PRP Records

Probable Primes Top 10000

(292102 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 ?
4751(26*10^114317-77)/3114318Robert Price11/2019
4752(4*10^114296+149)/9114296Robert Price04/2018
475388^58773-87114284Norbert Schneider11/2015
475427764^13065+13065^27764114280Hans Havermann01/2021
47552^379529-2790283114250Enzo Doria03/2016
47562^379522+1869115114248Enzo Doria05/2016
4757(145*10^114226-1)/9114228Serge Batalov12/2014
47582^379317-115033114186Enzo Doria06/2015
4759(22*10^114178+47)/3114179Robert Price06/2021
4760(17*2^379246-1)/17407114162Lelio R Paula03/2014
4761(2^379192+226)/2114148Stefano Morozzi09/2020
47626*10^114091+23114092Robert Price09/2020
4763(4*10^114076+143)/3114077Robert Price03/2018
4764(2^378820+3226)/2114036Stefano Morozzi01/2021
4765(2^378754+2058)/2114017Stefano Morozzi09/2020
476613643^27572-27572^13643114008Norbert Schneider12/2022
4768(46*10^113969+683)/9113970Robert Price03/2019
4767(83*10^113969+133)/9113970Robert Price08/2021
476932226^3439+3439^32226113966Hans Havermann02/2021
4770(77*10^113963-149)/9113964Robert Price03/2022
477178*10^113954-7113956Robert Price10/2020
47722*10^113941+9113942Dmitry Domanov11/2010
477310^113933+145897113934Patrick De Geest02/2021
4776(2^378478+1642)/2113933Stefano Morozzi09/2020
477410^113933-8000000001113933Robert Price11/2020
477510^113933-66167113933Patrick De Geest02/2021
47772339662057597*10^113903+9113916Robert Price03/2021
47784*10^113905+91113906Robert Price08/2018
477910^113894+76609113895Patrick De Geest02/2021
478110^113894-10000001113894Robert Price09/2020
478010^113894-373947113894Patrick De Geest02/2021
478233933^2270+2270^33933113881Hans Havermann02/2021
47834*10^113874-21113875Robert Price09/2018
47842^378272-16565113872Enzo Doria04/2013
47852^378217-109075113855Enzo Doria04/2014
47862^378198+67113849Lelio R Paula03/2013
47872^378173-3249113842Yves Minet12/2014
4788(2^378155-5)/6597113833Lelio R Paula03/2014
478992941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
479030030^6173+6173^30030113829Hans Havermann01/2021
47912^378128-262977113828Enzo Doria05/2014
47922^378123-113215113827Enzo Doria07/2014
47936^146274-18893113824Enzo Doria03/2013
479434596^1949+1949^34596113815Hans Havermann02/2021
47952^378078+75113813Lelio R Paula03/2013
4796(28*10^113810+449)/9113811Robert Price11/2021
479726273^21448+21448^26273113799Hans Havermann02/2021
47982^377966+255255113780Paul Bourdelais10/2021
47992^377940+63113772Lelio R Paula03/2013
48002^377941-2785843113772Enzo Doria04/2016
4801(7*10^113757+11)/9113757Tyler Busby01/2023
48022^377810+1875109113733Enzo Doria09/2016
48032^377803-1838635113731Enzo Doria05/2015
48042^377799+52223113729Yves Minet08/2010
4805(2^377791+3258)/2113727Stefano Morozzi02/2021
480611^109190-270113710Enzo Doria12/2012
480728206^10739+10739^28206113698Hans Havermann01/2021
48087*10^113693+9113694Robert Price09/2015
480913899^27442+27442^13899113692Norbert Schneider12/2020
4810(82*10^113681+161)/9113682Robert Price10/2019
481126121^22478+22478^26121113673Hans Havermann01/2021
48124*10^113658+49113659Robert Price01/2019
