2014 5721 (25*10^116601-331)/9 116602 Robert Price 08/2018 5722 25791^26428-26428^25791 116587 Frank Doornink 03/2024 5724 (17*2^387284-1)/59 116584 Lelio R Paula 04/2014 5723 (2^387284+3726)/2 116584 Stefano Morozzi 09/2020 5725 2^387211+111546435 116563 Paul Bourdelais 10/2021 5726 10^116557+987654321 116558 Robert Price 12/2019 5727 10^116557+9141 116558 Patrick De Geest 02/2020 5728 10^116557-609431 116557 Patrick De Geest 02/2020 5729 (28*10^116546+41)/3 116547 Robert Price 07/2021 5730 (2^387123+1814)/2 116536 Stefano Morozzi 02/2021 5731 (2^387076+2046)/2 116522 Stefano Morozzi 09/2020 5732 (2^387073+2570)/2 116521 Stefano Morozzi 09/2020 5733 (7*10^116514-1)/3 116515 Robert Price 08/2022 5734 (26*32^77406-390071011)/31 116508 Eric Chen 11/2023 5735 28846^10931+10931^28846 116500 Hans Havermann 02/2021 5736 10^116496+3593037 116497 Paul Bourdelais 10/2021 5737 (31*2^386968+1)/7 116490 Lelio R Paula 03/2014 5738 2^386947+1869143 116483 Enzo Doria 05/2016 5739 (30^78857-1)/29 116480 Robert Price 12/2011 5740 (2^386903-3)/5 116469 Lelio R Paula 03/2014 5741 28107^13892+13892^28107 116441 Hans Havermann 02/2021 5742 29110^9957+9957^29110 116386 Hans Havermann 02/2021 5743 26469^24838+24838^26469 116335 Hans Havermann 01/2021 5744 2^386389-1864783 116315 Enzo Doria 03/2016 5745 (8*32^77250-163)/31 116273 Eric Chen 11/2023 5746 (31*2^386231-1)/1711 116266 Lelio R Paula 03/2014 5747 297^47012+47012^297 116250 Norbert Schneider 07/2018 5748 (35*10^116223-341)/9 116224 Robert Price 08/2021 5749 (2^386087-5)/40959 116220 Lelio R Paula 03/2014 5750 (2^386054+714)/2 116214 Stefano Morozzi 09/2020

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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 12 2024 08:27 (Time in France)

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