PRP Records

Probable Primes Top 10000

(301421 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 ?
7251(2^355562+1702)/2107035Stefano Morozzi09/2020
725210^107028+3593037107029Paul Bourdelais10/2021
725310^107028-43301107028Alfred Reich08/2024
72542^355524-21237107024Enzo Doria06/2013
7256(10223*2^355515+1)/4855107022Lelio R Paula07/2014
725524843^20320+20320^24843107022Hans Havermann10/2020
72572^355494-19901107015Enzo Doria06/2013
72582^355454-869688105107003Lelio R Paula01/2017
72594*10^106997+13106998Robert Price02/2021
7260(8*10^106985-629)/9106985Robert Price01/2022
72612^355366+54615106976Lelio R Paula01/2017
7262(31*2^355346-1)/1563106969Lelio R Paula03/2014
72632^355275-19861106949Enzo Doria06/2013
726427503^7738+7738^27503106949Hans Havermann11/2020
7265(85*10^106943+77)/9106944Robert Price07/2022
7266(9179*2^355234-1)/1915106937Lelio R Paula05/2015
72674*10^106914-93106915Robert Price07/2020
72684*10^106892-3106893Robert Price10/2015
7269(66^58741+1)/67106881Paul Bourdelais08/2017
72702^355001+335931106866Enzo Doria08/2024
72712^354946-3106850M. Frind & P. Underwood08/2002
7272(2^354945+3134)/2106849Stefano Morozzi09/2020
7273(46^64384+1)/(46^128+1)106843Martin Hopf12/2023
72742^354873-18693106828Enzo Doria05/2013
7275(2^354831+3186)/2106815Stefano Morozzi09/2020
72772^354828+4257106814Lelio R Paula01/2017
727625216^17217+17217^25216106814Hans Havermann10/2020
7278(2^354799+1218)/2106805Stefano Morozzi09/2020
7279436^40459+40459^436106791Norbert Schneider03/2019
7280(21^80761+1)/22106783Paul Bourdelais03/2010
7281(115*10^106772-7)/9106774Robert Price02/2020
72822^354640-354640+1106758Robert Price10/2014
7283(2^354603+2606)/2106746Stefano Morozzi09/2020
72842^354585+95106741Lelio R Paula10/2011
7285(206*10^106737+1)/9106739Robert Price04/2022
72862^354553+189106732Lelio R Paula10/2011
7288(2^354546+1338)/2106729Stefano Morozzi02/2021
7287(8*10^106729-71)/9106729Serge Batalov11/2022
72892^354514-109031106720Enzo Doria04/2014
72902^354509-109465106718Enzo Doria04/2014
7291fibonacci(510628)+2106715Jon Grantham08/2023
7292(15*2^354478-1)/26983106706Lelio R Paula03/2014
7293Phi(217618,10)/899798636917106693Makoto Kamada06/2019
729415^90710+28106684Lelio R Paula04/2017
72957^126237+34106683Lelio R Paula03/2017
72962^354385-115315106681Enzo Doria06/2015
72972^354327-19305106664Enzo Doria06/2013
7298(35*10^106649+1)/9106650Serge Batalov11/2010
729910^106636+97106637Lelio R Paula02/2017
730010^106636-22923106636Patrick De Geest03/2017
73012^354220-57106631Lelio R Paula10/2011
7302(68*10^106628-329)/9106629Robert Price03/2021
7303(29*10^106620-77)/3106621Robert Price02/2020
7304(746*10^106618+1)/9106620Robert Price03/2020
73052*10^106613+29106614Robert Price02/2021
73062^354157-17041106612Enzo Doria05/2013
730712^98778+73106600Lelio R Paula02/2017
730833333^1576+1576^33333106585Hans Havermann11/2020
73092^354064+1870651106584Enzo Doria05/2016
731024568^21779+21779^24568106577Hans Havermann11/2020
73112^353992-57106563Lelio R Paula10/2011
73129*10^106559+59106560Robert Price01/2020
73137*10^106553+27106554Robert Price11/2020
731428847^4938+4938^28847106548Hans Havermann10/2020
7315NSW(139160)106535Robert Price12/2018
7316f(278321)106535Robert Price07/2023
7317(7*10^106516+113)/3106517Robert Price02/2018
73182^353832-1853849106515Enzo Doria09/2015
7319(7^126037-1)/6106513Paul Bourdelais09/2008
73202^353794-18453106503Enzo Doria05/2013
7321(2^353761+2094)/2106493Stefano Morozzi09/2020
73222^353728+7695106483Lelio R Paula01/2017
732326476^10509+10509^26476106475Hans Havermann10/2020
73242^353672-303106466Yves Minet02/2012
73256^136811+101106460Lelio R Paula02/2017
73262^353641+1871981106457Enzo Doria05/2016
7327(8*10^106454-29)/3106455Robert Price07/2018
732827845^6654+6654^27845106454Hans Havermann11/2020
732910^106449-700001106449Robert Price08/2021
733025316^16017+16017^25316106444Hans Havermann11/2020
73312^353553+54615106431Lelio R Paula01/2017
73322^353544-18897106428Enzo Doria05/2013
