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 ?
450130101^6630+6630^30101115032Hans Havermann01/2021
4502(89*10^115030-179)/9115031Robert Price12/2019
4503(2^381935+2774)/2114974Stefano Morozzi02/2021
450427300^16271+16271^27300114972Hans Havermann02/2021
45052^381883-59197114959Enzo Doria10/2015
450627423^15542+15542^27423114944Hans Havermann02/2021
4507(2^381820+1626)/2114939Stefano Morozzi09/2020
45092^381806-4481114936Yves Minet07/2011
45082^381808-1851507114936Enzo Doria08/2015
4510(2^381792+2502)/2114931Stefano Morozzi09/2020
45112^381774-112373114926Enzo Doria06/2014
451226341^22980+22980^26341114883Hans Havermann01/2021
45132^381555-109051114860Enzo Doria04/2014
45142^381546-113501114857Enzo Doria08/2014
4515(7*10^114845-19)/3114846Robert Price10/2020
451626675^20178+20178^26675114833Hans Havermann02/2021
4517(2^381436+1182)/2114824Stefano Morozzi09/2020
45183^240644+16114817Robert Price04/2020
45192^381360-110429114801Enzo Doria05/2014
4520(17*10^114795+79)/3114796Robert Price04/2019
4521(66^63079+1)/67114774Paul Bourdelais09/2017
45222^381252-115079114769Enzo Doria06/2015
4523(2^381251+3186)/2114768Stefano Morozzi09/2020
45242^381209-29323114756Enzo Doria07/2015
45252^381207-111546435114755Paul Bourdelais10/2021
4526569^41651-568^41651114754Jean-Louis Charton11/2009
45272^381201+1873205114753Enzo Doria06/2016
4528(85*10^114737+293)/9114738Robert Price12/2019
4529(265*10^114736+17)/3114738Robert Price03/2020
4530(2^381062+2170)/2114711Stefano Morozzi09/2020
45312^380974-112991114685Enzo Doria07/2014
453237097^1234+1234^37097114679Hans Havermann02/2021
453388^58949-87114626Norbert Schneider11/2015
4534(2^380773+662)/2114624Stefano Morozzi09/2020
453529913^6782+6782^29913114608Hans Havermann02/2021
4536(331*10^114605-7)/9114607Robert Price04/2022
45372^380700+91114603Lelio R Paula03/2013
4538(2^380632+2578)/2114582Stefano Morozzi09/2020
45397*10^114577+27114578Robert Price11/2020
454110^114575+3^114576114576Mike Oakes09/2010
454010^114575+66561114576Patrick De Geest02/2017
454210^114575-581081114575Patrick De Geest02/2017
45432^380587-115315114569Enzo Doria06/2015
454431874^3927+3927^31874114558Hans Havermann02/2021
45452^380513-216925114546Enzo Doria05/2014
45462^380451-1840087114528Enzo Doria06/2015
4547(2^380426+1510)/2114520Stefano Morozzi09/2020
4548(15*2^380388-1)/539114507Lelio R Paula04/2014
45492^380279-461347114476Enzo Doria07/2015
4550(331*10^114454-7)/9114456Robert Price04/2022
455127121^16590+16590^27121114447Hans Havermann01/2021
455225966^25555+25555^25966114445Hans Havermann01/2021
4553(11*10^114400+529)/9114401Robert Price09/2021
45542^380021+1871147114398Enzo Doria05/2016
45552^380005+1869707114393Enzo Doria05/2016
45562^379958-113297114379Enzo Doria07/2014
4557(2^379897+1274)/2114361Stefano Morozzi01/2021
45582^379881-109105114356Enzo Doria04/2014
4559(21*2^379857-1)/13114349Lelio R Paula03/2014
4560(4*10^114340+83)/3114341Robert Price02/2018
4561(26*10^114317-77)/3114318Robert Price11/2019
4562(4*10^114296+149)/9114296Robert Price04/2018
456388^58773-87114284Norbert Schneider11/2015
