PRP Records

Probable Primes Top 10000

(295148 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 ?
6251(31*2^363748+1)/49109499Lelio R Paula03/2014
6252(2^363670+100280245065)109476Paul Bourdelais05/2022
6253p(22245)#/2-8109462Robert Price01/2017
62542^363556+55109442Lelio R Paula01/2012
6255(509*10^109414+31)/9109416Robert Price08/2022
6256(2^363437+1682)/2109406Stefano Morozzi09/2020
6257(55459*2^363411+1)/81109401Lelio R Paula07/2014
62582^363406+1871569109397Enzo Doria05/2016
6259(2^363370+1338)/2109385Stefano Morozzi02/2021
6260(2^363349+7)/9109378Lelio R Paula01/2014
6261(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
62623^229236+100109374Lelio R Paula03/2017
6263(2^363315+3258)/2109369Stefano Morozzi02/2021
62642^363268-58695109355Lelio R Paula04/2017
62652^363191-112321109332Enzo Doria06/2014
626626231^14718+14718^26231109327Hans Havermann10/2020
626725461^19672+19672^25461109326Hans Havermann10/2020
62684*10^109316-63109317Robert Price10/2018
62692^363120+3109311Donovan Johnson04/2006
6270(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
62712^363042-114641109287Enzo Doria04/2015
62722^363020-112793109280Enzo Doria06/2014
6273(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
6274(85*10^109253+203)/9109254Robert Price09/2020
627524990^23431+23431^24990109202Hans Havermann10/2020
6276(2^362746+3738)/2109198Stefano Morozzi09/2020
6277(2^362716+1282)/2109189Stefano Morozzi01/2021
6278(67607*2^362695+1)/70499109183Lelio R Paula07/2014
627925060^22737+22737^25060109180Hans Havermann10/2020
6280(9*2^362644+1)/5109167Lelio R Paula03/2014
62815^156181+38109166Lelio R Paula02/2017
6282(2^362623+3618)/2109161Stefano Morozzi09/2020
628325138^21993+21993^25138109157Hans Havermann10/2020
62844*10^109142+91109143Robert Price08/2018
62853^228750+68109142Lelio R Paula03/2017
6286(2^362561+786)/2109142Stefano Morozzi09/2020
6287(23*10^109113+61)/3109114Robert Price01/2022
62882*10^109100-49109101Robert Price09/2020
6289(10223*2^362376+1)/9109090Lelio R Paula07/2014
629065^60167-64^60167109078Robert Price08/2013
62917*3^228589-2109066Lelio R Paula09/2014
629224874^24243+24243^24874109063Hans Havermann11/2020
6293(17*10^109059-161)/9109060Robert Price02/2021
629429158^5495+5495^29158109050Hans Havermann11/2020
6295(78557*2^362188+1)/189109033Lelio R Paula07/2014
62962*7^129008+9109025Lelio R Paula11/2014
629788*10^109022+7109024Robert Price03/2020
629828194^7337+7337^28194108985Hans Havermann10/2020
6299(5*10^108960+91)/3108961Robert Price04/2018
63002^361957+76367108960Enzo Doria05/2016
63012^361873-1411108935Yves Minet01/2013
6302(24737*2^361857+1)/35108933Lelio R Paula07/2014
6303115^52842-114108892Norbert Schneider07/2018
630413^97745-24108883Lelio R Paula03/2017
6305(2^361696+2562)/2108882Stefano Morozzi09/2020
630617^88475+8108864Lelio R Paula04/2017
63072^361567+51108843Lelio R Paula01/2012
63082^361563-109501108842Enzo Doria04/2014
630912^100852+83108838Lelio R Paula03/2017
63102^361497+767108822Lelio R Paula01/2012
631128019^7630+7630^28019108785Hans Havermann10/2020
631224723^24758-24758^24723108765Norbert Schneider11/2020
63132^361280-112349108757Enzo Doria06/2014
63142^361271-5955108754Lelio R Paula04/2017
631512^100757+19108736Lelio R Paula03/2017
631625368^19333+19333^25368108735Hans Havermann11/2020
6317(2^361195+3618)/2108731Stefano Morozzi09/2020
63182^361153-111546435108718Paul Bourdelais10/2021
631914^94849-61108710Lelio R Paula05/2017
632027267^9700+9700^27267108708Hans Havermann11/2020
6321(19^85009-5^85009)/14108705Robert Price07/2013
632224832^23853+23853^24832108704Hans Havermann11/2020
632327502^8963+8963^27502108701Hans Havermann11/2020
632425807^16278+16278^25807108689Hans Havermann11/2020
6325(11*2^361027+1)/40463108677Lelio R Paula03/2014
63262^360973+1299108664Lelio R Paula04/2017
63272^360959-109101108660Enzo Doria04/2014
63286*5^155454+7108659Lelio R Paula11/2014
632910^108656+79108657Lelio R Paula02/2017
633010^108656-50001108656Patrick De Geest03/2017
63312^360918-35108648Lelio R Paula01/2012
