PRP Records

Probable Primes Top 10000

(301822 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 ?
77512^350943-113269105645Enzo Doria07/2014
77522*10^105636-91105637Robert Price04/2020
775324231^22880+22880^24231105634Hans Havermann09/2020
775435296^983+983^35296105626Hans Havermann09/2020
77552^350868-19725105622Enzo Doria06/2013
77562^350858-59291105619Enzo Doria10/2015
7757V(758484)/1516967/19720583105618Serge Batalov07/2024
77582^350851+135105617Lelio R Paula10/2011
77592^350841-741105614Lelio R Paula01/2017
77603*10^105582+77105583Robert Price09/2018
776124915^17284+17284^24915105581Hans Havermann09/2020
7762(5*10^105576-53)/3105577Robert Price09/2020
77638*10^105571+3105572Robert Price08/2015
77642^350674-78557105564Jorge Menendez03/2018
77652*5^151026-3105563Lelio R Paula11/2014
7766(2^350702+5)/34264674063105562Lelio R Paula12/2013
77676^135647-5^135647105554Jean-Louis Charton02/2009
77683^221211+236105545Lelio R Paula11/2016
7769(32*10^105530-77)/9105531Robert Price06/2018
777010^105515+33105516Lelio R Paula11/2016
777124644^19125+19125^24644105516Hans Havermann10/2020
777210^105515-41033105515Patrick De Geest12/2016
7773(29*2^350473-1)/267927105499Lelio R Paula03/2014
77742^350455-430567105498Harrison Mesh06/2022
777517^85732-72105489Lelio R Paula01/2017
7776(2^350399+3618)/2105481Stefano Morozzi09/2020
7777(2^350379+1010)/2105475Stefano Morozzi09/2020
77782^350356+24241105468Enzo Doria10/2023
777925233^15118+15118^25233105462Hans Havermann09/2020
778026261^10366+10366^26261105454Hans Havermann09/2020
77812^350307-110329105453Enzo Doria05/2014
77822^350253-20365105437Enzo Doria06/2013
7783(3*29^72089-1075)/4105423Curtis Bright05/2015
7784(2^350187+2658)/2105417Stefano Morozzi09/2020
77854*10^105415-69105416Robert Price01/2022
778621^79725-22105414Anonymous09/2024
7787(22*10^105407+179)/3105408Robert Price02/2022
77882^350139-109009105403Enzo Doria04/2014
7789(2^350129+3026)/2105400Stefano Morozzi09/2020
7790(2^350097+2070)/2105390Stefano Morozzi09/2020
77913*5^150763+4105380Lelio R Paula11/2014
779212^97643+91105375Lelio R Paula02/2017
77936*5^150744-7105367Lelio R Paula11/2014
7794(2^350018+2074)/2105366Stefano Morozzi09/2020
77954*10^105364-39105365Robert Price09/2020
77972^349996-112169105360Enzo Doria06/2014
7796(2^349997+3702)/2105360Stefano Morozzi09/2020
7798(418*10^105343+23)/9105345Robert Price02/2020
779925490^13563+13563^25490105334Hans Havermann10/2020
7800(5^504004)%F(504004)105330Henri Lifchitz06/2025
780111^101142-1080105329Enzo Doria12/2012
7802(68*10^105320-41)/9105321Robert Price10/2013
780324800^17649+17649^24800105319Hans Havermann09/2020
78043^220712-9934105307Enzo Doria05/2014
78057*10^105296+9105297Robert Price09/2015
780689*10^105284-7105286Robert Price04/2020
78072^349739+1873373105282Enzo Doria06/2016
78087^124574+24105278Lelio R Paula11/2016
78092^349708-20957105273Enzo Doria06/2013
781034115^1218+1218^34115105267Hans Havermann09/2020
781124029^24029-24020^24020105265Henri Lifchitz09/2024
78122^349649-20469105255Enzo Doria06/2013
78132^349607-20109105243Enzo Doria06/2013
7814(85*10^105242+473)/9105243Robert Price01/2020
78152^349594-19085105239Enzo Doria05/2013
78162^349530+1874479105220Enzo Doria06/2016
7817(3^220528+8)/8081105215Lelio R Paula12/2013
7818(106*10^105199+17)/3105201Robert Price04/2021
7819(2^349452+3570)/2105196Stefano Morozzi09/2020
78203^220464-112852105189Enzo Doria07/2014
78212^349419-17349105186Enzo Doria05/2013
78222^349400-2579105180Yves Minet07/2014
78238*5^150471+3105176Lelio R Paula11/2014
7824(2^349359+2298)/2105168Stefano Morozzi02/2021
7825655^37342+37342^655105165Norbert Schneider08/2018
782613^94403+94105160Lelio R Paula12/2016
78272^349301-112309105151Enzo Doria06/2014
782830291^2960+2960^30291105149Hans Havermann09/2020
782927350^6981+6981^27350105132Hans Havermann09/2020
78319*2^349220+5105127Lelio R Paula09/2014
7830(2^349225+3122)/2105127Stefano Morozzi09/2020
78327*3^220317+8105119Lelio R Paula09/2014
78337^124386+88105119Lelio R Paula11/2016
