PRP Records

Probable Primes Top 10000

(301692 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 ?
75012^353832-1853849106515Enzo Doria09/2015
7502(7^126037-1)/6106513Paul Bourdelais09/2008
75032^353794-18453106503Enzo Doria05/2013
7504(2^353761+2094)/2106493Stefano Morozzi09/2020
75052^353728+7695106483Lelio R Paula01/2017
750626476^10509+10509^26476106475Hans Havermann10/2020
75072^353672-303106466Yves Minet02/2012
75086^136811+101106460Lelio R Paula02/2017
75092^353641+1871981106457Enzo Doria05/2016
7510(8*10^106454-29)/3106455Robert Price07/2018
751127845^6654+6654^27845106454Hans Havermann11/2020
751210^106449-700001106449Robert Price08/2021
751325316^16017+16017^25316106444Hans Havermann11/2020
75142^353553+54615106431Lelio R Paula01/2017
75152^353544-18897106428Enzo Doria05/2013
751628894^4823+4823^28894106426Hans Havermann11/2020
7517(19*10^106422+29)/3106423Robert Price12/2021
7518(694*10^106418+53)/9106420Robert Price02/2022
75196*10^106412-13106413Robert Price07/2022
752025696^13829+13829^25696106402Hans Havermann11/2020
75216^136729-133106396Lelio R Paula02/2017
75222^353418+1605106390Lelio R Paula01/2017
75232^353387+65106381Lelio R Paula10/2011
75242^353372+74311106376Enzo Doria04/2016
75252^353344-3693106368Yves Minet03/2017
7526(772*10^106365-7)/9106367Robert Price06/2022
7527(56*10^106351+619)/9106352Robert Price05/2021
75282^353277-20089106347Enzo Doria06/2013
75292^353275+72173106347Enzo Doria04/2016
75302^353268-17705106345Enzo Doria05/2013
75312^353267-19857106344Enzo Doria06/2013
7532(46*10^106343+143)/9106344Robert Price01/2019
7534(2^353189+3054)/2106321Stefano Morozzi09/2020
753335087^1072+1072^35087106321Hans Havermann10/2020
7535(2^353184+1290)/2106319Stefano Morozzi01/2021
7536F(508799)/24738824977/1990778864897106310Serge Batalov07/2024
753726985^8684+8684^26985106287Hans Havermann10/2020
7538(2^353051+606)/2106279Stefano Morozzi09/2020
7540222748^3+3^222748106278Anatoly F. Selevich12/2010
7539(46*10^106277+107)/9106278Robert Price06/2022
7541(9179*2^353019-1)/9106273Lelio R Paula05/2015
75422^353025+72257106272Enzo Doria04/2016
75452^352932-20345106244Enzo Doria06/2013
7543(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
754425628^13983+13983^25628106244Hans Havermann10/2020
75462^352883-187106229Lelio R Paula10/2011
754720^81649-19^81649106228Jean-Louis Charton03/2011
7548(55*10^106222+377)/9106223Robert Price02/2019
75492^352814-131106208Lelio R Paula10/2011
75502^352752+73951106189Enzo Doria04/2016
755111876*25^75945+357106171Eric Chen10/2023
75526^136434+5106167Lelio R Paula11/2014
755325296^15737+15737^25296106166Hans Havermann09/2020
75548*10^106157-13106158Robert Price08/2019
75552^352641+225677106156Enzo Doria08/2024
75567*5^151872-8106155Lelio R Paula11/2014
7557105^52520-2106153Lelio R Paula10/2017
7558(23*10^106152-29)/3106153Robert Price03/2022
75592^352601-1604809106144Enzo Doria05/2015
756012^98353-43106141Lelio R Paula02/2017
75612^352585-18901106139Enzo Doria05/2013
756226363^10614+10614^26363106135Hans Havermann09/2020
7563(2^352554-3)/193106128Lelio R Paula12/2013
75642^352540+15015106126Lelio R Paula01/2017
756525068^17119+17119^25068106125Hans Havermann09/2020
75662^352524-3149106121Yves Minet10/2014
7567(7*10^106119-67)/3106120Robert Price10/2021
75682^352486-1858781106109Enzo Doria04/2016
75692^352444+12705106097Lelio R Paula01/2017
757028561^5182+5182^28561106090Hans Havermann10/2020
7571(182*10^106083+43)/9106085Robert Price02/2020
7572(266*10^106066+1)/3106068Robert Price04/2020
7573(7*10^106066-187)/9106066Tyler Busby01/2023
75742^352228-18953106032Enzo Doria05/2013
7575(2^352223+1118)/2106030Stefano Morozzi09/2020
7576(2^352212+2250)/2106027Stefano Morozzi01/2021
7577(2^352136+2638)/2106004Stefano Morozzi09/2020
75782^352107+1872533105995Enzo Doria05/2016
7579(2^352096+2086)/2105992Stefano Morozzi09/2020
75802^352066-2591105983Yves Minet07/2014
75812^352030+715105972Lelio R Paula10/2011
75829*6^136176-5105967Lelio R Paula11/2014
