PRP Records

Probable Primes Top 10000

(291192 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 ?
2001(26*10^164643-167)/3164644Robert Price10/2019
2002(10^164643+83)/3164643Robert Price08/2021
20032^546398-59201164483Enzo Doria10/2015
20042^546332-114893164463Enzo Doria05/2015
2005(65*10^164427+277)/9164428Robert Price08/2021
20062^545958+1876189164350Enzo Doria07/2016
20072^545878-49841164326Enzo Doria10/2015
2008(10^164284+77)/3164284Robert Price01/2018
20092^545668-4019164263Yves Minet04/2017
201010^164216+780639164217Patrick De Geest08/2021
201210^164216-50000000001164216Robert Price12/2020
201110^164216-891051164216Patrick De Geest08/2021
2013(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
2014(16*10^164122+197)/3164123Robert Price04/2019
20152^545185+76757164118Enzo Doria05/2016
20162^545076-114329164085Enzo Doria01/2015
2017(2*10^164043-143)/3164043Robert Price03/2018
2018(29^112153+1)/30164011Lelio R Paula03/2017
20192^544757+1874777163989Enzo Doria06/2016
20202^544444-457199163894Enzo Doria01/2015
20212^544264-343529163840Enzo Doria07/2015
20227*10^163780+9163781Robert Price09/2015
20232^543989+2793047163758Enzo Doria02/2016
2024(28*10^163709+113)/3163710Robert Price03/2020
2025(23*10^163523+301)/9163524Robert Price06/2021
2026(68*10^163521-329)/9163522Robert Price03/2021
202735820^35899+35899^35820163489Norbert Schneider11/2021
20282^542870-69551163421Enzo Doria12/2015
20292^542395+72533163278Enzo Doria04/2016
20302^542072-3683163180Yves Minet03/2017
2031(682*10^163106-7)/9163108Robert Price08/2021
20322^541779-1867357163092Enzo Doria04/2016
2033(29*10^163056+313)/9163057Robert Price04/2021
20348*10^162924+9162925Robert Price12/2015
20352^540905+81557162829Enzo Doria08/2016
20362^540628-2939162746Yves Minet09/2014
2037919^54919-918^54919162743Jean-Louis Charton01/2013
2038(203*10^162689+1)/3162691Robert Price03/2020
20393*10^162620-59162621Robert Price09/2018
20403^340694-112960162553Enzo Doria07/2014
20412^539807-114081162499Enzo Doria12/2014
2042414^62093+62093^414162498Norbert Schneider03/2022
20432^539654-114893162453Enzo Doria05/2015
20449*10^162449-71162450Robert Price11/2020
20452^539617-1851583162441Enzo Doria08/2015
2046(509*10^162422+31)/9162424Robert Price08/2022
2047(91*10^162410+11)/3162412Robert Price02/2020
20482^539346+81049162360Enzo Doria07/2016
20492^539220-115499162322Enzo Doria07/2015
20502^539217-113713162321Enzo Doria09/2014
20519^170099-8^170099162316Jean-Louis Charton05/2005
20524*10^162263-39162264Robert Price09/2020
2053(115*10^162153-1)/3162155Serge Batalov12/2014
2054(10^162138+11)/3162138Serge Batalov07/2015
2055(61*10^162100-403)/9162101Robert Price10/2021
20562^538473-112723162097Enzo Doria06/2014
20572^538157+79337162002Enzo Doria06/2016
20582^538136-114749161996Enzo Doria05/2015
20592^538104+1531161986Lelio R Paula01/2013
2060(9*29^110727-1199)/14161927Curtis Bright05/2015
20612^537815-22737161899Enzo Doria07/2013
20622^537804-39839161896Enzo Doria09/2015
2063(754*10^161816-7)/9161818Robert Price05/2020
20642^537458-59201161791Enzo Doria10/2015
20652*10^161766+51161767Robert Price05/2018
2066(7*10^161760+131)/3161761Robert Price06/2020
20672^537209-49849161717Enzo Doria10/2015
2068(58*10^161691+329)/9161692Robert Price05/2019
206923*10^161668-3161670Robert Price10/2021
20702^536937+1879397161635Enzo Doria09/2016
207134*10^161593-9161595Robert Price06/2020
2072(31*10^161582-1)/3161584Robert Price02/2020
20732^536569-22881161524Enzo Doria07/2013
2074(46*10^161505+593)/9161506Robert Price04/2022
207510^161253+573493161254Patrick De Geest07/2018
207610^161253-8001161253Robert Price03/2018
207797*10^161247-3161249Robert Price05/2020
20787*10^161192-9161193Robert Price10/2015
20792^535415-19161176Stefano Morozzi07/2022
20802^535269-113803161133Enzo Doria09/2014
20812^535205-23295161113Enzo Doria08/2013
2082(49*10^161105+437)/9161106Robert Price09/2021
2083(89^82609+1)/90161036Paul Bourdelais10/2017