456427764^13065+13065^27764114280Hans Havermann01/2021
45652^379529-2790283114250Enzo Doria03/2016
45662^379522+1869115114248Enzo Doria05/2016
4567(145*10^114226-1)/9114228Serge Batalov12/2014
45682^379317-115033114186Enzo Doria06/2015
4569(22*10^114178+47)/3114179Robert Price06/2021
4570(17*2^379246-1)/17407114162Lelio R Paula03/2014
4571(2^379192+226)/2114148Stefano Morozzi09/2020
45726*10^114091+23114092Robert Price09/2020
4573(4*10^114076+143)/3114077Robert Price03/2018
4574(2^378820+3226)/2114036Stefano Morozzi01/2021
4575(2^378754+2058)/2114017Stefano Morozzi09/2020
4577(46*10^113969+683)/9113970Robert Price03/2019
4576(83*10^113969+133)/9113970Robert Price08/2021
457832226^3439+3439^32226113966Hans Havermann02/2021
4579(77*10^113963-149)/9113964Robert Price03/2022
458078*10^113954-7113956Robert Price10/2020
45812*10^113941+9113942Dmitry Domanov11/2010
458210^113933+145897113934Patrick De Geest02/2021
4585(2^378478+1642)/2113933Stefano Morozzi09/2020
458310^113933-8000000001113933Robert Price11/2020
458410^113933-66167113933Patrick De Geest02/2021
45862339662057597*10^113903+9113916Robert Price03/2021
45874*10^113905+91113906Robert Price08/2018
458810^113894+76609113895Patrick De Geest02/2021
459010^113894-10000001113894Robert Price09/2020
458910^113894-373947113894Patrick De Geest02/2021
459133933^2270+2270^33933113881Hans Havermann02/2021
45924*10^113874-21113875Robert Price09/2018
45932^378272-16565113872Enzo Doria04/2013
45942^378217-109075113855Enzo Doria04/2014
45952^378198+67113849Lelio R Paula03/2013
45962^378173-3249113842Yves Minet12/2014
4597(2^378155-5)/6597113833Lelio R Paula03/2014
459892941#+(355049#)/(92941#)113830Makoto Morimoto10/2017
459930030^6173+6173^30030113829Hans Havermann01/2021
46002^378128-262977113828Enzo Doria05/2014
46012^378123-113215113827Enzo Doria07/2014
46026^146274-18893113824Enzo Doria03/2013
460334596^1949+1949^34596113815Hans Havermann02/2021
46042^378078+75113813Lelio R Paula03/2013
4605(28*10^113810+449)/9113811Robert Price11/2021
460626273^21448+21448^26273113799Hans Havermann02/2021
46072^377966+255255113780Paul Bourdelais10/2021
46082^377940+63113772Lelio R Paula03/2013
46092^377941-2785843113772Enzo Doria04/2016
46102^377810+1875109113733Enzo Doria09/2016
46112^377803-1838635113731Enzo Doria05/2015
46122^377799+52223113729Yves Minet08/2010
4613(2^377791+3258)/2113727Stefano Morozzi02/2021
461411^109190-270113710Enzo Doria12/2012
461528206^10739+10739^28206113698Hans Havermann01/2021
46167*10^113693+9113694Robert Price09/2015
461713899^27442+27442^13899113692Norbert Schneider12/2020
4618(82*10^113681+161)/9113682Robert Price10/2019
461926121^22478+22478^26121113673Hans Havermann01/2021
46204*10^113658+49113659Robert Price01/2019
4621(10^113656+7)/40231/6439001113645Alfred Reich06/2021
4622(2*10^113631+529)/9113631Robert Price01/2018
46232^377408-2798279113612Enzo Doria04/2016
462413706^27459+27459^13706113596Norbert Schneider12/2020
46255*10^113586+57113587Robert Price12/2018
4626(2^377242+2794)/2113561Stefano Morozzi02/2021
46272^377222+93679113556Yves Minet02/2011
