PRP Records

Probable Primes Top 10000

(277034 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 ?
75012^280118+5461584324Lelio R Paula09/2013
7502(509203*2^280090-1)/384321Lelio R Paula04/2015
75036^108354+4784316Lelio R Paula12/2015
7504(2^280069+462)/284309Stefano Morozzi01/2020
750520657^12058+12058^2065784307Hans Havermann07/2020
750610^84305+14196384306Patrick De Geest07/2013
750710^84305-5784305Robert Price05/2011
75089^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
750975843!4-3284295Robert Price11/2019
75103^176648-11280484283Enzo Doria06/2014
75116^108310+11584282Lelio R Paula12/2015
7512(11*2^279968-1)/584280Lelio R Paula02/2014
75136^108288-1664384265Enzo Doria02/2013
75142^279917-5869584264Lelio R Paula08/2013
751565^46477+3684259Lelio R Paula01/2016
7516(2^279883+3230)/284253Stefano Morozzi01/2020
7517(2^279876+1422)/284251Stefano Morozzi01/2020
75182^279866-190784249Yves Minet05/2013
751923140^4373+4373^2314084248Hans Havermann07/2020
752019736^18567+18567^1973684248Hans Havermann07/2020
7522(3^176580-5)/2807684246Lelio R Paula12/2012
7521(p(17530)#+4)/284246Robert Price09/2017
7523(2*10^84239+1)/384239Serge Batalov07/2009
752418^67103-4184233Lelio R Paula11/2015
752520^64743-4384233Lelio R Paula01/2016
7526(2^279807+2454)/284230Stefano Morozzi01/2020
752719717^18672+18672^1971784216Hans Havermann07/2020
7528(2^279754+3574)/284215Stefano Morozzi01/2020
7529143^39070+39070^14384209Serge Batalov05/2014
753011^80857-540084204Enzo Doria01/2013
7531(2^279642+3130)/284181Stefano Morozzi01/2020
7532(13*10^84179+161)/384180Robert Price04/2017
75332^279634-11040584179Enzo Doria05/2014
7534(74*10^84170+313)/984171Robert Price11/2017
75352^279582-101784163Lelio R Paula08/2013
7536(22*10^84159-19)/384160Robert Price02/2017
7537p(17513)#/2+51284156Robert Price05/2017
7538(19*10^84144-43)/384145Robert Price10/2017
7539(9*2^279507-1)/13784139Lelio R Paula02/2014
754011^80792-81084137Enzo Doria11/2012
7541(97*10^84134-1)/384136Serge Batalov12/2014
7542p(17507)#/2+3284125Robert Price12/2016
7543(1750^25939-1)/174984118Serge Batalov08/2020
754421485^8224+8224^2148584116Hans Havermann04/2017
75453^176294-34084114Lelio R Paula12/2015
7546(3^176287+4)/219184107Lelio R Paula12/2012
75472^279388-71984105Yves Minet05/2012
7548(22699*2^279378+1)/22184104Lelio R Paula06/2014
7549(28*10^84095-67)/384096Robert Price10/2020
7550(2^279343+578)/284091Stefano Morozzi01/2020
75512^279332-11044784088Enzo Doria05/2014
75522^279320+784084Lelio R Paula06/2012
7553127^39966-284081Lelio R Paula10/2017
7554(2^279299+2490)/284078Stefano Morozzi01/2020
7555(2^279301+1694)/284078Stefano Morozzi01/2020
7556(2^279285+962)/284073Stefano Morozzi01/2020
7557(2^279269+1122)/284069Stefano Morozzi01/2020
7558(11*2^279240-1)/9584059Lelio R Paula02/2014
75592^279218-11134784053Enzo Doria05/2014
756035^54435+284052Lelio R Paula05/2013
7561(2^279176+2998)/284041Stefano Morozzi01/2020
7562(31*2^279191-1)/1251152384040Lelio R Paula02/2014
756320996^10059+10059^2099684038Hans Havermann05/2017
756497*10^84033-384035Robert Price01/2017
7565(2^279153+1326)/284034Stefano Morozzi01/2020
7566(2^279155+3534)/284034Stefano Morozzi01/2020
756721234^9067+9067^2123484033Hans Havermann05/2017
7568(134569^16384+1)/284033Richard Fischer06/2018
7569(5858^22303-1)/585784029Serge Batalov08/2020
75702^279095-10971784016Enzo Doria04/2014
7571(2^279054+1438)/284004Stefano Morozzi01/2020
757210^83997-4000183997Robert Price01/2021
757314^73282-9983991Lelio R Paula11/2015
757421457^8200+8200^2145783979Hans Havermann06/2017
757589*10^83976-783978Robert Price03/2017
75762^278955+17383974Lelio R Paula06/2012
7577(7*2^278851+1)/3983942Lelio R Paula12/2012
7578(9913*2^278844-1)/4080383940Lelio R Paula04/2015
75795^120076-1484683930Enzo Doria02/2013
7580(85*10^83921-1)/383923Robert Price07/2017
7581(2^278770-3)/2383917Lelio R Paula12/2012
7582(10^83916+449)/983916Serge Batalov12/2014