4813(10^113656+7)/40231/6439001113645Alfred Reich06/2021
4814(2*10^113631+529)/9113631Robert Price01/2018
48152^377408-2798279113612Enzo Doria04/2016
481613706^27459+27459^13706113596Norbert Schneider12/2020
48175*10^113586+57113587Robert Price12/2018
4818(2^377242+2794)/2113561Stefano Morozzi02/2021
48192^377222+93679113556Yves Minet02/2011
4821262147#+316847113552Makoto Morimoto02/2016
482027172^15101+15101^27172113552Hans Havermann01/2021
4822(2^377131+2018)/2113528Stefano Morozzi09/2020
48232^377026-458903113497Enzo Doria04/2015
4824(2^377014+2202)/2113493Stefano Morozzi09/2020
482534791^1828+1828^34791113488Hans Havermann02/2021
4826(2^376967+258)/2113479Stefano Morozzi09/2020
4827(29*10^113468-17)/3113469Robert Price09/2019
482835^73477-34^73477113454Robert Price05/2012
4829(14*10^113451-89)/3113452Robert Price05/2020
48302^376790+27113426Lelio R Paula03/2013
48312^376786-112701113424Enzo Doria06/2014
48322^376731+21113408Lelio R Paula03/2013
48339*10^113394-73113395Robert Price01/2021
483429660^6651+6651^29660113387Hans Havermann01/2021
48362^376634+1871245113379Enzo Doria05/2016
4835(4^188318+17)/3113379Robert Price02/2017
4837E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
48382^376576-344369113361Enzo Doria07/2015
48392^376549-4543113353Yves Minet03/2019
4840(17*2^376526-1)/223113345Lelio R Paula03/2014
4841(27*2^376441-1)/811113319Lelio R Paula03/2014
4842(2^376350+3538)/2113293Stefano Morozzi09/2020
484327265^14272+14272^27265113273Hans Havermann02/2021
484432174^3315+3315^32174113269Hans Havermann02/2021
4845(2*10^113248+73)/3113248Robert Price09/2020
48462^376128-21237113226Enzo Doria06/2013
48475*10^113224-81113225Robert Price01/2019
484810^113220+51409113221Patrick De Geest02/2021
485010^113220-1000001113220Robert Price08/2020
484910^113220-61779113220Patrick De Geest02/2021
4851(2^376102+1578)/2113218Stefano Morozzi09/2020
4852(2^375996+3102)/2113186Stefano Morozzi09/2020
485337258^1091+1091^37258113184Hans Havermann02/2021
4854(94*10^113176+11)/3113178Robert Price04/2020
4855(46*10^113162+521)/9113163Robert Price02/2019
4856(2^375885+3614)/2113153Stefano Morozzi09/2020
4857(2^375873+2006)/2113149Stefano Morozzi09/2020
48583*10^113137+23113138Robert Price03/2022
4859(8*10^113135-269)/9113135Robert Price09/2021
4860(2^375726+694)/2113105Stefano Morozzi09/2020
486126050^21959+21959^26050113100Hans Havermann02/2021
48622^375638-1787171113079Enzo Doria03/2016
4863(2^375563+2178)/2113056Stefano Morozzi09/2020
48642^375537+4847113048Yves Minet02/2011
4865(17^91837+16^91837)/33113000Robert Price08/2013
48665*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
48672^375350-3221112992Yves Minet07/2011
4868(13*2^375306+1)/7112979Lelio R Paula03/2014
48692^375305+76757112979Enzo Doria05/2016
48702^375258+1874989112964Enzo Doria07/2016
4871(29^77237-1)/28112950Robert Price04/2012
487226620^17483+17483^26620112939Hans Havermann01/2021
48732^375154+74959112933Enzo Doria04/2016
4874(266*10^112930-17)/3112932Robert Price07/2020
4875(2^375134+778)/2112927Stefano Morozzi09/2020