758317099*2^351991+58329105965Paul Vanderveen12/2017
7584122^50789-50789^122105965Norman Luhn09/2024
758528582^5097+5097^28582105963Hans Havermann09/2020
7586155^48377+2105962Lelio R Paula08/2013
7587(23*10^105944-119)/3105945Robert Price07/2021
75882^351865+1869707105922Enzo Doria05/2016
758924974^17427+17427^24974105921Hans Havermann09/2020
759025163^16194+16194^25163105920Hans Havermann09/2020
75912^351831+23105912Lelio R Paula10/2011
7592(2^351818+3798)/2105908Stefano Morozzi02/2021
75939*2^351784-5105899Lelio R Paula09/2014
7594(2^351776+2766)/2105895Stefano Morozzi01/2021
7595(85*10^105881+203)/9105882Robert Price09/2020
75962^351671-112387105864Enzo Doria06/2014
75972^351669-109501105863Enzo Doria04/2014
75982^351644+74731105856Enzo Doria04/2016
759913^95025-42105853Lelio R Paula12/2016
76002^351599+15015105842Lelio R Paula01/2017
760119^82763+90105834Lelio R Paula01/2017
7602(205*10^105831-1)/3105833Robert Price11/2021
760326050^11551+11551^26050105832Hans Havermann09/2020
7604(9179*2^351540-1)/221105826Lelio R Paula05/2015
760520^81329-51105812Lelio R Paula01/2017
7606(5*10^105811+211)/9105811Robert Price02/2018
76072^351483+28425105807Lelio R Paula01/2017
760825231^15610+15610^25231105804Hans Havermann09/2020
760915^89960+86105802Lelio R Paula02/2017
76102^351460-17289105801Enzo Doria05/2013
761119^82735+22105798Lelio R Paula01/2017
76122^351435-109077105793Enzo Doria04/2014
76132^351393+1089105780Lelio R Paula01/2017
76142^351364+72631105772Enzo Doria04/2016
7615(2^351333+3626)/2105762Stefano Morozzi09/2020
761626818^8783+8783^26818105761Hans Havermann09/2020
76192^351305+1872467105754Enzo Doria05/2016
76183^221649+16105754Lelio R Paula11/2016
761732511^1790+1790^32511105754Hans Havermann09/2020
76208*3^221637-5105749Lelio R Paula09/2014
76212^351279-2780449105746Enzo Doria03/2016
7622(2^351263+3198)/2105741Stefano Morozzi09/2020
762315^89903-26105735Lelio R Paula02/2017
76252^351213-73105726Lelio R Paula10/2011
7624(2^351214+1210)/2105726Stefano Morozzi09/2020
76262^351192-4589105720Yves Minet07/2011
762720^81250-33105709Lelio R Paula12/2016
7628(2^351133+3530)/2105702Stefano Morozzi09/2020
7629(2^351103+534)/2105693Stefano Morozzi09/2020
76302^351076-113159105685Enzo Doria07/2014
763193^53688-2105684Lelio R Paula09/2013
76322^351060-4559105680Yves Minet07/2011
7633((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
763411^101473-750105674Enzo Doria11/2012
76353*5^151181-8105672Lelio R Paula11/2014
763615^89831-34105650Lelio R Paula02/2017
763811^101448-360105648Enzo Doria08/2012
76373*7^125011+4105648Lelio R Paula11/2014
76392^350943-113269105645Enzo Doria07/2014
76402*10^105636-91105637Robert Price04/2020
764124231^22880+22880^24231105634Hans Havermann09/2020
764235296^983+983^35296105626Hans Havermann09/2020
76432^350868-19725105622Enzo Doria06/2013
76442^350858-59291105619Enzo Doria10/2015
7645V(758484)/1516967/19720583105618Serge Batalov07/2024
76462^350851+135105617Lelio R Paula10/2011
76472^350841-741105614Lelio R Paula01/2017
76483*10^105582+77105583Robert Price09/2018
764924915^17284+17284^24915105581Hans Havermann09/2020
7650(5*10^105576-53)/3105577Robert Price09/2020
76518*10^105571+3105572Robert Price08/2015
76522^350674-78557105564Jorge Menendez03/2018
76532*5^151026-3105563Lelio R Paula11/2014
7654(2^350702+5)/34264674063105562Lelio R Paula12/2013
76556^135647-5^135647105554Jean-Louis Charton02/2009
76563^221211+236105545Lelio R Paula11/2016
7657(32*10^105530-77)/9105531Robert Price06/2018
765810^105515+33105516Lelio R Paula11/2016
765924644^19125+19125^24644105516Hans Havermann10/2020
766010^105515-41033105515Patrick De Geest12/2016
7661(29*2^350473-1)/267927105499Lelio R Paula03/2014
76622^350455-430567105498Harrison Mesh06/2022
766317^85732-72105489Lelio R Paula01/2017
7664(2^350399+3618)/2105481Stefano Morozzi09/2020
7665(2^350379+1010)/2105475Stefano Morozzi09/2020
76662^350356+24241105468Enzo Doria10/2023
766725233^15118+15118^25233105462Hans Havermann09/2020