4629262147#+316847113552Makoto Morimoto02/2016
462827172^15101+15101^27172113552Hans Havermann01/2021
4630(2^377131+2018)/2113528Stefano Morozzi09/2020
46312^377026-458903113497Enzo Doria04/2015
4632(2^377014+2202)/2113493Stefano Morozzi09/2020
463334791^1828+1828^34791113488Hans Havermann02/2021
4634(2^376967+258)/2113479Stefano Morozzi09/2020
4635(29*10^113468-17)/3113469Robert Price09/2019
463635^73477-34^73477113454Robert Price05/2012
4637(14*10^113451-89)/3113452Robert Price05/2020
46382^376790+27113426Lelio R Paula03/2013
46392^376786-112701113424Enzo Doria06/2014
46402^376731+21113408Lelio R Paula03/2013
46419*10^113394-73113395Robert Price01/2021
464229660^6651+6651^29660113387Hans Havermann01/2021
46442^376634+1871245113379Enzo Doria05/2016
4643(4^188318+17)/3113379Robert Price02/2017
4645E(29532)/492842728006750534663978950979381235113367Thomas Ritschel01/2021
46462^376576-344369113361Enzo Doria07/2015
46472^376549-4543113353Yves Minet03/2019
4648(17*2^376526-1)/223113345Lelio R Paula03/2014
4649(27*2^376441-1)/811113319Lelio R Paula03/2014
4650(2^376350+3538)/2113293Stefano Morozzi09/2020
465127265^14272+14272^27265113273Hans Havermann02/2021
465232174^3315+3315^32174113269Hans Havermann02/2021
4653(2*10^113248+73)/3113248Robert Price09/2020
46542^376128-21237113226Enzo Doria06/2013
46555*10^113224-81113225Robert Price01/2019
465610^113220+51409113221Patrick De Geest02/2021
465810^113220-1000001113220Robert Price08/2020
465710^113220-61779113220Patrick De Geest02/2021
4659(2^376102+1578)/2113218Stefano Morozzi09/2020
4660(2^375996+3102)/2113186Stefano Morozzi09/2020
466137258^1091+1091^37258113184Hans Havermann02/2021
4662(94*10^113176+11)/3113178Robert Price04/2020
4663(46*10^113162+521)/9113163Robert Price02/2019
4664(2^375885+3614)/2113153Stefano Morozzi09/2020
4665(2^375873+2006)/2113149Stefano Morozzi09/2020
46663*10^113137+23113138Robert Price03/2022
4667(8*10^113135-269)/9113135Robert Price09/2021
4668(2^375726+694)/2113105Stefano Morozzi09/2020
466926050^21959+21959^26050113100Hans Havermann02/2021
46702^375638-1787171113079Enzo Doria03/2016
4671(2^375563+2178)/2113056Stefano Morozzi09/2020
46722^375537+4847113048Yves Minet02/2011
4673(17^91837+16^91837)/33113000Robert Price08/2013
46745*F(270343)*(F(270343)+1)+1112997Serge Batalov04/2015
46752^375350-3221112992Yves Minet07/2011
4676(13*2^375306+1)/7112979Lelio R Paula03/2014
46772^375305+76757112979Enzo Doria05/2016
46782^375258+1874989112964Enzo Doria07/2016
4679(29^77237-1)/28112950Robert Price04/2012
468026620^17483+17483^26620112939Hans Havermann01/2021
46812^375154+74959112933Enzo Doria04/2016
4682(266*10^112930-17)/3112932Robert Price07/2020
4683(2^375134+778)/2112927Stefano Morozzi09/2020
4684(85*10^112919+293)/9112920Robert Price12/2019
468529412^6899+6899^29412112907Hans Havermann02/2021
4686(191*10^112903-17)/3112905Robert Price11/2021
4687(2^375022+1210)/2112893Stefano Morozzi09/2020
468825992^22039+22039^25992112889Hans Havermann02/2021
46892^374993-2787163112885Enzo Doria11/2015
4690(697*10^112869+23)/9112871Robert Price04/2021