4876(85*10^112919+293)/9112920Robert Price12/2019
487729412^6899+6899^29412112907Hans Havermann02/2021
4878(191*10^112903-17)/3112905Robert Price11/2021
4879(2^375022+1210)/2112893Stefano Morozzi09/2020
488025992^22039+22039^25992112889Hans Havermann02/2021
48812^374993-2787163112885Enzo Doria11/2015
4882(697*10^112869+23)/9112871Robert Price04/2021
4883(19*10^112851+377)/9112852Alfred Reich11/2022
488430420^5111+5111^30420112813Hans Havermann02/2021
488513699^27268+27268^13699112800Norbert Schneider12/2020
4886123^53970+2112793Lelio R Paula06/2013
488728942^7887+7887^28942112785Hans Havermann01/2021
48882^374640-4685112778Yves Minet05/2019
488957290^93+93^57290112775Hans Havermann01/2021
489013608^27277-27277^13608112758Norbert Schneider12/2022
4891(2^374556+682)/2112753Stefano Morozzi09/2020
4892p(22852)#/2+512112745Robert Price05/2017
4893(11*10^112742-131)/3112743Robert Price09/2018
48942^374441-21049112718Enzo Doria06/2013
48954*10^112706-93112707Robert Price07/2020
4896(2^374321+1)/3112682H.&R. Lifchitz12/2000
4897(2^374213+1766)/2112650Stefano Morozzi09/2020
4898(2^374094+2674)/2112614Stefano Morozzi09/2020
4899(13^101089-1)/12112607Paul Bourdelais03/2010
49003^236011-8828112606Enzo Doria05/2014
490131854^3427+3427^31854112602Hans Havermann02/2021
4902(85*10^112530-373)/9112531Robert Price05/2021
4903(2^373748+1090)/2112510Stefano Morozzi09/2020
4904(2^373727+1806)/2112503Stefano Morozzi01/2021
490527618^11821+11821^27618112479Hans Havermann01/2021
490626343^18580+18580^26343112460Hans Havermann01/2021
490739^70666+2112435Lelio R Paula11/2013
4908(134*10^112400+7)/3112402Robert Price02/2020
4909(2^373365+326)/2112394Stefano Morozzi09/2020
4910(2^373350-7)/3112390Lelio R Paula03/2014
49112^373306-1840931112377Enzo Doria06/2015
49128*10^112371-37112372Robert Price03/2022
4913(2^373262+270)/2112363Stefano Morozzi09/2020
49146*10^112359-79112360Robert Price03/2022
491534409^1842+1842^34409112356Hans Havermann02/2021
4916(142*10^112352-7)/9112354Robert Price12/2019
491725580^24633+24633^25580112336Hans Havermann01/2021
49182^373117+1872107112320Enzo Doria05/2016
4919(2^373083+2226)/2112309Stefano Morozzi01/2021
4920(35*10^112308+37)/9112309Robert Price05/2022
492127963^10376+10376^27963112301Hans Havermann01/2021
49222^373040+2792761112297Enzo Doria03/2016
4923EPrime(112280)112280Eric W. Weisstein10/2010
49242^372950+7112270Lelio R Paula03/2013
49252^372945+1872167112268Enzo Doria05/2016
492636274^1243+1243^36274112249Hans Havermann02/2021
4927(55*10^112246+629)/9112247Robert Price01/2022
4928(2^372872+3798)/2112246Stefano Morozzi02/2021
492925513^25060+25060^25513112232Hans Havermann02/2021
4930(53*10^112229-611)/9112230Robert Price02/2022
4931(2^372754+3094)/2112210Stefano Morozzi09/2020
49326*10^112208+43112209Robert Price07/2020
4933(2^372728+3058)/2112203Stefano Morozzi09/2020
493432061^3158+3158^32061112195Hans Havermann02/2021
49352^372695+72113112193Enzo Doria04/2016
49362^372689-2563112191Yves Minet07/2014
49372^372638-1859441112176Enzo Doria03/2016
49383^235074-113056112159Enzo Doria07/2014
