PRP Records

Probable Primes Top 10000

(290751 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 ?
5016^389756+5303290Paul Bourdelais02/2021
50271016^18649+18649^71016303285Hans Havermann01/2022
50380160^6047+6047^80160303129Hans Havermann01/2022
50467434^31237+31237^67434303094Hans Havermann03/2022
50565537^42102+42102^65537303063Hans Havermann02/2022
50671790^16553+16553^71790302874Hans Havermann11/2021
50765208^44129+44129^65208302874Hans Havermann11/2021
50884181^3960+3960^84181302858Hans Havermann11/2021
50971956^16087+16087^71956302682Hans Havermann11/2021
5102^1005326+383059302634Enzo Doria12/2016
5112^1004929+1877567302514Enzo Doria08/2016
51269341^22978+22978^69341302418Hans Havermann12/2021
513111443^516+516^111443302306Hans Havermann12/2021
51467638^29387+29387^67638302218Hans Havermann11/2021
5152^1003494+1874899302082Enzo Doria06/2016
51675189^10400+10400^75189302037Hans Havermann12/2021
51767237^31042+31042^67237302026Hans Havermann12/2021
51864540^47791+47791^64540302005Hans Havermann11/2021
5192^1003046+60529301947Enzo Doria04/2016
52083278^4209+4209^83278301815Hans Havermann09/2021
52164431^48250+48250^64431301763Hans Havermann09/2021
52267237^30714+30714^67237301716Hans Havermann09/2021
52364641^46288+46288^64641301581Hans Havermann09/2021
52471513^16482+16482^71513301572Hans Havermann10/2021
52572017^15396+15396^72017301565Hans Havermann09/2021
52665534^39927+39927^65534301540Hans Havermann10/2021
527(23^221411-1)/22301501Paul Bourdelais08/2020
52863169^59152+59152^63169301441Hans Havermann09/2021
52975055^10348+10348^75055301336Hans Havermann09/2021
5302^1000647+1881353301225Enzo Doria11/2016
53183686^3961+3961^83686301086Hans Havermann10/2021
53268529^24742+24742^68529301078Hans Havermann09/2021
53365207^41416+41416^65207301072Hans Havermann10/2021
5342^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
53590762^2071+2071^90762300984Hans Havermann06/2021
53663909^51142+51142^63909300934Hans Havermann08/2021
5372^999646+1874029300924Enzo Doria06/2016
53866280^34607+34607^66280300856Hans Havermann06/2021
53965534^38925+38925^65534300817Hans Havermann07/2021
54063296^56517+56517^63296300794Hans Havermann06/2021
541110610^523+523^110610300694Hans Havermann06/2021
54266428^33609+33609^66428300684Hans Havermann06/2021
54374247^11210+11210^74247300672Hans Havermann06/2021
544(59^169777-1)/58300649Paul Bourdelais08/2020
54510^300476+3300477Ed Trice10/2012
54610^300476-530913300476Patrick De Geest03/2016
54766703^31960+31960^66703300471Hans Havermann06/2021
54863722^51915+51915^63722300468Hans Havermann06/2021
5492^998053+1879667300444Enzo Doria09/2016
55077018^7959+7959^77018300437Hans Havermann07/2021
551314738^9+9^314738300337Anatoly F. Selevich02/2011
55269478^20987+20987^69478300281Hans Havermann07/2021
55364088^48393+48393^64088300239Hans Havermann07/2021
55464605^44146+44146^64605300084Hans Havermann08/2021
5557^355039-6^355039300043Jean-Louis Charton05/2011
55667594^27465+27465^67594300035Hans Havermann06/2021
55710^300000+287389300001Patrick De Geest10/2019
55810^300000-83657300000Patrick De Geest10/2019
55970599^17756+17756^70599300000Hans Havermann06/2021
560numbpart(72526161452)299999Serge Batalov04/2017
5612^996182-114431299881Enzo Doria02/2015
5622^995214-2788361299590Enzo Doria12/2015
5632^994791-114319299462Enzo Doria01/2015
5642^994490-1863791299372Enzo Doria01/2016
5652^993322+1885729299020Enzo Doria03/2017
566(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
5672^992711-2788807298836Enzo Doria12/2015
5682^992525-114199298780Enzo Doria12/2014
5692^992329+1884707298721Enzo Doria02/2017
570(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
5712^989562+25297888Stefano Morozzi05/2021
572(2^986191+1)/3296873Vincent Diepeveen06/2008
5732^985217-114553296580Enzo Doria03/2015
574(76^157649-1)/75296507Paul Bourdelais07/2019
5752^984131-1828009296253Enzo Doria01/2015
5762^983620+60451296100Phil Moore03/2008
