PRP Records

Probable Primes Top 10000

(288949 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
50166428^33609+33609^66428300684Hans Havermann06/2021
50274247^11210+11210^74247300672Hans Havermann06/2021
503(59^169777-1)/58300649Paul Bourdelais08/2020
50410^300476+3300477Ed Trice10/2012
50510^300476-530913300476Patrick De Geest03/2016
50666703^31960+31960^66703300471Hans Havermann06/2021
50763722^51915+51915^63722300468Hans Havermann06/2021
5082^998053+1879667300444Enzo Doria09/2016
50977018^7959+7959^77018300437Hans Havermann07/2021
510314738^9+9^314738300337Anatoly F. Selevich02/2011
51169478^20987+20987^69478300281Hans Havermann07/2021
51264088^48393+48393^64088300239Hans Havermann07/2021
51364605^44146+44146^64605300084Hans Havermann08/2021
5147^355039-6^355039300043Jean-Louis Charton05/2011
51567594^27465+27465^67594300035Hans Havermann06/2021
51610^300000+287389300001Patrick De Geest10/2019
51710^300000-83657300000Patrick De Geest10/2019
51870599^17756+17756^70599300000Hans Havermann06/2021
519numbpart(72526161452)299999Serge Batalov04/2017
5202^996182-114431299881Enzo Doria02/2015
5212^995214-2788361299590Enzo Doria12/2015
5222^994791-114319299462Enzo Doria01/2015
5232^994490-1863791299372Enzo Doria01/2016
5242^993322+1885729299020Enzo Doria03/2017
5252^992711-2788807298836Enzo Doria12/2015
5262^992525-114199298780Enzo Doria12/2014
5272^992329+1884707298721Enzo Doria02/2017
528(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
5292^989562+25297888Stefano Morozzi05/2021
530(2^986191+1)/3296873Vincent Diepeveen06/2008
5312^985217-114553296580Enzo Doria03/2015
532(76^157649-1)/75296507Paul Bourdelais07/2019
5332^984131-1828009296253Enzo Doria01/2015
5342^983620+60451296100Phil Moore03/2008
5352^982721-2683295829Yves Minet02/2016
5362^981298-2788421295401Enzo Doria12/2015
5372^981163-2790967295360Enzo Doria12/2015
5382^979594+1865839294888Enzo Doria02/2016
5392^976760+1885021294035Enzo Doria02/2017
5402^974441+1878407293336Enzo Doria08/2016
5412^974180+1876831293258Enzo Doria07/2016
5422^974170+453319293255Enzo Doria01/2017
5432^972744-114419292826Enzo Doria03/2015
54411^281143+6292781Paul Bourdelais03/2021
545CopelandErdos(292447)292447Mark Rodenkirch12/2015
5462^970911+1873373292274Enzo Doria07/2016
5472^970670+383059292201Enzo Doria12/2016
5482^970141-100363292042Enzo Doria02/2014
5492^969945+1874717291983Enzo Doria06/2016
5502^969384+1880701291814Enzo Doria10/2016
551(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
5522^962194+60139289650Enzo Doria02/2016
5532^959307-1861507288781Enzo Doria11/2015
55414^251797-3288592Paul Bourdelais12/2020
5552^957372+283531288198Enzo Doria02/2017
5562^957192-1864049288144Enzo Doria01/2016
5572^956446+1875199287919Enzo Doria06/2016
558(17^233689+1)/18287542Paul Bourdelais09/2013
5592^955178+1883587287538Enzo Doria12/2016
5602^954127-954127^2287221Henri Lifchitz01/2021
5612^954001+1875257287183Enzo Doria07/2016
562(23891^65536+1)/2286932Serge Batalov03/2018
5632^952268+1878601286662Enzo Doria09/2016
5642^950801+81557286220Enzo Doria08/2016
56522845^65536+22844^65536285658Kellen Shenton03/2021
566(11*2^948635-13)/15285568Renaud Lifchitz11/2011
567(54^164839+1)/55285565Paul Bourdelais07/2019
5682^948510+782569285530Enzo Doria10/2016
5692^948374-114137285490Enzo Doria01/2015
5702^947739+1872923285298Enzo Doria06/2016
5712^942533+82067283731Enzo Doria09/2016
5722^940950+1874989283255Enzo Doria06/2016
5732^940426-2786141283097Enzo Doria11/2015
5742^939881-114115282933Enzo Doria12/2014
57510^282493+632551282494Patrick De Geest02/2017
57710^282493-9^282493282493Jean-Louis Charton03/2007
57610^282493-132327282493Patrick De Geest02/2017
5783^591827-2^591827282374Mike Oakes08/2009
579Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
5802^936716-1835519281980Enzo Doria04/2015
