PRP Records

Probable Primes Top 10000

(300935 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 ?
67512^363769+5711109506Lelio R Paula04/2017
6752(31*2^363748+1)/49109499Lelio R Paula03/2014
675326^77372+25109480Anonymous09/2024
6754(2^363670+100280245065)109476Paul Bourdelais05/2022
6755p(22245)#/2-8109462Robert Price01/2017
67562^363556+55109442Lelio R Paula01/2012
6757(509*10^109414+31)/9109416Robert Price08/2022
6758(2^363437+1682)/2109406Stefano Morozzi09/2020
6759(55459*2^363411+1)/81109401Lelio R Paula07/2014
67602^363406+1871569109397Enzo Doria05/2016
6761(129^51829-1)/128109388Anonymous06/2024
6762(2^363370+1338)/2109385Stefano Morozzi02/2021
6763(2^363349+7)/9109378Lelio R Paula01/2014
6764(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
67653^229236+100109374Lelio R Paula03/2017
6766(2^363315+3258)/2109369Stefano Morozzi02/2021
67672^363268-58695109355Lelio R Paula04/2017
67682^363191-112321109332Enzo Doria06/2014
676926231^14718+14718^26231109327Hans Havermann10/2020
677025461^19672+19672^25461109326Hans Havermann10/2020
67714*10^109316-63109317Robert Price10/2018
67722^363120+3109311Donovan Johnson04/2006
6773(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
67742^363042-114641109287Enzo Doria04/2015
67752^363020-112793109280Enzo Doria06/2014
6776(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
6777(85*10^109253+203)/9109254Robert Price09/2020
677824990^23431+23431^24990109202Hans Havermann10/2020
6779(2^362746+3738)/2109198Stefano Morozzi09/2020
6780(2^362716+1282)/2109189Stefano Morozzi01/2021
6781(67607*2^362695+1)/70499109183Lelio R Paula07/2014
678225060^22737+22737^25060109180Hans Havermann10/2020
6783(9*2^362644+1)/5109167Lelio R Paula03/2014
67845^156181+38109166Lelio R Paula02/2017
6785(2^362623+3618)/2109161Stefano Morozzi09/2020
678625138^21993+21993^25138109157Hans Havermann10/2020
67874*10^109142+91109143Robert Price08/2018
67883^228750+68109142Lelio R Paula03/2017
6789(2^362561+786)/2109142Stefano Morozzi09/2020
6790(23*10^109113+61)/3109114Robert Price01/2022
67912*10^109100-49109101Robert Price09/2020
6792(10223*2^362376+1)/9109090Lelio R Paula07/2014
679365^60167-64^60167109078Robert Price08/2013
67947*3^228589-2109066Lelio R Paula09/2014
679524874^24243+24243^24874109063Hans Havermann11/2020
6796(17*10^109059-161)/9109060Robert Price02/2021
679729158^5495+5495^29158109050Hans Havermann11/2020
6798(78557*2^362188+1)/189109033Lelio R Paula07/2014
67992*7^129008+9109025Lelio R Paula11/2014
680088*10^109022+7109024Robert Price03/2020
680128194^7337+7337^28194108985Hans Havermann10/2020
6802(5*10^108960+91)/3108961Robert Price04/2018
68032^361957+76367108960Enzo Doria05/2016
68042^361873-1411108935Yves Minet01/2013
6805(24737*2^361857+1)/35108933Lelio R Paula07/2014
680647^65132-65132^47108908Norman Luhn09/2024
6807115^52842-114108892Norbert Schneider07/2018
680813^97745-24108883Lelio R Paula03/2017
6809(2^361696+2562)/2108882Stefano Morozzi09/2020
681017^88475+8108864Lelio R Paula04/2017
68112^361567+51108843Lelio R Paula01/2012
68122^361563-109501108842Enzo Doria04/2014
681312^100852+83108838Lelio R Paula03/2017
68142^361497+767108822Lelio R Paula01/2012
6815L(520691)/78103651/1057002731/42794551909108791Serge Batalov07/2024
681628019^7630+7630^28019108785Hans Havermann10/2020
681724723^24758-24758^24723108765Norbert Schneider11/2020
68182^361280-112349108757Enzo Doria06/2014
68192^361271-5955108754Lelio R Paula04/2017
682012^100757+19108736Lelio R Paula03/2017
682125368^19333+19333^25368108735Hans Havermann11/2020
6822(2^361195+3618)/2108731Stefano Morozzi09/2020
68232^361153-111546435108718Paul Bourdelais10/2021
682414^94849-61108710Lelio R Paula05/2017
682527267^9700+9700^27267108708Hans Havermann11/2020
6826(19^85009-5^85009)/14108705Robert Price07/2013
682724832^23853+23853^24832108704Hans Havermann11/2020
682827502^8963+8963^27502108701Hans Havermann11/2020
6829(130^51419-1)/129108695Anonymous06/2024
683025807^16278+16278^25807108689Hans Havermann11/2020