5772^982721-2683295829Yves Minet02/2016
5782^981298-2788421295401Enzo Doria12/2015
5792^981163-2790967295360Enzo Doria12/2015
5802^979594+1865839294888Enzo Doria02/2016
5812^976760+1885021294035Enzo Doria02/2017
5822^974441+1878407293336Enzo Doria08/2016
5832^974180+1876831293258Enzo Doria07/2016
5842^974170+453319293255Enzo Doria01/2017
5852^972744-114419292826Enzo Doria03/2015
58611^281143+6292781Paul Bourdelais03/2021
587CopelandErdos(292447)292447Mark Rodenkirch12/2015
5882^970911+1873373292274Enzo Doria07/2016
5892^970670+383059292201Enzo Doria12/2016
5902^970141-100363292042Enzo Doria02/2014
5912^969945+1874717291983Enzo Doria06/2016
5922^969384+1880701291814Enzo Doria10/2016
593(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
5942^962194+60139289650Enzo Doria02/2016
5952^959307-1861507288781Enzo Doria11/2015
59614^251797-3288592Paul Bourdelais12/2020
5972^957372+283531288198Enzo Doria02/2017
5982^957192-1864049288144Enzo Doria01/2016
5992^956446+1875199287919Enzo Doria06/2016
600(17^233689+1)/18287542Paul Bourdelais09/2013
6012^955178+1883587287538Enzo Doria12/2016
6022^954127-954127^2287221Henri Lifchitz01/2021
6032^954001+1875257287183Enzo Doria07/2016
604(23891^65536+1)/2286932Serge Batalov03/2018
6052^952268+1878601286662Enzo Doria09/2016
6062^950801+81557286220Enzo Doria08/2016
60722845^65536+22844^65536285658Kellen Shenton03/2021
608(11*2^948635-13)/15285568Renaud Lifchitz11/2011
609(54^164839+1)/55285565Paul Bourdelais07/2019
6102^948510+782569285530Enzo Doria10/2016
6112^948374-114137285490Enzo Doria01/2015
6122^947739+1872923285298Enzo Doria06/2016
6132^942533+82067283731Enzo Doria09/2016
6142^940950+1874989283255Enzo Doria06/2016
6152^940426-2786141283097Enzo Doria11/2015
6162^939881-114115282933Enzo Doria12/2014
61710^282493+632551282494Patrick De Geest02/2017
61910^282493-9^282493282493Jean-Louis Charton03/2007
61810^282493-132327282493Patrick De Geest02/2017
6203^591827-2^591827282374Mike Oakes08/2009
621Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
6222^936716-1835519281980Enzo Doria04/2015
6232^936588+79411281942Enzo Doria06/2016
6242^936047+1877423281779Enzo Doria08/2016
6252^935713+1869377281678Enzo Doria05/2016
6262^933082+1877059280886Enzo Doria08/2016
627(5*10^280710+1)/3280711Serge Batalov10/2014
6282^931976+25280553Stefano Morozzi05/2021
629(42^172663+1)/43280274Paul Bourdelais07/2019
630(10^279978+11)/3279978Serge Batalov07/2015
6312^929524-1864829279815Enzo Doria01/2016
6322^929152+60181279703Enzo Doria02/2016
6332^928621-2787883279543Enzo Doria11/2015
634(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
6352^927429+1882277279184Enzo Doria12/2016
636(71^150697-1)/70278978Paul Bourdelais07/2019
637(33^183661-1)/32278891Paul Bourdelais12/2018
638(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
6392^925330-1301278553Yves Minet06/2015
640(21^210599+1)/22278457Paul Bourdelais08/2013
6412^923261-69175277930Enzo Doria11/2015
642757^96487-756^96487277796Jean-Louis Charton12/2012
6432^922301+57277641Stefano Morozzi05/2021
644((((((((((((((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
645(5^396413-1)/4277081Paul Bourdelais06/2010
6462^920318+2792299277044Enzo Doria02/2016
6472^918596-2786939276525Enzo Doria11/2015
6482^916639+60563275936Enzo Doria04/2016
6492^916385-2786383275860Enzo Doria11/2015
6502^915928+82081275722Enzo Doria09/2016
6512^915576-114137275616Enzo Doria01/2015
6522^914828+1876741275391Enzo Doria07/2016
6532^914757-2203275370Yves Minet12/2015
6542^911900+1871245274510Enzo Doria05/2016
6552^910999+9274239Stefano Morozzi05/2021
6562^910490+283429274085Enzo Doria01/2017
6572^909988-1862249273934Enzo Doria12/2015
6582^909297+1879157273726Enzo Doria08/2016
6592^909257-1864423273714Enzo Doria01/2016
6602^908579-1861747273510Enzo Doria12/2015
6612^907635-2791597273226Enzo Doria01/2016
662(53^158341+1)/54273022Paul Bourdelais07/2019
6632^906594-113201272912Enzo Doria08/2014
6642^904773+1872167272364Enzo Doria06/2016