75842^278715+9983902Lelio R Paula06/2012
7583(132109^16384+1)/283902Richard Fischer05/2018
758540235!2-2^4023583899Robert Price09/2015
75862^278698-17183897Lelio R Paula06/2012
7587(19*10^83894-43)/383895Robert Price10/2017
75886^107802+2583887Lelio R Paula12/2015
75898*10^83880+3983881Robert Price01/2017
7590(58*10^83878+23)/983879Robert Price09/2015
75917^99244-9083871Lelio R Paula10/2015
7592(2^278601+1674)/283867Stefano Morozzi01/2020
75932^278554+425783854Lelio R Paula08/2013
75942^278504-10961983839Enzo Doria04/2014
75952^278499+187043383837Enzo Doria05/2016
7596(2^278487+570)/283833Stefano Morozzi01/2020
7597105^41475+10483829Norbert Schneider11/2016
759815^71276-6883828Lelio R Paula11/2015
75992^278464-21641383827Enzo Doria04/2013
7600(2^278440+1602)/283819Stefano Morozzi01/2020
7601(76*10^83816-211)/983817Robert Price10/2017
7602(2^278429+1950)/283816Stefano Morozzi01/2020
7603(2^278428+1750)/283815Stefano Morozzi01/2020
7604(8*10^83811-101)/383812Robert Price10/2017
76052^278400+4075583807Lelio R Paula08/2013
7606(2^278394+3718)/283805Stefano Morozzi01/2020
7607(2^278388+3586)/283803Stefano Morozzi01/2020
7608(9*2^278381-1)/783802Lelio R Paula02/2014
76093*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
761019551^19268+19268^1955183773Hans Havermann05/2017
761120625^11522+11522^2062583770Hans Havermann05/2017
7612(44*10^83768-791)/983769Robert Price10/2017
7613(87^43189+1)/8883764Paul Bourdelais08/2017
76142^278235-4983758Lelio R Paula06/2012
761523543^3610+3610^2354383755Hans Havermann05/2017
761718^66711-9183741Lelio R Paula11/2015
76164*10^83740-8983741Robert Price08/2017
7618(3*2^278172-1)/1183738Lelio R Paula02/2014
7619(15*29^57251+2561)/2883724Curtis Bright05/2015
76204*7^99059-983716Lelio R Paula10/2014
7621(2^278128-3)/12684472414983714Lelio R Paula12/2012
76222^278077+186721183710Enzo Doria03/2016
7623(85*10^83708+203)/983709Robert Price09/2020
76242^278059-2783705Lelio R Paula06/2012
7625214^35917+35917^21483702Norbert Schneider12/2014
7626(23*10^83693+7)/383694Robert Price10/2015
762785^43375-283689Lelio R Paula09/2013
76285*3^175360+483669Lelio R Paula07/2014
7629(23^61441-1)/2283665Robert Price01/2012
763020091^14596+14596^2009183664Hans Havermann03/2017
76312^277907-11062983659Enzo Doria05/2014
763219522^19283+19283^1952283656Hans Havermann04/2017
7633(2^277881+2570)/283651Stefano Morozzi01/2020
76348*5^119664-383643Lelio R Paula10/2014
76358*3^175299-783640Lelio R Paula07/2014
7636(26*10^83638-413)/983639Robert Price10/2017
7637(197*10^83636+7)/383638Robert Price12/2020
76383^175250+2283616Robert Price12/2013
763911^80285+3083609Lelio R Paula10/2015
764026870^1293+1293^2687083609Hans Havermann03/2017
7641(6730^21841-1)/672983604Serge Batalov08/2020
7642(2828^24223-1)/282783602Serge Batalov08/2020
76432^277691+187442383594Enzo Doria06/2016
764413^75022-6083571Lelio R Paula11/2015
7645(2^277593+2622)/283564Stefano Morozzi01/2020
764614^72905-5183559Lelio R Paula11/2015
7647(17*2^277565-1)/54383554Lelio R Paula02/2014
76485^119532-1283550Lelio R Paula10/2015
76496^107358-1625383541Enzo Doria02/2013
76502^277478-46021183530Enzo Doria06/2015
7651(2^277474+814)/283528Stefano Morozzi01/2020
7652(22*10^83525-7)/383526Erik Branger09/2014
7653(30^56543+1)/3183520Robert Price07/2013
76542^277417-46078383511Paul Bourdelais04/2013
7655(2^277404+3582)/283507Stefano Morozzi01/2020
7656(22699*2^277387+1)/21983504Lelio R Paula06/2014
7657(31*2^277383-1)/24783500Lelio R Paula02/2014
765821368^8085+8085^2136883500Hans Havermann04/2017
7659(2^277353+3750)/283492Stefano Morozzi01/2020
7660(2^277348+3538)/283490Stefano Morozzi01/2020
7661(9*2^277342+1)/1383489Lelio R Paula12/2012
76625^119439-6683485Lelio R Paula10/2015
7663(14*10^83471-101)/383472Robert Price04/2017
76645*6^107263+783468Lelio R Paula10/2014
7665(64*10^83461-1)/983462Serge Batalov11/2010