7834(2^349197+570)/2105119Stefano Morozzi09/2020
78352^349171-19657105111Enzo Doria06/2013
7836(2^349115+590)/2105094Stefano Morozzi09/2020
7837(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
7838(2^349111-5)/3105093Lelio R Paula12/2013
7839675^37142+37142^675105087Norbert Schneider08/2018
78402^348981-2797573105054Enzo Doria04/2016
7841(445^39667+1)/446105050Jinyuan Wang05/2024
78422^348869-6555105021Lelio R Paula01/2017
784310^105003-17319105003Alfred Reich08/2024
78445^150217+78104998Lelio R Paula11/2016
7845(88*10^104989-1)/3104991Robert Price04/2020
7846(28*10^104972+149)/3104973Robert Price12/2019
784724927^16262+16262^24927104972Hans Havermann10/2020
78482^348703-113005104971Enzo Doria06/2014
7849(191*10^104956-17)/3104958Robert Price11/2021
78502^348612-809104943Yves Minet05/2013
7851(73*10^104942-1)/9104943Robert Price01/2015
78522^348583-350407104934Enzo Doria06/2015
78532^348531-949104919Yves Minet05/2012
785420^80636-59104910Lelio R Paula12/2016
78558*10^104893-13104894Robert Price08/2019
78572^348437+35104890Lelio R Paula09/2011
785625208^14487+14487^25208104890Hans Havermann09/2020
78582^348348+135104864Lelio R Paula09/2011
7859(29*10^104858+349)/9104859Robert Price06/2021
78606*10^104852-31104853Robert Price07/2020
7862(2^348284+9)/25104843Lelio R Paula12/2013
786175^55914-74104843Norbert Schneider01/2015
78632^348268+255255104840Lelio R Paula01/2017
786435540^891+891^35540104839Hans Havermann09/2020
78655^149985-52104836Lelio R Paula11/2016
78662^348224-20249104826Enzo Doria06/2013
7867(2^348217+2522)/2104824Stefano Morozzi09/2020
78682^348212-20105104823Enzo Doria06/2013
786924647^17898+17898^24647104819Hans Havermann10/2020
787020^80562+19104814Lelio R Paula12/2016
78712*10^104811-87104812Robert Price04/2018
78722^348149-20053104804Enzo Doria06/2013
78732^348095-171104788Lelio R Paula09/2011
787425383^13412+13412^25383104769Hans Havermann09/2020
78752^348003-20377104760Enzo Doria06/2013
787626^74036-27104759Anonymous09/2024
78782^347994-741104757Lelio R Paula12/2016
7877(2^347993+2234)/2104757Stefano Morozzi01/2021
7879(2^347990+790)/2104756Stefano Morozzi09/2020
788025137^14702+14702^25137104756Hans Havermann09/2020
7881(13*2^347972-1)/282309104746Lelio R Paula03/2014
788212883^25484-25484^12883104740Norbert Schneider08/2022
78832^347910-109937104732Enzo Doria04/2014
7884(88*10^104709-637)/9104710Robert Price11/2020
7885(13*10^104702+71)/3104703Robert Price06/2021
78865^149794+28104702Lelio R Paula11/2016
7887105^51800-2104698Lelio R Paula10/2017
7888(16^86939+3^86939)/19104684Robert Price06/2013
7889(15^89009-1)/14104682Paul Bourdelais03/2010
78902^347731-18609104678Enzo Doria05/2013
78914*6^134519+7104677Lelio R Paula11/2014
7892(34*10^104672-259)/9104673Robert Price12/2021
789325321^13588+13588^25321104656Hans Havermann09/2020
78942^347625+5367104646Riley Fisher04/2023
78952^347612-18545104642Enzo Doria05/2013
78966^134465+95104635Lelio R Paula11/2016
7897(2^347588+3718)/2104635Stefano Morozzi09/2020
7898(166*10^104633-7)/3104635Robert Price11/2020
7899V(750972)/15019441104621Serge Batalov07/2024
79002^347517-17301104614Enzo Doria05/2013
7901(2^347493+3186)/2104606Stefano Morozzi09/2020
7902(2^347490+2574)/2104605Stefano Morozzi09/2020
79033^219222-310104596Lelio R Paula11/2016
790425993^10554+10554^25993104581Hans Havermann09/2020
7905(15*2^347399-1)/13104578Lelio R Paula03/2014
79062^347372-17853104570Enzo Doria05/2013
79072^347314+99104552Lelio R Paula09/2011
79082^347300-22233104548Enzo Doria06/2013
79092^347287-19845104544Enzo Doria06/2013
79102^347258-231191104536Harrison Mesh06/2022
7911(31*2^347254-1)/891104533Lelio R Paula03/2014
79125*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
79137*2^347239-3104531Lelio R Paula09/2014
7914(3^219098-8)/514147439969104525Lelio R Paula12/2013
79155*3^219047+8104513Lelio R Paula09/2014
79162^347148-109073104502Enzo Doria04/2014
79172^347129-20145104497Enzo Doria06/2013
79184*10^104461-57104462Robert Price10/2018
79192^346999+198831104458Stefano Morozzi11/2024