6656^349903+5272278Paul Bourdelais02/2021
6662^904149-1862473272176Enzo Doria12/2015
667(7*10^271757-61)/9271757Erik Branger03/2012
6682^902497+1880117271679Enzo Doria09/2016
6692^901858+77689271487Enzo Doria06/2016
6702^901372+1875301271341Enzo Doria06/2016
6712^899121-115033270663Enzo Doria07/2015
6722^898900+883021270596Enzo Doria12/2016
6732^898762-251511270555Enzo Doria12/2013
6742^898589+47270503Lelio R Paula03/2016
675187322*10^270343-187321270349Danilo Nitsche09/2013
67648358*10^270343-48357270348Danilo Nitsche09/2013
677(10^270343-1)/9270343Maksym Voznyy07/2007
6782^897867-3217270285Yves Minet12/2016
6792^897849-115273270280Enzo Doria07/2015
6802^896616-114179269909Enzo Doria12/2014
6812^894928+583561269401Enzo Doria04/2017
6822^894673-39343269324Enzo Doria08/2015
683F(1285607)268676Henri Lifchitz11/2008
6842^892112+187663268553Enzo Doria08/2016
685(10^268207+1)/11268206Paul Bourdelais02/2010
6862^890957-69583268205Enzo Doria12/2015
68732841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
6882^890122-351401267954Enzo Doria07/2015
689(19^209359-1)/18267718Paul Bourdelais08/2010
690(85^138647+1)/86267507Paul Bourdelais07/2019
691(485^99523-1)/484267291Michael Stocker05/2020
6922^886324+77791266811Enzo Doria06/2016
6932^884714+1880527266326Enzo Doria10/2016
69411^255426+255426^11265999Serge Batalov05/2014
6952^883462-343421265949Enzo Doria07/2015
6962^883442+1875019265943Enzo Doria06/2016
6972^883333-291583265910Enzo Doria07/2015
6982^880411+1882673265031Enzo Doria12/2016
6992^879530-2788031264765Enzo Doria12/2015
7002^878118+2793079264340Enzo Doria02/2016
701(37^168527-1)/36264283Paul Bourdelais08/2019
7022^875748-461129263627Enzo Doria07/2015
7032^875181-2789923263456Enzo Doria12/2015
7042^875101-350083263432Enzo Doria08/2015
7052^874684+1883587263307Enzo Doria01/2017
7062^874616+1872211263286Enzo Doria05/2016
7073^551491+16263129Robert Price04/2020
7082^874073+2792957263123Enzo Doria02/2016
7092^873628+1878751262989Enzo Doria08/2016
7102^873288-269262886Yves Minet01/2015
7112^871991-4207262496Yves Minet03/2021
7122^871146-3173262242Yves Minet07/2016
7132^869601-163261776Yves Minet01/2015
7142^869326+282859261694Enzo Doria11/2016
7152^869035-114181261606Enzo Doria12/2014
7162^865715+80303260607Enzo Doria07/2016
7172^865048+1882411260406Enzo Doria12/2016
7182^864899-113871260361Enzo Doria10/2014
719(7*10^260198-61)/9260198Erik Branger11/2011
7202^864298-2788421260180Enzo Doria12/2015
7212^864039-2791357260102Enzo Doria01/2016
7222^863621-113833259976Enzo Doria10/2014
7232^862837+75767259740Enzo Doria05/2016
7242^862637-31259680Jorge Menendez05/2019
7252^862088+1874941259515Enzo Doria06/2016
7262^861987-134557259484Hans Havermann10/2018
7272^861516-1854029259343Enzo Doria09/2015
7282^860975-1853977259180Enzo Doria09/2015
7293^543128+16259138Robert Price04/2020
7302^860625-1858843259074Enzo Doria10/2015
7312^860110+77689258919Enzo Doria05/2016
7322^859600+1880371258766Enzo Doria10/2016
7332^859433+494711258716Makoto Morimoto10/2013
734(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
735(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
7362^859240+1875271258658Enzo Doria06/2016
737Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
738(144^119671+1)/145258292Paul Bourdelais08/2019
7392^857608+105258166Stefano Morozzi05/2021
740(11*2^857159-13)/15258031Renaud Lifchitz08/2011
7412^857016-633113257988Enzo Doria12/2013
7422^855732-113969257602Enzo Doria10/2014
7432^853682-3911256984Enzo Doria05/2014
74411^246668-90256879Enzo Doria12/2012
7452^851904-113939256449Enzo Doria10/2014
7462^851725-851725^2256395Henri Lifchitz03/2019
74711^246167-90256357Enzo Doria12/2012
748(10^256187+7)/63443/148782853256175Alfred Reich10/2021
7492^850700-569049256087Enzo Doria11/2013
7502^850675+153256079Stefano Morozzi05/2021


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 23 2022 21:24 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!