PRP Records

Probable Primes Top 10000

(252675 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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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 ?
12512^551507-23557166021Enzo Doria08/2013
12527*10^165916-3165917Robert Price08/2015
125381^86837-80^86837165728Robert Price01/2015
12542^550270-69551165648Enzo Doria12/2015
12552^550000-23625165567Enzo Doria08/2013
12562^549675-1852057165469Enzo Doria08/2015
1257-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1258(28*10^165358-1)/9165359Serge Batalov10/2014
12592^549278+1879669165350Enzo Doria09/2016
1260(7*10^165350-439)/9165350Robert Price02/2018
12612^549252-351269165342Enzo Doria06/2015
1262(14*10^165282+73)/3165283Robert Price12/2018
12632^549049+2797607165281Enzo Doria04/2016
1264(7*10^165239+107)/3165240Robert Price02/2018
1265(44^100511-1)/43165184Paul Bourdelais11/2017
1266(7*10^165134+107)/3165135Robert Price02/2018
12672^547178-1856501164717Enzo Doria10/2015
126811^158160-60164707Enzo Doria07/2012
12692^546398-59201164483Enzo Doria10/2015
12702^546332-114893164463Enzo Doria05/2015
12712^545958+1876189164350Enzo Doria07/2016
12722^545878-49841164326Enzo Doria10/2015
1273(10^164284+77)/3164284Robert Price01/2018
12742^545668-4019164263Yves Minet04/2017
1275(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
1276(16*10^164122+197)/3164123Robert Price04/2019
12772^545185+76757164118Enzo Doria05/2016
12782^545076-114329164085Enzo Doria01/2015
1279(2*10^164043-143)/3164043Robert Price03/2018
1280(29^112153+1)/30164011Lelio R Paula03/2017
12812^544757+1874777163989Enzo Doria06/2016
12822^544444-457199163894Enzo Doria01/2015
12832^544264-343529163840Enzo Doria07/2015
12847*10^163780+9163781Robert Price09/2015
12852^543989+2793047163758Enzo Doria02/2016
12862^542870-69551163421Enzo Doria12/2015
12872^542395+72533163278Enzo Doria04/2016
12882^542072-3683163180Yves Minet03/2017
12892^541779-1867357163092Enzo Doria04/2016
12908*10^162924+9162925Robert Price12/2015
12912^540905+81557162829Enzo Doria08/2016
12922^540628-2939162746Yves Minet09/2014
1293919^54919-918^54919162743Jean-Louis Charton01/2013
12943*10^162620-59162621Robert Price09/2018
12953^340694-112960162553Enzo Doria07/2014
12962^539807-114081162499Enzo Doria12/2014
12972^539654-114893162453Enzo Doria05/2015
12982^539617-1851583162441Enzo Doria08/2015
12992^539346+81049162360Enzo Doria07/2016
13002^539220-115499162322Enzo Doria07/2015
13012^539217-113713162321Enzo Doria09/2014
13029^170099-8^170099162316Jean-Louis Charton05/2005
1303(115*10^162153-1)/3162155Serge Batalov12/2014
1304(10^162138+11)/3162138Serge Batalov07/2015
13052^538473-112723162097Enzo Doria06/2014
13062^538157+79337162002Enzo Doria06/2016
13072^538136-114749161996Enzo Doria05/2015
13082^538104+1531161986Lelio R Paula01/2013
1309(9*29^110727-1199)/14161927Curtis Bright05/2015
13102^537815-22737161899Enzo Doria07/2013
13112^537804-39839161896Enzo Doria09/2015
13122^537458-59201161791Enzo Doria10/2015
13132*10^161766+51161767Robert Price05/2018
13142^537209-49849161717Enzo Doria10/2015
13152^536937+1879397161635Enzo Doria09/2016
13162^536569-22881161524Enzo Doria07/2013
131710^161253+573493161254Patrick De Geest07/2018
131810^161253-8001161253Robert Price03/2018
13197*10^161192-9161193Robert Price10/2015
13202^535269-113803161133Enzo Doria09/2014
13212^535205-23295161113Enzo Doria08/2013
1322(89^82609+1)/90161036Paul Bourdelais10/2017
13232^534359-23229160859Enzo Doria08/2013
132467^88037-66^88037160763Robert Price10/2013
13252^533948-1852559160735Enzo Doria08/2015
13262^533665-23335160650Enzo Doria08/2013
13273^336353-2^336353160482Mike Oakes10/2007
13282^532253+1868417160225Enzo Doria04/2016
13292^532108-291989160181Enzo Doria07/2015
1330(17*10^160143+67)/3160144Robert Price01/2019
13312^531110-1853771159881Enzo Doria09/2015
13322^530992-1845299159845Enzo Doria07/2015