63324*10^108646-47108647Robert Price10/2021
6333(11*2^360886-1)/7108638Lelio R Paula03/2014
63343*10^108624-49108625Robert Price07/2018
6335(2^360831+666)/2108621Stefano Morozzi09/2020
6336(134*10^108610+7)/3108612Robert Price02/2020
63372*10^108609+29108610Robert Price02/2021
6338(10^108604+7)/71/191108600Alfred Reich06/2021
6339(2^360742+3222)/2108594Stefano Morozzi09/2020
63402^360706-458903108584Enzo Doria04/2015
634131112^3087+3087^31112108567Hans Havermann11/2020
63422^360641-113185108564Enzo Doria07/2014
6343(29*10^108559-71)/3108560Robert Price07/2021
63442^360618+75019108557Enzo Doria04/2016
63452^360607-216367108554Harrison Mesh06/2022
6346(14*10^108545-221)/9108546Robert Price04/2018
6347(44*10^108544-233)/9108545Robert Price01/2019
63483*5^155286+2108541Lelio R Paula11/2014
63497^128422+4108530Lelio R Paula11/2014
63507^128421-80108529Lelio R Paula03/2017
63512^360497+53807108521Yves Minet07/2010
63522^360468-4559108512Yves Minet03/2019
6353(2^360451+578)/2108507Stefano Morozzi09/2020
63542^360366+1459108481Lelio R Paula09/2011
63552^360364-1499108481Yves Minet05/2013
635625662^16871+16871^25662108477Hans Havermann10/2020
635725009^21748+21748^25009108475Hans Havermann10/2020
635814^94642-23108472Lelio R Paula05/2017
6359(197*10^108446-11)/3108448Robert Price03/2020
6360(2^360229+1290)/2108440Stefano Morozzi01/2021
63614*10^108412+9108413Robert Price05/2015
6362(259*10^108409-1)/3108411Robert Price12/2020
6363(2^360122+1194)/2108408Stefano Morozzi09/2020
6364133^51042-132108406Norbert Schneider02/2019
63652^360093-351103108399Enzo Doria06/2015
63662^360042+723108384Lelio R Paula01/2012
636785^56164-2108364Lelio R Paula10/2013
63682^359937-29323108352Enzo Doria07/2015
6369(2^359922+1762)/2108348Stefano Morozzi09/2020
6370(2^359903+758)/2108342Stefano Morozzi09/2020
63712^359898-19997108341Enzo Doria06/2013
6372(2^359886+2122)/2108337Stefano Morozzi09/2020
63732*5^154948-7108305Lelio R Paula11/2014
637410^108303+13108304Lelio R Paula02/2017
637510^108303-207959108303Patrick De Geest03/2017
63767*10^108300+69108301Robert Price07/2019
63772^359730+753108290Lelio R Paula12/2011
6378(8*10^108273+13)/3108274Robert Price06/2018
63792^359650-19797108266Enzo Doria06/2013
6380(47*10^108261+259)/9108262Robert Price03/2022
638191^55259-90^55259108255Robert Price07/2015
638210^108251+85749108252Patrick De Geest02/2021
638310^108251-50000000001108251Robert Price12/2020
638410^108251-252081108251Patrick De Geest02/2021
63854*10^108238-71108239Robert Price12/2018
63863^226845+68108233Lelio R Paula03/2017
638731836^2509+2509^31836108227Hans Havermann10/2020
63885^154822-12866108216Enzo Doria05/2014
6389(9*2^359480+1)/5108215Lelio R Paula03/2014
63902^359454-177108207Lelio R Paula12/2011
6391(19*10^108184+191)/3108185Robert Price05/2019
63926^139022-59108181Lelio R Paula02/2017
6393(19*10^108176-43)/3108177Robert Price05/2019
63942^359352-179108176Lelio R Paula12/2011
63952^359338-1858781108172Enzo Doria04/2016
639612^100230-97108167Lelio R Paula03/2017
639727028^10043+10043^27028108163Hans Havermann11/2020
6398(25*2^359297-1)/137108159Lelio R Paula03/2014
6399(2^359262-509203)/9108148Lelio R Paula12/2013
640026583^11702+11702^26583108147Hans Havermann11/2020
6401(3^226648-8)/352715633108131Lelio R Paula12/2013
64026^138956-59108129Lelio R Paula02/2017
64032^359184+30285108126Lelio R Paula04/2017
640413^97059+10108119Lelio R Paula03/2017
64052^359137-81108112Lelio R Paula12/2011
6407(15185*2^359105-1)/567108103Lelio R Paula05/2015
64062^359110-11655108103Lelio R Paula04/2017
64082^359069-933075108091Paul Bourdelais06/2021
640926227^13222+13222^26227108090Hans Havermann10/2020
64108*6^138875+5108067Lelio R Paula11/2014
64112^358987-216919108066Enzo Doria05/2014
6412(2^358977+2714)/2108063Stefano Morozzi09/2020
641339^67918-67918^39108062Norbert Schneider02/2017
641424^78283-1*78283^24108048Dylan Delgado12/2019
641525282^18767+18767^25282108040Hans Havermann11/2020
64162^358785-16933108006Enzo Doria05/2013