6831(11*2^361027+1)/40463108677Lelio R Paula03/2014
68322^360973+1299108664Lelio R Paula04/2017
683324^78728+23108662Anonymous09/2024
68342^360959-109101108660Enzo Doria04/2014
68356*5^155454+7108659Lelio R Paula11/2014
683610^108656+79108657Lelio R Paula02/2017
683710^108656-50001108656Patrick De Geest03/2017
68382^360918-35108648Lelio R Paula01/2012
68394*10^108646-47108647Robert Price10/2021
6840(11*2^360886-1)/7108638Lelio R Paula03/2014
68413*10^108624-49108625Robert Price07/2018
6842(2^360831+666)/2108621Stefano Morozzi09/2020
6843(134*10^108610+7)/3108612Robert Price02/2020
68442*10^108609+29108610Robert Price02/2021
6845(10^108604+7)/71/191108600Alfred Reich06/2021
6846(2^360742+3222)/2108594Stefano Morozzi09/2020
68472^360706-458903108584Enzo Doria04/2015
684831112^3087+3087^31112108567Hans Havermann11/2020
68492^360641-113185108564Enzo Doria07/2014
6850(29*10^108559-71)/3108560Robert Price07/2021
68522^360618+75019108557Enzo Doria04/2016
68512^360618+2025108557Henri Lifchitz01/2025
68532^360607-216367108554Harrison Mesh06/2022
6854(14*10^108545-221)/9108546Robert Price04/2018
6855(44*10^108544-233)/9108545Robert Price01/2019
68563*5^155286+2108541Lelio R Paula11/2014
68577^128422+4108530Lelio R Paula11/2014
68587^128421-80108529Lelio R Paula03/2017
68592^360497+53807108521Yves Minet07/2010
68602^360468-4559108512Yves Minet03/2019
6861(2^360451+578)/2108507Stefano Morozzi09/2020
68622^360366+1459108481Lelio R Paula09/2011
68632^360364-1499108481Yves Minet05/2013
686425662^16871+16871^25662108477Hans Havermann10/2020
686525009^21748+21748^25009108475Hans Havermann10/2020
686614^94642-23108472Lelio R Paula05/2017
6867(197*10^108446-11)/3108448Robert Price03/2020
6868(2^360229+1290)/2108440Stefano Morozzi01/2021
68694*10^108412+9108413Robert Price05/2015
6870(259*10^108409-1)/3108411Robert Price12/2020
6871(2^360122+1194)/2108408Stefano Morozzi09/2020
6872133^51042-132108406Norbert Schneider02/2019
68732^360093-351103108399Enzo Doria06/2015
68742^360042+723108384Lelio R Paula01/2012
687585^56164-2108364Lelio R Paula10/2013
68762^359937-29323108352Enzo Doria07/2015
687722^80712-23108350Anonymous09/2024
6878(2^359922+1762)/2108348Stefano Morozzi09/2020
6879(2^359903+758)/2108342Stefano Morozzi09/2020
68802^359898-19997108341Enzo Doria06/2013
6881(2^359886+2122)/2108337Stefano Morozzi09/2020
68822*5^154948-7108305Lelio R Paula11/2014
688310^108303+13108304Lelio R Paula02/2017
688410^108303-207959108303Patrick De Geest03/2017
68857*10^108300+69108301Robert Price07/2019
6886198^47155-47155^198108300Norman Luhn09/2024
68872^359730+753108290Lelio R Paula12/2011
6888(8*10^108273+13)/3108274Robert Price06/2018
68892^359650-19797108266Enzo Doria06/2013
6890(47*10^108261+259)/9108262Robert Price03/2022
689191^55259-90^55259108255Robert Price07/2015
689210^108251+85749108252Patrick De Geest02/2021
689310^108251-50000000001108251Robert Price12/2020
689410^108251-252081108251Patrick De Geest02/2021
68954*10^108238-71108239Robert Price12/2018
68963^226845+68108233Lelio R Paula03/2017
689731836^2509+2509^31836108227Hans Havermann10/2020
68985^154822-12866108216Enzo Doria05/2014
6899(9*2^359480+1)/5108215Lelio R Paula03/2014
69002^359454-177108207Lelio R Paula12/2011
6901(19*10^108184+191)/3108185Robert Price05/2019
69026^139022-59108181Lelio R Paula02/2017
6903(19*10^108176-43)/3108177Robert Price05/2019
69042^359352-179108176Lelio R Paula12/2011
69052^359338-1858781108172Enzo Doria04/2016
690612^100230-97108167Lelio R Paula03/2017
690727028^10043+10043^27028108163Hans Havermann11/2020
6908(25*2^359297-1)/137108159Lelio R Paula03/2014
6909(2^359262-509203)/9108148Lelio R Paula12/2013
691026583^11702+11702^26583108147Hans Havermann11/2020
6911(3^226648-8)/352715633108131Lelio R Paula12/2013
69126^138956-59108129Lelio R Paula02/2017
69132^359184+30285108126Lelio R Paula04/2017
691413^97059+10108119Lelio R Paula03/2017
69152^359137-81108112Lelio R Paula12/2011
6917(15185*2^359105-1)/567108103Lelio R Paula05/2015
69162^359110-11655108103Lelio R Paula04/2017