766826261^10366+10366^26261105454Hans Havermann09/2020
76692^350307-110329105453Enzo Doria05/2014
76702^350253-20365105437Enzo Doria06/2013
7671(3*29^72089-1075)/4105423Curtis Bright05/2015
7672(2^350187+2658)/2105417Stefano Morozzi09/2020
76734*10^105415-69105416Robert Price01/2022
767421^79725-22105414Anonymous09/2024
7675(22*10^105407+179)/3105408Robert Price02/2022
76762^350139-109009105403Enzo Doria04/2014
7677(2^350129+3026)/2105400Stefano Morozzi09/2020
7678(2^350097+2070)/2105390Stefano Morozzi09/2020
76793*5^150763+4105380Lelio R Paula11/2014
768012^97643+91105375Lelio R Paula02/2017
76816*5^150744-7105367Lelio R Paula11/2014
7682(2^350018+2074)/2105366Stefano Morozzi09/2020
76834*10^105364-39105365Robert Price09/2020
76852^349996-112169105360Enzo Doria06/2014
7684(2^349997+3702)/2105360Stefano Morozzi09/2020
7686(418*10^105343+23)/9105345Robert Price02/2020
768725490^13563+13563^25490105334Hans Havermann10/2020
7688(5^504004)%F(504004)105330Henri Lifchitz06/2025
768911^101142-1080105329Enzo Doria12/2012
7690(68*10^105320-41)/9105321Robert Price10/2013
769124800^17649+17649^24800105319Hans Havermann09/2020
76923^220712-9934105307Enzo Doria05/2014
76937*10^105296+9105297Robert Price09/2015
769489*10^105284-7105286Robert Price04/2020
76952^349739+1873373105282Enzo Doria06/2016
76967^124574+24105278Lelio R Paula11/2016
76972^349708-20957105273Enzo Doria06/2013
769834115^1218+1218^34115105267Hans Havermann09/2020
769924029^24029-24020^24020105265Henri Lifchitz09/2024
77002^349649-20469105255Enzo Doria06/2013
77012^349607-20109105243Enzo Doria06/2013
7702(85*10^105242+473)/9105243Robert Price01/2020
77032^349594-19085105239Enzo Doria05/2013
77042^349530+1874479105220Enzo Doria06/2016
7705(3^220528+8)/8081105215Lelio R Paula12/2013
7706(106*10^105199+17)/3105201Robert Price04/2021
7707(2^349452+3570)/2105196Stefano Morozzi09/2020
77083^220464-112852105189Enzo Doria07/2014
77092^349419-17349105186Enzo Doria05/2013
77102^349400-2579105180Yves Minet07/2014
77118*5^150471+3105176Lelio R Paula11/2014
7712(2^349359+2298)/2105168Stefano Morozzi02/2021
7713655^37342+37342^655105165Norbert Schneider08/2018
771413^94403+94105160Lelio R Paula12/2016
77152^349301-112309105151Enzo Doria06/2014
771630291^2960+2960^30291105149Hans Havermann09/2020
771727350^6981+6981^27350105132Hans Havermann09/2020
77199*2^349220+5105127Lelio R Paula09/2014
7718(2^349225+3122)/2105127Stefano Morozzi09/2020
77207*3^220317+8105119Lelio R Paula09/2014
77217^124386+88105119Lelio R Paula11/2016
7722(2^349197+570)/2105119Stefano Morozzi09/2020
77232^349171-19657105111Enzo Doria06/2013
7724(2^349115+590)/2105094Stefano Morozzi09/2020
7725(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
7726(2^349111-5)/3105093Lelio R Paula12/2013
7727675^37142+37142^675105087Norbert Schneider08/2018
77282^348981-2797573105054Enzo Doria04/2016
7729(445^39667+1)/446105050Jinyuan Wang05/2024
77302^348869-6555105021Lelio R Paula01/2017
773110^105003-17319105003Alfred Reich08/2024
77325^150217+78104998Lelio R Paula11/2016
7733(88*10^104989-1)/3104991Robert Price04/2020
7734(28*10^104972+149)/3104973Robert Price12/2019
773524927^16262+16262^24927104972Hans Havermann10/2020
77362^348703-113005104971Enzo Doria06/2014
7737(191*10^104956-17)/3104958Robert Price11/2021
77382^348612-809104943Yves Minet05/2013
7739(73*10^104942-1)/9104943Robert Price01/2015
77402^348583-350407104934Enzo Doria06/2015
77412^348531-949104919Yves Minet05/2012
774220^80636-59104910Lelio R Paula12/2016
77438*10^104893-13104894Robert Price08/2019
77452^348437+35104890Lelio R Paula09/2011
774425208^14487+14487^25208104890Hans Havermann09/2020
77462^348348+135104864Lelio R Paula09/2011
7747(29*10^104858+349)/9104859Robert Price06/2021
77486*10^104852-31104853Robert Price07/2020
7750(2^348284+9)/25104843Lelio R Paula12/2013
774975^55914-74104843Norbert Schneider01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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