79202^346996+166273104457Stefano Morozzi11/2024
79212^346997+105755104457Stefano Morozzi11/2024
79222^346997+115259104457Stefano Morozzi11/2024
79232^346992+97515104456Stefano Morozzi11/2024
79242^346992+169593104456Stefano Morozzi11/2024
79252^346994+182215104456Stefano Morozzi11/2024
79262^346994+187933104456Stefano Morozzi11/2024
7927(7*10^(2*52227+1)+9*10^52227-7)/9104455Robert Price10/2023
7930(2^346989+590)/2104454Stefano Morozzi09/2020
79282^346988+295104454Stefano Morozzi11/2024
79292^346988+47241104454Stefano Morozzi11/2024
79312^346983+4203104453Stefano Morozzi11/2024
79322^346983+119259104453Stefano Morozzi11/2024
79332^346983+47729104453Stefano Morozzi11/2024
79342^346985+124437104453Stefano Morozzi11/2024
79352^346979+72443104452Stefano Morozzi11/2024
79362^346980+167731104452Stefano Morozzi11/2024
79372^346978+64933104451Stefano Morozzi11/2024
79382^346974+105865104450Stefano Morozzi11/2024
79392^346972+95343104449Stefano Morozzi11/2024
79402^346966+63519104448Stefano Morozzi11/2024
79412^346963+42825104447Stefano Morozzi11/2024
79422^346963+140153104447Stefano Morozzi11/2024
79432^346965+144537104447Stefano Morozzi11/2024
79442^346962+128917104446Stefano Morozzi11/2024
79452^346956+110455104445Stefano Morozzi11/2024
79462^346956+72711104445Stefano Morozzi11/2024
79472^346954+178093104444Stefano Morozzi11/2024
79482^346955+46205104444Stefano Morozzi11/2024
79492^346954+186043104444Stefano Morozzi11/2024
79502^346949+140865104443Stefano Morozzi11/2024
79512^346950+79857104443Stefano Morozzi11/2024
79522^346951+161939104443Stefano Morozzi11/2024
79532^346950+143647104443Stefano Morozzi11/2024
79542^346950+103369104443Stefano Morozzi11/2024
79552^346952+128895104443Stefano Morozzi11/2024
79562^346946+106593104442Stefano Morozzi11/2024
79572^346947+63431104442Stefano Morozzi11/2024
79582^346947+75735104442Stefano Morozzi11/2024
79592^346948+135547104442Stefano Morozzi11/2024
79602^346944+20295104441Stefano Morozzi11/2024
79612^346944+93783104441Stefano Morozzi11/2024
79622^346939+116879104440Stefano Morozzi11/2024
79632^346939+138489104440Stefano Morozzi11/2024
79642^346940+40675104440Stefano Morozzi11/2024
79652^346942+108495104440Stefano Morozzi11/2024
79662^346942+137535104440Stefano Morozzi11/2024
79672^346936+78235104439Stefano Morozzi11/2024
79682^346936+156271104439Stefano Morozzi11/2024
79692^346937+180909104439Stefano Morozzi11/2024
79702^346938+159885104439Stefano Morozzi11/2024
79712^346933+7865104438Stefano Morozzi11/2024
79722^346933+119759104438Stefano Morozzi11/2024
79732^346934+187797104438Stefano Morozzi11/2024
79742^346935+198629104438Stefano Morozzi11/2024
79752^346929+85449104437Stefano Morozzi11/2024
79762^346929+155487104437Stefano Morozzi11/2024
79772^346931+60719104437Stefano Morozzi11/2024
79782^346932+49215104437Stefano Morozzi11/2024
79792^346927+65709104436Stefano Morozzi11/2024
79802^346928+126963104436Stefano Morozzi11/2024
79812^346928+143721104436Stefano Morozzi11/2024
79862^346923-19585104435Enzo Doria05/2013
79822^346923+73001104435Stefano Morozzi11/2024
79832^346924+28671104435Stefano Morozzi11/2024
79842^346924+58657104435Stefano Morozzi11/2024
79852^346924+173475104435Stefano Morozzi11/2024
79872^346921+59357104434Stefano Morozzi11/2024
79882^346916+18183104433Stefano Morozzi11/2024
79892^346914+44625104432Stefano Morozzi11/2024
79902^346912+26343104431Stefano Morozzi11/2024
79912^346912+42367104431Stefano Morozzi11/2024
79922^346908+123705104430Stefano Morozzi11/2024
79932^346899+194015104428Stefano Morozzi11/2024
79942^346900+63393104428Stefano Morozzi11/2024
79952^346901+106215104428Stefano Morozzi11/2024
79962^346901+119309104428Stefano Morozzi11/2024
79972^346902+62587104428Stefano Morozzi11/2024
79982^346897+120207104427Stefano Morozzi11/2024
79992^346897+121107104427Stefano Morozzi11/2024
80002^346897+134289104427Stefano Morozzi11/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 23 2025 10:09 (Time in France)

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