469130420^5111+5111^30420112813Hans Havermann02/2021
469213699^27268+27268^13699112800Norbert Schneider12/2020
4693123^53970+2112793Lelio R Paula06/2013
469428942^7887+7887^28942112785Hans Havermann01/2021
46952^374640-4685112778Yves Minet05/2019
469657290^93+93^57290112775Hans Havermann01/2021
4697(2^374556+682)/2112753Stefano Morozzi09/2020
4698p(22852)#/2+512112745Robert Price05/2017
4699(11*10^112742-131)/3112743Robert Price09/2018
47002^374441-21049112718Enzo Doria06/2013
47014*10^112706-93112707Robert Price07/2020
4702(2^374321+1)/3112682H.&R. Lifchitz12/2000
4703(2^374213+1766)/2112650Stefano Morozzi09/2020
4704(2^374094+2674)/2112614Stefano Morozzi09/2020
4705(13^101089-1)/12112607Paul Bourdelais03/2010
47063^236011-8828112606Enzo Doria05/2014
470731854^3427+3427^31854112602Hans Havermann02/2021
4708(85*10^112530-373)/9112531Robert Price05/2021
4709(2^373748+1090)/2112510Stefano Morozzi09/2020
4710(2^373727+1806)/2112503Stefano Morozzi01/2021
471127618^11821+11821^27618112479Hans Havermann01/2021
471226343^18580+18580^26343112460Hans Havermann01/2021
471339^70666+2112435Lelio R Paula11/2013
4714(134*10^112400+7)/3112402Robert Price02/2020
4715(2^373365+326)/2112394Stefano Morozzi09/2020
4716(2^373350-7)/3112390Lelio R Paula03/2014
47172^373306-1840931112377Enzo Doria06/2015
47188*10^112371-37112372Robert Price03/2022
4719(2^373262+270)/2112363Stefano Morozzi09/2020
47206*10^112359-79112360Robert Price03/2022
472134409^1842+1842^34409112356Hans Havermann02/2021
4722(142*10^112352-7)/9112354Robert Price12/2019
472325580^24633+24633^25580112336Hans Havermann01/2021
47242^373117+1872107112320Enzo Doria05/2016
4725(2^373083+2226)/2112309Stefano Morozzi01/2021
4726(35*10^112308+37)/9112309Robert Price05/2022
472727963^10376+10376^27963112301Hans Havermann01/2021
47282^373040+2792761112297Enzo Doria03/2016
4729EPrime(112280)112280Eric W. Weisstein10/2010
47302^372950+7112270Lelio R Paula03/2013
47312^372945+1872167112268Enzo Doria05/2016
473236274^1243+1243^36274112249Hans Havermann02/2021
4733(55*10^112246+629)/9112247Robert Price01/2022
4734(2^372872+3798)/2112246Stefano Morozzi02/2021
473525513^25060+25060^25513112232Hans Havermann02/2021
4736(53*10^112229-611)/9112230Robert Price02/2022
4737(2^372754+3094)/2112210Stefano Morozzi09/2020
47386*10^112208+43112209Robert Price07/2020
4739(2^372728+3058)/2112203Stefano Morozzi09/2020
474032061^3158+3158^32061112195Hans Havermann02/2021
47412^372695+72113112193Enzo Doria04/2016
47422^372689-2563112191Yves Minet07/2014
47432^372638-1859441112176Enzo Doria03/2016
47443^235074-113056112159Enzo Doria07/2014
4745-E(29242)/489848365125303139750087112140Thomas Ritschel01/2021
4746(2^372514+1822)/2112138Stefano Morozzi02/2021
474729468^6387+6387^29468112135Hans Havermann02/2021
4748(2^372428+3742)/2112112Stefano Morozzi01/2021
474925375^25454-25454^25375112110Norbert Schneider01/2021
4750131^52949-130112108Norbert Schneider02/2019


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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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