1333(136*10^159736-1)/9159738Serge Batalov12/2014
13342^530417-113833159672Enzo Doria09/2014
13352^530406-69701159669Enzo Doria02/2016
13365*10^159656+41159657Robert Price03/2019
13377^188858-188858^7159604Norbert Schneider05/2018
1338(24^115597-1)/23159547Paul Bourdelais09/2017
1339(17*10^159438-377)/9159439Robert Price03/2018
13402^528944-461315159229Enzo Doria07/2015
1341(13*10^159147+161)/3159148Robert Price11/2018
13422^528620-113879159131Enzo Doria10/2014
13432^528000-23307158944Enzo Doria08/2013
1344(29*10^158909+61)/9158910Robert Price08/2018
13452^527817+1876817158889Enzo Doria07/2016
13462^527774-49451158876Enzo Doria10/2015
13472^527745-291553158868Enzo Doria07/2015
13482^527644-1856999158837Enzo Doria10/2015
1349(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
13502^527573-1863253158816Enzo Doria12/2015
13512^527553-23401158810Enzo Doria08/2013
135211^152420-210158730Enzo Doria09/2012
1353(13*10^158694+401)/9158695Robert Price01/2018
13542^527052-69059158659Enzo Doria11/2015
13552^526849-113233158598Enzo Doria07/2014
1356(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
13572^526658-3551158540Yves Minet03/2017
13582^526375-23115158455Enzo Doria08/2013
13592^526028-112793158351Enzo Doria07/2014
13602^525690-9221158249Lelio R Paula01/2013
13612*10^158242-7158243Robert Price10/2015
13622^525667-525667^2158242Henri Lifchitz12/2017
13632^525186-1857431158097Enzo Doria10/2015
13642^524515-23245157895Enzo Doria08/2013
13652^524499-109087157890Enzo Doria04/2014
13662^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
13672^524288+189093157827Makoto Morimoto01/2016
1368(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
1369(10^157792+359)/9157792Serge Batalov12/2014
13702^523924+1876591157717Enzo Doria07/2016
1371(17*10^157705+67)/3157706Robert Price01/2019
1372(46^94841+1)/47157696Robert Price01/2014
13732^523774+77839157672Enzo Doria05/2016
13742^523587+2799143157616Enzo Doria04/2016
13752^523371+1872113157551Enzo Doria05/2016
13762^522535-351457157299Enzo Doria07/2015
13772^522226+2799079157206Enzo Doria04/2016
13782^522134-1849451157178Enzo Doria08/2015
13794*10^157150+93157151Robert Price08/2018
13802^521401-29593156958Enzo Doria08/2015
13812^521348-23397156942Enzo Doria08/2013
1382(98^78797+1)/99156901Paul Bourdelais12/2017
138365^86522+64156857Lelio R Paula04/2016
13848^173687-7^173687156855Jean-Louis Charton09/2004
13852^520977-1858183156830Enzo Doria10/2015
1386(8*10^156718-101)/3156719Robert Price08/2018
13872^520314-1849481156631Enzo Doria08/2015
1388(13*10^156522+89)/3156523Robert Price09/2018
1389(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
13903*10^156435-97156436Robert Price07/2018
1391(8*10^156371-77)/3156372Robert Price07/2018
139253^90679-52^90679156356Robert Price01/2013
13932^519106-59141156267Enzo Doria10/2015
13942^519053+6077156251Enzo Doria02/2016
13952^518968-1860989156225Enzo Doria11/2015
1396(25*10^156221-7)/9156222Robert Price05/2018
13972^518931-2782297156214Enzo Doria09/2015
13982^518608-2939156117Yves Minet09/2014
139910*27^109005+697156027Curtis Bright05/2015
14002^517967-113485155924Enzo Doria08/2014
14012^517698+4429155843Lelio R Paula01/2013
14022^517543-113257155796Enzo Doria07/2014
1403(14*10^155740-143)/3155741Robert Price11/2018
140431^104309-30^104309155563Henri Lifchitz08/2013
14052^516742-39851155555Enzo Doria09/2015
14062^516440+1878421155464Enzo Doria08/2016
14072^515863-1867237155291Enzo Doria03/2016
14082^515786-461861155268Enzo Doria07/2015
14092^515644-113247155225Enzo Doria07/2014
1410(7*10^155203+107)/3155204Robert Price02/2018
1411(17*10^155133-89)/9155134Robert Price07/2018
14122^515227-114997155099Enzo Doria06/2015
1414EPrime(155025)155025Eric W. Weisstein10/2010
1413(14*10^155024-221)/9155025Robert Price04/2018
1415(4*10^155022+173)/3155023Robert Price02/2018
1416(115*10^154869-1)/3154871Serge Batalov12/2014