733328894^4823+4823^28894106426Hans Havermann11/2020
7334(19*10^106422+29)/3106423Robert Price12/2021
7335(694*10^106418+53)/9106420Robert Price02/2022
73366*10^106412-13106413Robert Price07/2022
733725696^13829+13829^25696106402Hans Havermann11/2020
73386^136729-133106396Lelio R Paula02/2017
73392^353418+1605106390Lelio R Paula01/2017
73402^353387+65106381Lelio R Paula10/2011
73412^353372+74311106376Enzo Doria04/2016
73422^353344-3693106368Yves Minet03/2017
7343(772*10^106365-7)/9106367Robert Price06/2022
7344(56*10^106351+619)/9106352Robert Price05/2021
73452^353277-20089106347Enzo Doria06/2013
73462^353275+72173106347Enzo Doria04/2016
73472^353268-17705106345Enzo Doria05/2013
73482^353267-19857106344Enzo Doria06/2013
7349(46*10^106343+143)/9106344Robert Price01/2019
7350(2^353189+3054)/2106321Stefano Morozzi09/2020
735135087^1072+1072^35087106321Hans Havermann10/2020
7352(2^353184+1290)/2106319Stefano Morozzi01/2021
7353F(508799)/24738824977/1990778864897106310Serge Batalov07/2024
735426985^8684+8684^26985106287Hans Havermann10/2020
7355(2^353051+606)/2106279Stefano Morozzi09/2020
7357222748^3+3^222748106278Anatoly F. Selevich12/2010
7356(46*10^106277+107)/9106278Robert Price06/2022
7358(9179*2^353019-1)/9106273Lelio R Paula05/2015
73592^353025+72257106272Enzo Doria04/2016
73622^352932-20345106244Enzo Doria06/2013
7360(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
736125628^13983+13983^25628106244Hans Havermann10/2020
73632^352883-187106229Lelio R Paula10/2011
736420^81649-19^81649106228Jean-Louis Charton03/2011
7365(55*10^106222+377)/9106223Robert Price02/2019
73662^352814-131106208Lelio R Paula10/2011
73672^352752+73951106189Enzo Doria04/2016
736811876*25^75945+357106171Eric Chen10/2023
73696^136434+5106167Lelio R Paula11/2014
737025296^15737+15737^25296106166Hans Havermann09/2020
73718*10^106157-13106158Robert Price08/2019
73722^352641+225677106156Enzo Doria08/2024
73737*5^151872-8106155Lelio R Paula11/2014
7374105^52520-2106153Lelio R Paula10/2017
7375(23*10^106152-29)/3106153Robert Price03/2022
73762^352601-1604809106144Enzo Doria05/2015
737712^98353-43106141Lelio R Paula02/2017
73782^352585-18901106139Enzo Doria05/2013
737926363^10614+10614^26363106135Hans Havermann09/2020
7380(2^352554-3)/193106128Lelio R Paula12/2013
73812^352540+15015106126Lelio R Paula01/2017
738225068^17119+17119^25068106125Hans Havermann09/2020
73832^352524-3149106121Yves Minet10/2014
7384(7*10^106119-67)/3106120Robert Price10/2021
73852^352486-1858781106109Enzo Doria04/2016
73862^352444+12705106097Lelio R Paula01/2017
738728561^5182+5182^28561106090Hans Havermann10/2020
7388(182*10^106083+43)/9106085Robert Price02/2020
7389(266*10^106066+1)/3106068Robert Price04/2020
7390(7*10^106066-187)/9106066Tyler Busby01/2023
73912^352228-18953106032Enzo Doria05/2013
7392(2^352223+1118)/2106030Stefano Morozzi09/2020
7393(2^352212+2250)/2106027Stefano Morozzi01/2021
7394(2^352136+2638)/2106004Stefano Morozzi09/2020
73952^352107+1872533105995Enzo Doria05/2016
7396(2^352096+2086)/2105992Stefano Morozzi09/2020
73972^352066-2591105983Yves Minet07/2014
73982^352030+715105972Lelio R Paula10/2011
73999*6^136176-5105967Lelio R Paula11/2014
740017099*2^351991+58329105965Paul Vanderveen12/2017
7401122^50789-50789^122105965Norman Luhn09/2024
740228582^5097+5097^28582105963Hans Havermann09/2020
7403155^48377+2105962Lelio R Paula08/2013
7404(23*10^105944-119)/3105945Robert Price07/2021
74052^351865+1869707105922Enzo Doria05/2016
740624974^17427+17427^24974105921Hans Havermann09/2020
740725163^16194+16194^25163105920Hans Havermann09/2020
74082^351831+23105912Lelio R Paula10/2011
7409(2^351818+3798)/2105908Stefano Morozzi02/2021
74109*2^351784-5105899Lelio R Paula09/2014
7411(2^351776+2766)/2105895Stefano Morozzi01/2021
7412(85*10^105881+203)/9105882Robert Price09/2020
74132^351671-112387105864Enzo Doria06/2014
74142^351669-109501105863Enzo Doria04/2014
74152^351644+74731105856Enzo Doria04/2016
741613^95025-42105853Lelio R Paula12/2016
74172^351599+15015105842Lelio R Paula01/2017