5812^936588+79411281942Enzo Doria06/2016
5822^936047+1877423281779Enzo Doria08/2016
5832^935713+1869377281678Enzo Doria05/2016
5842^933082+1877059280886Enzo Doria08/2016
585(5*10^280710+1)/3280711Serge Batalov10/2014
5862^931976+25280553Stefano Morozzi05/2021
587(42^172663+1)/43280274Paul Bourdelais07/2019
588(10^279978+11)/3279978Serge Batalov07/2015
5892^929524-1864829279815Enzo Doria01/2016
5902^929152+60181279703Enzo Doria02/2016
5912^928621-2787883279543Enzo Doria11/2015
592(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
5932^927429+1882277279184Enzo Doria12/2016
594(71^150697-1)/70278978Paul Bourdelais07/2019
595(33^183661-1)/32278891Paul Bourdelais12/2018
596(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
5972^925330-1301278553Yves Minet06/2015
598(21^210599+1)/22278457Paul Bourdelais08/2013
5992^923261-69175277930Enzo Doria11/2015
600757^96487-756^96487277796Jean-Louis Charton12/2012
6012^922301+57277641Stefano Morozzi05/2021
602((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
603(5^396413-1)/4277081Paul Bourdelais06/2010
6042^920318+2792299277044Enzo Doria02/2016
6052^918596-2786939276525Enzo Doria11/2015
6062^916639+60563275936Enzo Doria04/2016
6072^916385-2786383275860Enzo Doria11/2015
6082^915928+82081275722Enzo Doria09/2016
6092^915576-114137275616Enzo Doria01/2015
6102^914828+1876741275391Enzo Doria07/2016
6112^914757-2203275370Yves Minet12/2015
6122^911900+1871245274510Enzo Doria05/2016
6132^910999+9274239Stefano Morozzi05/2021
6142^910490+283429274085Enzo Doria01/2017
6152^909988-1862249273934Enzo Doria12/2015
6162^909297+1879157273726Enzo Doria08/2016
6172^909257-1864423273714Enzo Doria01/2016
6182^908579-1861747273510Enzo Doria12/2015
6192^907635-2791597273226Enzo Doria01/2016
620(53^158341+1)/54273022Paul Bourdelais07/2019
6212^906594-113201272912Enzo Doria08/2014
6222^904773+1872167272364Enzo Doria06/2016
6236^349903+5272278Paul Bourdelais02/2021
6242^904149-1862473272176Enzo Doria12/2015
625(7*10^271757-61)/9271757Erik Branger03/2012
6262^902497+1880117271679Enzo Doria09/2016
6272^901858+77689271487Enzo Doria06/2016
6282^901372+1875301271341Enzo Doria06/2016
6292^899121-115033270663Enzo Doria07/2015
6302^898900+883021270596Enzo Doria12/2016
6312^898762-251511270555Enzo Doria12/2013
6322^898589+47270503Lelio R Paula03/2016
633187322*10^270343-187321270349Danilo Nitsche09/2013
63448358*10^270343-48357270348Danilo Nitsche09/2013
635(10^270343-1)/9270343Maksym Voznyy07/2007
6362^897867-3217270285Yves Minet12/2016
6372^897849-115273270280Enzo Doria07/2015
6382^896616-114179269909Enzo Doria12/2014
6392^894928+583561269401Enzo Doria04/2017
6402^894673-39343269324Enzo Doria08/2015
641F(1285607)268676Henri Lifchitz11/2008
6422^892112+187663268553Enzo Doria08/2016
643(10^268207+1)/11268206Paul Bourdelais02/2010
6442^890957-69583268205Enzo Doria12/2015
64532841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
6462^890122-351401267954Enzo Doria07/2015
647(19^209359-1)/18267718Paul Bourdelais08/2010
648(85^138647+1)/86267507Paul Bourdelais07/2019
649(485^99523-1)/484267291Michael Stocker05/2020
6502^886324+77791266811Enzo Doria06/2016
6512^884714+1880527266326Enzo Doria10/2016
65211^255426+255426^11265999Serge Batalov05/2014
6532^883462-343421265949Enzo Doria07/2015
6542^883442+1875019265943Enzo Doria06/2016
6552^883333-291583265910Enzo Doria07/2015
6562^880411+1882673265031Enzo Doria12/2016
6572^879530-2788031264765Enzo Doria12/2015
6582^878118+2793079264340Enzo Doria02/2016
659(37^168527-1)/36264283Paul Bourdelais08/2019
6602^875748-461129263627Enzo Doria07/2015
6612^875181-2789923263456Enzo Doria12/2015
6622^875101-350083263432Enzo Doria08/2015
6632^874684+1883587263307Enzo Doria01/2017
6642^874616+1872211263286Enzo Doria05/2016
6653^551491+16263129Robert Price04/2020