14172^514361+78167154839Enzo Doria05/2016
14182^514281-115033154815Enzo Doria06/2015
14192^514194-3311154788Yves Minet12/2014
1420(14*10^154773+37)/3154774Robert Price12/2018
14212^513437+1879337154560Enzo Doria09/2016
14222^513306-113201154521Enzo Doria07/2014
1423(10^154494-13)/3154494Robert Price12/2017
14242^513042-113787154442Enzo Doria09/2014
14252^512628-114053154317Enzo Doria11/2014
14262^512529-49783154287Enzo Doria10/2015
14272^512315-115297154223Enzo Doria06/2015
14282^512168+79561154178Enzo Doria06/2016
14294*10^154078-57154079Robert Price10/2018
14302^511658-114371154025Enzo Doria02/2015
1431(57^87719+1)/58154022Paul Bourdelais11/2017
14322^511580-1846679154001Enzo Doria07/2015
14332^511541-113713153990Enzo Doria09/2014
14342^511077-112723153850Enzo Doria06/2014
143569^83653-68^83653153826Robert Price12/2013
14362^510963-113707153816Enzo Doria09/2014
1437(154*10^153810-1)/9153812Serge Batalov12/2014
1438(181*25^109991-75077)/8153763Curtis Bright05/2015
14392*10^153746-3153747Robert Price07/2015
14402^510626+1179379153714Enzo Doria05/2016
1441(7*10^153664+113)/3153665Robert Price02/2018
14422^510420+81121153652Enzo Doria07/2016
1443(197*7^181761-1)/2153608Karsten Bonath05/2017
14442^509894-459161153494Enzo Doria05/2015
14452^509841+71657153478Enzo Doria04/2016
14462^509533-1846723153385Enzo Doria07/2015
14472^509468-39989153366Enzo Doria09/2015
144870^83117-69^83117153360Robert Price01/2014
1449(112*10^153025-1)/3153027Serge Batalov12/2014
14502^508174-1855151152976Enzo Doria09/2015
1451181^67757-2152974Lelio R Paula12/2017
14522^508160-1864829152972Enzo Doria01/2016
14532^507857-1848199152881Enzo Doria07/2015
14542^507638-115361152815Enzo Doria07/2015
14552^507551-114025152789Enzo Doria11/2014
1456(6^196337+1)/7152780Paul Bourdelais02/2010
1457(22*10^152670-13)/9152671Robert Price06/2018
14582^506451-22339152457Enzo Doria07/2013
14592^505995-113185152320Enzo Doria07/2014
1460(4*10^152253+149)/9152253Robert Price04/2018
1461578^55117-577^55117152230Jean-Louis Charton08/2012
14622^505431-505431152150Henri Lifchitz04/2005
14632^505053+73097152037Enzo Doria04/2016
1464(2^504793-7)/46765151954Lelio R Paula12/2017
1465350377#+797581151937Nicolas PALAU08/2017
14662^504618-343991151906Enzo Doria07/2015
14672^504212-461939151783Enzo Doria07/2015
14682^504054-2231151736Yves Minet10/2011
14692^503361-39883151527Enzo Doria09/2015
14702^503225+382667151486Enzo Doria10/2016
1471(26*10^151391-503)/9151392Robert Price07/2018
14722^502769+1877567151349Enzo Doria08/2016
14732^502576-4019151291Yves Minet10/2011
14745*10^151257+41151258Robert Price03/2019
14752^502290-2792501151205Enzo Doria02/2016
14762^502181+1868417151172Enzo Doria04/2016
14772^501781-1850503151052Enzo Doria08/2015
1478(5*10^151007+37)/3151008Robert Price03/2018
14792^501627-991151005Yves Minet02/2014
14802^501577-115333150990Enzo Doria07/2015
14818*10^150975+3150976Robert Price08/2015
14822^501512-113669150971Enzo Doria09/2014
1483(12^139739+1)/13150803Paul Bourdelais09/2011
1484(31^101111-1)/30150792Alexander Zhirkov11/2010
14852^500899-500899150786Henri Lifchitz04/2005
14862^500832+1876801150766Enzo Doria07/2016
1487(23*10^150763-59)/9150764Robert Price05/2018
14882^500699+1884953150726Enzo Doria02/2017
1489(13*10^150675-37)/3150676Robert Price01/2019
1490(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
14912^500337-71101150617Enzo Doria04/2016
14924*10^150577+91150578Robert Price08/2018
14932^500160+80071150564Enzo Doria06/2016
1494(2^500120+5)/9150551Lelio R Paula12/2017
1495(43*10^150515-421)/9150516Robert Price01/2019
1496(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
1497(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
14982^499861-29503150474Enzo Doria08/2015
14992^499653-113533150411Enzo Doria08/2014
15002^499534-221150375Yves Minet06/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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