6417(2^358783+5)/33383108000Lelio R Paula12/2013
64186^138770-77107985Lelio R Paula02/2017
6419(2^358727-1017)/94178479107980Lelio R Paula12/2013
642010^107976+19107977Lelio R Paula02/2017
642110^107976-202103107976Patrick De Geest03/2017
64222^358684+75781107975Enzo Doria04/2016
642324928^21411+21411^24928107955Hans Havermann10/2020
642499^54094+2107952Lelio R Paula06/2013
6425(2^358583-9)/391107942Lelio R Paula12/2013
6426(2^358562+838)/2107938Stefano Morozzi02/2021
64272^358538+55107931Lelio R Paula12/2011
64282^358517-109009107925Enzo Doria03/2014
642926395^12258+12258^26395107914Hans Havermann10/2020
64303^226159+104107906Lelio R Paula03/2017
64317*10^107870+39107871Robert Price01/2023
64322^358310-11655107863Lelio R Paula03/2017
6433(68*10^107852-329)/9107853Robert Price03/2021
64342^358275-112987107852Enzo Doria07/2014
64353^226038+4107848Tyler NeSmith01/2021
64362^358233-20005107839Enzo Doria06/2013
64372^358194+175107828Lelio R Paula12/2011
6438107^53125-106107812Norbert Schneider12/2016
6439(25*10^107804+161)/3107805Robert Price09/2019
64403^225922-2107793Lelio R Paula10/2013
644112^99874-95107783Lelio R Paula03/2017
6442(2^358042+3042)/2107782Stefano Morozzi09/2020
64432^358030-171107778Lelio R Paula12/2011
644411^103488-4170107772Enzo Doria12/2012
64452^357930-4547107748Yves Minet03/2019
64462^357911-20089107742Enzo Doria06/2013
64472^357885+12857107735Yves Minet07/2010
6448(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
64497^127473+40107728Lelio R Paula03/2017
64505*2^357850+9107725Lelio R Paula09/2014
64512^357786-291191107705Enzo Doria06/2015
645228907^5320+5320^28907107705Hans Havermann10/2020
645318^85798-23107700Lelio R Paula04/2017
64543*10^107697+61107698Robert Price09/2020
6455(14*10^107694-83)/3107695Robert Price12/2018
64562^357688-1854269107675Enzo Doria09/2015
64572^357671-112225107670Enzo Doria06/2014
645834323^1370+1370^34323107662Hans Havermann11/2020
64592^357618-21005107654Enzo Doria06/2013
64602^357615-17505107653Enzo Doria05/2013
646126350^12171+12171^26350107649Hans Havermann11/2020
6462(30^72871-1)/29107638Robert Price12/2011
646325021^20026+20026^25021107631Hans Havermann11/2020
64642^357521+1870217107625Enzo Doria05/2016
64652^357477-1203107612Lelio R Paula03/2017
646626008^13693+13693^26008107583Hans Havermann10/2020
646725432^16991+16991^25432107583Hans Havermann10/2020
6468(2^357371+3726)/2107580Stefano Morozzi09/2020
64695^153894-18107568Lelio R Paula02/2017
64702^357324-69059107566Enzo Doria11/2015
6471467^40296+40296^467107563Norbert Schneider03/2019
647229446^4495+4495^29446107559Hans Havermann10/2020
6473(8*10^107556-149)/3107557Robert Price12/2021
64742^357283-869688105107553Lelio R Paula01/2017
64752^357280-16805107552Enzo Doria05/2013
647610^107547+481719107548Patrick De Geest03/2017
647710^107547-47107547Lelio R Paula02/2017
6478(23*10^107540+37)/3107541Robert Price02/2022
647917^87396-32107537Lelio R Paula04/2017
6480(746*10^107505+1)/9107507Robert Price03/2020
6481(2^357125+1730)/2107506Stefano Morozzi09/2020
64822^357081+107107493Lelio R Paula12/2011
64832^357058-3911107486Yves Minet04/2017
64843^225274+64107484Lelio R Paula03/2017
64855*10^107482-57107483Robert Price03/2021
648618^85619-95107476Lelio R Paula04/2017
6487(2^357013+2526)/2107472Stefano Morozzi09/2020
64883^225248-130107471Lelio R Paula03/2017
6489(5*2^356961+1)/143107455Lelio R Paula03/2014
649027029^9448+9448^27029107450Hans Havermann11/2020
64912^356935-18085107449Enzo Doria05/2013
649255396^87+87^55396107442Hans Havermann10/2020
6493(14*10^107439-137)/3107440Robert Price04/2021
649410^107409+37107410Lelio R Paula02/2017
649510^107409-329633107409Patrick De Geest03/2017
6496(2^356799+3134)/2107407Stefano Morozzi09/2020
64972^356787-109027107404Enzo Doria04/2014
6498(2^356767+78557)/5107397Lelio R Paula12/2013
64993*10^107389+77107390Robert Price09/2018
6500(11*10^107385+61)/9107386Tyler Busby01/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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