69182^359069-933075108091Paul Bourdelais06/2021
691926227^13222+13222^26227108090Hans Havermann10/2020
69208*6^138875+5108067Lelio R Paula11/2014
69212^358987-216919108066Enzo Doria05/2014
6922(2^358977+2714)/2108063Stefano Morozzi09/2020
692339^67918-67918^39108062Norbert Schneider02/2017
692424^78283-1*78283^24108048Dylan Delgado12/2019
692525282^18767+18767^25282108040Hans Havermann11/2020
69262^358785-16933108006Enzo Doria05/2013
6927(2^358783+5)/33383108000Lelio R Paula12/2013
69286^138770-77107985Lelio R Paula02/2017
6929(2^358727-1017)/94178479107980Lelio R Paula12/2013
693010^107976+19107977Lelio R Paula02/2017
693110^107976-202103107976Patrick De Geest03/2017
69322^358684+75781107975Enzo Doria04/2016
693324928^21411+21411^24928107955Hans Havermann10/2020
693499^54094+2107952Lelio R Paula06/2013
6935(2^358583-9)/391107942Lelio R Paula12/2013
6936(2^358562+838)/2107938Stefano Morozzi02/2021
69372^358538+55107931Lelio R Paula12/2011
69382^358517-109009107925Enzo Doria03/2014
693926395^12258+12258^26395107914Hans Havermann10/2020
69403^226159+104107906Lelio R Paula03/2017
69417*10^107870+39107871Robert Price01/2023
69422^358310-11655107863Lelio R Paula03/2017
6943(68*10^107852-329)/9107853Robert Price03/2021
69442^358275-112987107852Enzo Doria07/2014
69453^226038+4107848Tyler NeSmith01/2021
69462^358233-20005107839Enzo Doria06/2013
69472^358194+175107828Lelio R Paula12/2011
6948107^53125-106107812Norbert Schneider12/2016
6949(25*10^107804+161)/3107805Robert Price09/2019
69503^225922-2107793Lelio R Paula10/2013
695112^99874-95107783Lelio R Paula03/2017
6952(2^358042+3042)/2107782Stefano Morozzi09/2020
69532^358030-171107778Lelio R Paula12/2011
695411^103488-4170107772Enzo Doria12/2012
69552^357930-4547107748Yves Minet03/2019
69562^357911-20089107742Enzo Doria06/2013
69572^357885+12857107735Yves Minet07/2010
6958(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
69597^127473+40107728Lelio R Paula03/2017
69605*2^357850+9107725Lelio R Paula09/2014
69612^357786-291191107705Enzo Doria06/2015
696228907^5320+5320^28907107705Hans Havermann10/2020
696318^85798-23107700Lelio R Paula04/2017
69643*10^107697+61107698Robert Price09/2020
6965(14*10^107694-83)/3107695Robert Price12/2018
69662^357688-1854269107675Enzo Doria09/2015
69672^357671-112225107670Enzo Doria06/2014
696834323^1370+1370^34323107662Hans Havermann11/2020
69692^357618-21005107654Enzo Doria06/2013
69702^357615-17505107653Enzo Doria05/2013
697126350^12171+12171^26350107649Hans Havermann11/2020
6972(30^72871-1)/29107638Robert Price12/2011
697325021^20026+20026^25021107631Hans Havermann11/2020
69742^357521+1870217107625Enzo Doria05/2016
69752^357477-1203107612Lelio R Paula03/2017
697626008^13693+13693^26008107583Hans Havermann10/2020
697725432^16991+16991^25432107583Hans Havermann10/2020
6978(2^357371+3726)/2107580Stefano Morozzi09/2020
69795^153894-18107568Lelio R Paula02/2017
69802^357324-69059107566Enzo Doria11/2015
6981467^40296+40296^467107563Norbert Schneider03/2019
698229446^4495+4495^29446107559Hans Havermann10/2020
6983(8*10^107556-149)/3107557Robert Price12/2021
69842^357283-869688105107553Lelio R Paula01/2017
69852^357280-16805107552Enzo Doria05/2013
698610^107547+481719107548Patrick De Geest03/2017
698710^107547-47107547Lelio R Paula02/2017
6988(23*10^107540+37)/3107541Robert Price02/2022
698917^87396-32107537Lelio R Paula04/2017
6990(746*10^107505+1)/9107507Robert Price03/2020
6991(2^357125+1730)/2107506Stefano Morozzi09/2020
69922^357081+107107493Lelio R Paula12/2011
69932^357058-3911107486Yves Minet04/2017
69943^225274+64107484Lelio R Paula03/2017
69955*10^107482-57107483Robert Price03/2021
699618^85619-95107476Lelio R Paula04/2017
6997(2^357013+2526)/2107472Stefano Morozzi09/2020
69983^225248-130107471Lelio R Paula03/2017
6999(5*2^356961+1)/143107455Lelio R Paula03/2014
700027029^9448+9448^27029107450Hans Havermann11/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 07 2025 10:37 (Time in France)

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