6662^874073+2792957263123Enzo Doria02/2016
6672^873628+1878751262989Enzo Doria08/2016
6682^873288-269262886Yves Minet01/2015
6692^871991-4207262496Yves Minet03/2021
6702^871146-3173262242Yves Minet07/2016
6712^869601-163261776Yves Minet01/2015
6722^869326+282859261694Enzo Doria11/2016
6732^869035-114181261606Enzo Doria12/2014
6742^865715+80303260607Enzo Doria07/2016
6752^865048+1882411260406Enzo Doria12/2016
6762^864899-113871260361Enzo Doria10/2014
677(7*10^260198-61)/9260198Erik Branger11/2011
6782^864298-2788421260180Enzo Doria12/2015
6792^864039-2791357260102Enzo Doria01/2016
6802^863621-113833259976Enzo Doria10/2014
6812^862837+75767259740Enzo Doria05/2016
6822^862637-31259680Jorge Menendez05/2019
6832^862088+1874941259515Enzo Doria06/2016
6842^861987-134557259484Hans Havermann10/2018
6852^861516-1854029259343Enzo Doria09/2015
6862^860975-1853977259180Enzo Doria09/2015
6873^543128+16259138Robert Price04/2020
6882^860625-1858843259074Enzo Doria10/2015
6892^860110+77689258919Enzo Doria05/2016
6902^859600+1880371258766Enzo Doria10/2016
6912^859433+494711258716Makoto Morimoto10/2013
692(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
693(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
6942^859240+1875271258658Enzo Doria06/2016
695Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
696(144^119671+1)/145258292Paul Bourdelais08/2019
6972^857608+105258166Stefano Morozzi05/2021
698(11*2^857159-13)/15258031Renaud Lifchitz08/2011
6992^857016-633113257988Enzo Doria12/2013
7002^855732-113969257602Enzo Doria10/2014
7012^853682-3911256984Enzo Doria05/2014
70211^246668-90256879Enzo Doria12/2012
7032^851904-113939256449Enzo Doria10/2014
7042^851725-851725^2256395Henri Lifchitz03/2019
70511^246167-90256357Enzo Doria12/2012
706(10^256187+7)/63443/148782853256175Alfred Reich10/2021
7072^850700-569049256087Enzo Doria11/2013
7082^850675+153256079Stefano Morozzi05/2021
70921^193601-20^193601255983Jean-Louis Charton02/2015
710(37^163193+1)/38255918Paul Bourdelais07/2019
7112^849177-114025255628Enzo Doria12/2014
7122^848502-3173255425Yves Minet07/2016
7132^848178-140291255328Enzo Doria01/2014
7142^847622-2441255160Yves Minet02/2016
7152^847291+182843255061Enzo Doria11/2016
7162^847174+1879429255025Enzo Doria09/2016
71724*29^174239+13361254809Curtis Bright04/2015
7182^845633-933075254561Paul Bourdelais11/2021
7192^845610-1868591254554Enzo Doria04/2016
7202^845484+81931254517Enzo Doria08/2016
7212^845402-114761254492Enzo Doria05/2015
7222^844334-2792441254170Enzo Doria02/2016
72311^243796-90253888Enzo Doria12/2012
724(10^253891+7)/44777/79843/16940711253875Alfred Reich10/2021
72530^171733-29^171733253671Jean-Louis Charton10/2018
7262^842209+1876037253531Enzo Doria07/2016
7272^842123-59197253505Enzo Doria10/2015
7282^840797-3253106Paul Bourdelais06/2019
7292^840716-2969253081Yves Minet05/2016
7302^840358-462491252973Enzo Doria08/2015
7312^840310+1878379252959Enzo Doria08/2016
73211^242579-60252620Enzo Doria10/2012
73345^152659+2252378Robert Price09/2015
734(95^127583+1)/96252322Paul Bourdelais07/2019
7352^837725+1869377252181Enzo Doria05/2016
7362^837536-311039252124Enzo Doria06/2015
73721^190632-2252058Robert Price07/2015
7382^837242+1873297252035Enzo Doria06/2016
7392^836656-2787929251859Enzo Doria11/2015
7402^836380+1875541251776Enzo Doria07/2016
741(359^98327-1)/358251233Alexander Zhirkov11/2017
742tau(41^28288)250924Nik Lygeros / Olivier Rozier10/2013
7432^832511-461197250611Enzo Doria07/2015
7442^832505+1881137250609Enzo Doria11/2016
7452^832363+583295250567Enzo Doria12/2016
7462^832244-403635250531Enzo Doria01/2014
7472^831157+1880657250204Enzo Doria11/2016
7482^831088-7200899250183Enzo Doria01/2015
7492^830956-1349250143Yves Minet07/2015
7502^830037+282317249867Enzo Doria09/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!