20842^534429-19160880Stefano Morozzi07/2022
20852^534359-23229160859Enzo Doria08/2013
2086457^60454+60454^457160803Norbert Schneider07/2021
20878*10^160782+53160783Robert Price08/2020
208867^88037-66^88037160763Robert Price10/2013
2089(88*10^160761-637)/9160762Robert Price11/2020
20902^533948-1852559160735Enzo Doria08/2015
20912^533665-23335160650Enzo Doria08/2013
2092(19*10^160619+77)/3160620Robert Price05/2019
20932^533350-5160555Stefano Morozzi07/2022
2094(38*10^160508+151)/9160509Robert Price03/2022
20953^336353-2^336353160482Mike Oakes10/2007
20962*10^160339-63160340Robert Price01/2022
2097(91*10^160249+11)/3160251Robert Price02/2020
2098(772*10^160239-7)/9160241Robert Price06/2022
2099(2*10^160226+187)/9160226Robert Price06/2022
21002^532253+1868417160225Enzo Doria04/2016
21012^532108-291989160181Enzo Doria07/2015
2102(28*10^160171-79)/3160172Robert Price02/2021
2103(26*10^160166-131)/3160167Robert Price10/2019
210455*10^160145+9160147Robert Price03/2022
2105(17*10^160143+67)/3160144Robert Price01/2019
2106(19*10^159921-49)/3159922Robert Price05/2019
21072^531110-1853771159881Enzo Doria09/2015
2108(275^65536+53^65536)/2159864Kellen Shenton11/2020
21092^530992-1845299159845Enzo Doria07/2015
21102^530810+25159790Stefano Morozzi04/2021
2111(136*10^159736-1)/9159738Serge Batalov12/2014
21122^530417-113833159672Enzo Doria09/2014
21132^530406-69701159669Enzo Doria02/2016
21145*10^159656+41159657Robert Price03/2019
21158*10^159614+29159615Robert Price11/2021
21167^188858-188858^7159604Norbert Schneider05/2018
2117(24^115597-1)/23159547Paul Bourdelais09/2017
2118(17*10^159438-377)/9159439Robert Price03/2018
2119(203*10^159381+1)/3159383Robert Price03/2020
212089*10^159258-9159260Robert Price05/2020
21212^528944-461315159229Enzo Doria07/2015
2122(13*10^159147+161)/3159148Robert Price11/2018
21232^528620-113879159131Enzo Doria10/2014
2124(47*10^159083+259)/9159084Robert Price03/2022
21252^528000-23307158944Enzo Doria08/2013
2126(29*10^158909+61)/9158910Robert Price08/2018
21272^527817+1876817158889Enzo Doria07/2016
21282^527774-49451158876Enzo Doria10/2015
21292^527745-291553158868Enzo Doria07/2015
2130(91*10^158862+11)/3158864Robert Price02/2020
21312^527644-1856999158837Enzo Doria10/2015
2132(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
21332^527573-1863253158816Enzo Doria12/2015
21342^527553-23401158810Enzo Doria08/2013
2135(49*10^158783+437)/9158784Robert Price09/2021
213610^158755+310207158756Patrick De Geest08/2021
213710^158755-50001158755Robert Price08/2020
2138(61*10^158748-619)/9158749Robert Price03/2022
213911^152420-210158730Enzo Doria09/2012
2140(13*10^158694+401)/9158695Robert Price01/2018
21412^527052-69059158659Enzo Doria11/2015
21422^526849-113233158598Enzo Doria07/2014
2143(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
2144(299*10^158544-17)/3158546Robert Price04/2020
21452^526658-3551158540Yves Minet03/2017
21467*10^158465-11158466Robert Price06/2019
21472^526375-23115158455Enzo Doria08/2013
2148(77*10^158407-293)/9158408Robert Price09/2019
21492^526028-112793158351Enzo Doria07/2014
2150(229*10^158339-1)/3158341Robert Price07/2020
21512^525690-9221158249Lelio R Paula01/2013
21522*10^158242-7158243Robert Price10/2015
21532^525667-525667^2158242Henri Lifchitz12/2017
2154(56*10^158230+187)/9158231Robert Price10/2021
215510^158209-7000000001158209Robert Price12/2021
21562^525186-1857431158097Enzo Doria10/2015
21572^524515-23245157895Enzo Doria08/2013
21582^524499-109087157890Enzo Doria04/2014
21592^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
21602^524288+189093157827Makoto Morimoto01/2016
21612^524288-164073157827Matthias Baur03/2020
2162(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
2163(10^157792+359)/9157792Serge Batalov12/2014
21642^524154+25157787Stefano Morozzi04/2021
21652^523924+1876591157717Enzo Doria07/2016
2166(17*10^157705+67)/3157706Robert Price01/2019
2167(46^94841+1)/47157696Robert Price01/2014