4939-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
4940(2^372514+1822)/2112138Stefano Morozzi02/2021
494129468^6387+6387^29468112135Hans Havermann02/2021
4942(2^372428+3742)/2112112Stefano Morozzi01/2021
494325375^25454-25454^25375112110Norbert Schneider01/2021
4944131^52949-130112108Norbert Schneider02/2019
4945(91*10^112098-1)/9112100Robert Price04/2015
4946(68*10^112087-149)/9112088Robert Price07/2022
49472^372310-85061112077Paul Bourdelais02/2012
4948(10^112067+53)/9112067Serge Batalov07/2015
4949(2^372237+2082)/2112055Stefano Morozzi09/2020
495075^59760+2112054Lelio R Paula08/2013
4951(2^372200+1710)/2112044Stefano Morozzi09/2020
4952(10^112048+7)/8747/373157112039Alfred Reich06/2021
4953(2^372181+2250)/2112038Stefano Morozzi01/2021
4954(2^372161+2574)/2112032Stefano Morozzi09/2020
49558*10^112018-49112019Robert Price08/2019
49572^372108+74221112016Enzo Doria04/2016
4956(2^372109+2046)/2112016Stefano Morozzi09/2020
49588*10^112011-73112012Robert Price01/2022
4959(184*10^112007-1)/3112009Robert Price02/2020
49605*10^112003+81112004Robert Price03/2019
4961215^48018+48018^215112000Norbert Schneider10/2018
496225549^24148+24148^25549111979Hans Havermann02/2021
49632^371970-459491111975Enzo Doria05/2015
496441^69427-40^69427111971Robert Price07/2012
4965(2^371782+358)/2111918Stefano Morozzi01/2021
4966(34*10^111902-547)/9111903Robert Price03/2021
4967(10^111902+71)/9111902Serge Batalov07/2015
4968(2^371625+1610)/2111870Stefano Morozzi09/2020
496929080^7027+7027^29080111865Hans Havermann01/2021
497031307^3730+3730^31307111820Hans Havermann02/2021
49712^371440-112865111815Enzo Doria06/2014
49722^371426-459161111811Enzo Doria05/2015
497325768^21771+21771^25768111779Hans Havermann02/2021
497428022^9747+9747^28022111777Hans Havermann02/2021
4975(94*10^111770+11)/3111772Robert Price04/2020
49762^371276-461267111766Enzo Doria07/2015
49776*10^111760+43111761Robert Price07/2020
497898079!4-1024111747Robert Price11/2019
4979(2^371186+3162)/2111738Stefano Morozzi09/2020
49802^371098-113261111712Enzo Doria07/2014
4981(7*10^111706-61)/9111706Erik Branger01/2011
49822^371044+1869391111696Enzo Doria05/2016
498326310^17581+17581^26310111688Hans Havermann01/2021
498488^57416+87111645Norbert Schneider11/2015
49852^370829-109693111631Enzo Doria04/2014
498615^94906-2111619Lelio R Paula11/2013
498725835^20904+20904^25835111614Hans Havermann02/2021
4988(2^370726+1198)/2111600Stefano Morozzi09/2020
498927758^10479+10479^27758111597Hans Havermann02/2021
49902^370695-4627111591Yves Minet05/2019
49917*10^111579-87111580Robert Price06/2020
49932^370643-37111575Yves Minet01/2012
4992(2^370655-5)/2439111575Lelio R Paula03/2014
49942^370610-3911111565Yves Minet04/2017
4995(154*10^111549+17)/9111551Robert Price06/2022
499626200^18097+18097^26200111550Hans Havermann01/2021
4997286^45405+45405^286111532Norbert Schneider04/2015
49984*5^159563-9111531Lelio R Paula11/2014
49995*10^111528-21111529Robert Price12/2021
5000(4^185225+23)/3111517Robert Price10/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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