741819^82763+90105834Lelio R Paula01/2017
7419(205*10^105831-1)/3105833Robert Price11/2021
742026050^11551+11551^26050105832Hans Havermann09/2020
7421(9179*2^351540-1)/221105826Lelio R Paula05/2015
742220^81329-51105812Lelio R Paula01/2017
7423(5*10^105811+211)/9105811Robert Price02/2018
74242^351483+28425105807Lelio R Paula01/2017
742525231^15610+15610^25231105804Hans Havermann09/2020
742615^89960+86105802Lelio R Paula02/2017
74272^351460-17289105801Enzo Doria05/2013
742819^82735+22105798Lelio R Paula01/2017
74292^351435-109077105793Enzo Doria04/2014
74302^351393+1089105780Lelio R Paula01/2017
74312^351364+72631105772Enzo Doria04/2016
7432(2^351333+3626)/2105762Stefano Morozzi09/2020
743326818^8783+8783^26818105761Hans Havermann09/2020
74362^351305+1872467105754Enzo Doria05/2016
74353^221649+16105754Lelio R Paula11/2016
743432511^1790+1790^32511105754Hans Havermann09/2020
74378*3^221637-5105749Lelio R Paula09/2014
74382^351279-2780449105746Enzo Doria03/2016
7439(2^351263+3198)/2105741Stefano Morozzi09/2020
744015^89903-26105735Lelio R Paula02/2017
74422^351213-73105726Lelio R Paula10/2011
7441(2^351214+1210)/2105726Stefano Morozzi09/2020
74432^351192-4589105720Yves Minet07/2011
744420^81250-33105709Lelio R Paula12/2016
7445(2^351133+3530)/2105702Stefano Morozzi09/2020
7446(2^351103+534)/2105693Stefano Morozzi09/2020
74472^351076-113159105685Enzo Doria07/2014
744893^53688-2105684Lelio R Paula09/2013
74492^351060-4559105680Yves Minet07/2011
7450((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
745111^101473-750105674Enzo Doria11/2012
74523*5^151181-8105672Lelio R Paula11/2014
745315^89831-34105650Lelio R Paula02/2017
745511^101448-360105648Enzo Doria08/2012
74543*7^125011+4105648Lelio R Paula11/2014
74562^350943-113269105645Enzo Doria07/2014
74572*10^105636-91105637Robert Price04/2020
745824231^22880+22880^24231105634Hans Havermann09/2020
745935296^983+983^35296105626Hans Havermann09/2020
74602^350868-19725105622Enzo Doria06/2013
74612^350858-59291105619Enzo Doria10/2015
7462V(758484)/1516967/19720583105618Serge Batalov07/2024
74632^350851+135105617Lelio R Paula10/2011
74642^350841-741105614Lelio R Paula01/2017
74653*10^105582+77105583Robert Price09/2018
746624915^17284+17284^24915105581Hans Havermann09/2020
7467(5*10^105576-53)/3105577Robert Price09/2020
74688*10^105571+3105572Robert Price08/2015
74692^350674-78557105564Jorge Menendez03/2018
74702*5^151026-3105563Lelio R Paula11/2014
7471(2^350702+5)/34264674063105562Lelio R Paula12/2013
74726^135647-5^135647105554Jean-Louis Charton02/2009
74733^221211+236105545Lelio R Paula11/2016
7474(32*10^105530-77)/9105531Robert Price06/2018
747510^105515+33105516Lelio R Paula11/2016
747624644^19125+19125^24644105516Hans Havermann10/2020
747710^105515-41033105515Patrick De Geest12/2016
7478(29*2^350473-1)/267927105499Lelio R Paula03/2014
74792^350455-430567105498Harrison Mesh06/2022
748017^85732-72105489Lelio R Paula01/2017
7481(2^350399+3618)/2105481Stefano Morozzi09/2020
7482(2^350379+1010)/2105475Stefano Morozzi09/2020
74832^350356+24241105468Enzo Doria10/2023
748425233^15118+15118^25233105462Hans Havermann09/2020
748526261^10366+10366^26261105454Hans Havermann09/2020
74862^350307-110329105453Enzo Doria05/2014
74872^350253-20365105437Enzo Doria06/2013
7488(3*29^72089-1075)/4105423Curtis Bright05/2015
7489(2^350187+2658)/2105417Stefano Morozzi09/2020
74904*10^105415-69105416Robert Price01/2022
749121^79725-22105414Anonymous09/2024
7492(22*10^105407+179)/3105408Robert Price02/2022
74932^350139-109009105403Enzo Doria04/2014
7494(2^350129+3026)/2105400Stefano Morozzi09/2020
7495(2^350097+2070)/2105390Stefano Morozzi09/2020
74963*5^150763+4105380Lelio R Paula11/2014
749712^97643+91105375Lelio R Paula02/2017
74986*5^150744-7105367Lelio R Paula11/2014
7499(2^350018+2074)/2105366Stefano Morozzi09/2020
75004*10^105364-39105365Robert Price09/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 19 2025 12:52 (Time in France)

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