21682^523774+77839157672Enzo Doria05/2016
21692^523587+2799143157616Enzo Doria04/2016
21702^523371+1872113157551Enzo Doria05/2016
21718*10^157477+27157478Robert Price09/2021
2172(8*10^157368+49)/3157369Robert Price05/2020
2173(82*10^157319+449)/9157320Robert Price11/2019
21742^522535-351457157299Enzo Doria07/2015
21752^522226+2799079157206Enzo Doria04/2016
2176(134*10^157191-11)/3157193Robert Price01/2022
21772^522134-1849451157178Enzo Doria08/2015
21789*10^157152+71157153Robert Price08/2020
21794*10^157150+93157151Robert Price08/2018
21802^521401-29593156958Enzo Doria08/2015
21817*10^156956+87156957Robert Price07/2019
21822^521348-23397156942Enzo Doria08/2013
218310^156902+34509156903Patrick De Geest08/2021
218510^156902-80000001156902Robert Price04/2021
218410^156902-69789156902Patrick De Geest08/2021
2186(98^78797+1)/99156901Paul Bourdelais12/2017
218765^86522+64156857Lelio R Paula04/2016
21888^173687-7^173687156855Jean-Louis Charton09/2004
21892^520977-1858183156830Enzo Doria10/2015
2190(8*10^156718-101)/3156719Robert Price08/2018
2191(10^156640+7)/53156639Alfred Reich07/2021
21922^520314-1849481156631Enzo Doria08/2015
2193(16*10^156563-637)/9156564Robert Price09/2022
2194(13*10^156522+89)/3156523Robert Price09/2018
2195(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
2196(2^519925-5)/3156513Stefano Morozzi08/2022
2197(4*10^156501+119)/3156502Robert Price12/2021
2198(83*10^156476-101)/9156477Robert Price08/2021
21993*10^156435-97156436Robert Price07/2018
2200(8*10^156371-77)/3156372Robert Price07/2018
220153^90679-52^90679156356Robert Price01/2013
2202(418*10^156309-31)/9156311Robert Price05/2022
22032^519106-59141156267Enzo Doria10/2015
22042^519053+6077156251Enzo Doria02/2016
22052^518968-1860989156225Enzo Doria11/2015
2206(25*10^156221-7)/9156222Robert Price05/2018
22072^518931-2782297156214Enzo Doria09/2015
22082^518608-2939156117Yves Minet09/2014
220910*27^109005+697156027Curtis Bright05/2015
2210(49*10^155933-319)/9155934Robert Price10/2021
22112^517967-113485155924Enzo Doria08/2014
2212(103*10^155904+17)/3155906Robert Price08/2020
2213(8*10^155887-719)/9155887Robert Price03/2021
22144*10^155853-39155854Robert Price09/2020
22152^517698+4429155843Lelio R Paula01/2013
22162^517543-113257155796Enzo Doria07/2014
2217(14*10^155740-143)/3155741Robert Price11/2018
221831^104309-30^104309155563Henri Lifchitz08/2013
22192^516742-39851155555Enzo Doria09/2015
2220(22*10^155543+47)/3155544Robert Price06/2021
2221(19*10^155504+131)/3155505Robert Price06/2020
22227*10^155496+61155497Robert Price08/2019
22232^516440+1878421155464Enzo Doria08/2016
22242^515863-1867237155291Enzo Doria03/2016
22252^515786-461861155268Enzo Doria07/2015
22262^515644-113247155225Enzo Doria07/2014
2227(7*10^155203+107)/3155204Robert Price02/2018
222810^155163+206871155164Patrick De Geest05/2021
222910^155163-40001155163Robert Price01/2021
2230(17*10^155133-89)/9155134Robert Price07/2018
22312^515227-114997155099Enzo Doria06/2015
2233EPrime(155025)155025Eric W. Weisstein10/2010
2232(14*10^155024-221)/9155025Robert Price04/2018
2234(4*10^155022+173)/3155023Robert Price02/2018
2235(266*10^154897+1)/3154899Robert Price04/2020
2236(115*10^154869-1)/3154871Serge Batalov12/2014
2237(86*10^154853-221)/9154854Robert Price09/2019
22382^514361+78167154839Enzo Doria05/2016
22392^514281-115033154815Enzo Doria06/2015
22402^514194-3311154788Yves Minet12/2014
2241(14*10^154773+37)/3154774Robert Price12/2018
2242(16*10^154748+131)/3154749Robert Price03/2022
22436*10^154742-31154743Robert Price07/2020
2244(14*10^154645+139)/9154646Robert Price11/2021
22455*10^154618-79154619Robert Price03/2021
2246(167*10^154595+1)/3154597Robert Price04/2021
22472^513437+1879337154560Enzo Doria09/2016
22482^513306-113201154521Enzo Doria07/2014
2249(10^154494-13)/3154494Robert Price12/2017
22502^513042-113787154442Enzo Doria09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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