76662^277244-17570983459Hans Havermann10/2018
7667(2^277230+1450)/283455Stefano Morozzi01/2020
7668(2^277232+3658)/283455Stefano Morozzi01/2020
766917^67796-9283420Lelio R Paula11/2015
76702^277106-11005783418Enzo Doria04/2014
76716^107200-1983418Lelio R Paula12/2015
767211^80096-183083412Enzo Doria12/2012
76733^174801+5683402Lelio R Paula12/2015
76742^277033-11197383396Enzo Doria05/2014
7675120^40105-11983386Norbert Schneider09/2018
7676(2^276992+2046)/283383Stefano Morozzi01/2020
7677(2^276990+474)/283382Stefano Morozzi01/2020
767820519^11572+11572^2051983378Hans Havermann03/2017
767920850^9971+9971^2085083374Hans Havermann03/2017
76826^107122-1886383358Enzo Doria03/2013
7680(2^276908+2322)/283358Stefano Morozzi01/2020
7681(2^276910+2734)/283358Stefano Morozzi01/2020
76834*10^83354-8983355Robert Price08/2017
76843^174697-3483352Robert Price11/2013
7686(9787*2^276855-1)/234583343Lelio R Paula04/2015
7685(2^276860+1678)/283343Stefano Morozzi01/2020
7687(2^276841+3354)/283338Stefano Morozzi01/2020
76892^276825+7522783333Enzo Doria04/2016
768834*10^83331-983333Robert Price06/2020
76905^119214+8483328Lelio R Paula10/2015
76912^276803-15983327Lelio R Paula06/2012
7692(3*2^276753-1)/2583311Lelio R Paula02/2014
76937*10^83297-3983298Robert Price07/2020
7694114^40495+40495^11483295Norbert Schneider12/2014
769539967!2+102483282Robert Price02/2015
7696(1894^25411-1)/189383279Serge Batalov08/2020
76982^276641+5783278Lelio R Paula06/2012
769935^53934-341483278Enzo Doria03/2013
769721777^6670+6670^2177783278Hans Havermann06/2020
7700(2^276655+78557)/36542583276Lelio R Paula12/2012
77012^276615-403583270Lelio R Paula08/2013
77022^276588+115583262Lelio R Paula08/2013
77032^276587-93783261Yves Minet10/2009
77042^276584-11318383261Enzo Doria07/2014
7705(2^276592-1017)/1384373983256Lelio R Paula12/2012
77062^276547-10959183249Enzo Doria04/2014
770713^74733-3283249Lelio R Paula11/2015
77082^276523-258783242Yves Minet07/2014
770918^66311-4383239Lelio R Paula11/2015
771011^79919-153083228Enzo Doria12/2012
77112^276468-10974583226Enzo Doria04/2014
77122^276462+538583224Lelio R Paula08/2013
7713(9787*2^276422-1)/383215Lelio R Paula04/2015
77152^276391-1583202Lelio R Paula06/2012
7714(4*10^83201+173)/383202Robert Price01/2017
7716(259*10^83186-1)/383188Robert Price12/2020
7717(2^276327+534)/283183Stefano Morozzi01/2020
77182^276316-10965583180Enzo Doria04/2014
77192^276305-11206383177Enzo Doria06/2014
7720(2^276296+3406)/283174Stefano Morozzi01/2020
7721(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
7722(2^276277+3254)/283168Stefano Morozzi01/2020
772374913!4-283161Robert Price07/2017
7724(3023^23893-1)/302283155Serge Batalov08/2020
77252^276227-183720783153Enzo Doria05/2015
7727(2^276227+3)/783152Lelio R Paula12/2012
7726(2^276229+12)/2883152Stefano Morozzi03/2020
7728(2^276205+1190)/283146Stefano Morozzi01/2020
77292^276184-6338983140Paul Bourdelais02/2012
7730(2^276165+2046)/283134Stefano Morozzi01/2020
7731(2^276105+1274)/283116Stefano Morozzi01/2020
77322^276066-11160383105Enzo Doria05/2014
773319438^18837+18837^1943883098Hans Havermann07/2020
7734(431^31543-1)/43083097Serge Batalov08/2020
7735(2^276028-3)*6-783094Gilbert Mozzo09/2016
7736(26*10^83067+79)/383068Robert Price09/2020
77372^275926-469183063Yves Minet05/2019
7738(2^275919+1386)/283060Stefano Morozzi01/2020
7739(2^275897+9)/115383051Lelio R Paula12/2012
77402^275879-10980783048Enzo Doria04/2014
7742F(397379)83047Henri Lifchitz08/2003
7741U(397379)83047Serge Batalov03/2015
77433^174040-1483039Robert Price08/2013
7744(86*10^83038-221)/983039Robert Price06/2017
774521632^6897+6897^2163283038Hans Havermann05/2020
77462^275841-688383037Lelio R Paula07/2011
774719610^17127+17127^1961083023Hans Havermann06/2020
77483^174002-14083021Lelio R Paula12/2015
77496^106681+7783014Lelio R Paula12/2015
7750187^36539-283011Lelio R Paula10/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!