PRP Records

Probable Primes Top 10000

(294113 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 ?
57512^364936-1867979109857Enzo Doria04/2016
575227013^11652+11652^27013109846Hans Havermann10/2020
57532^364867-112087109836Enzo Doria06/2014
57544^182415-85061109825Mike Oakes06/2011
5755(2^364809+1034)/2109819Stefano Morozzi09/2020
5756(53*10^109809-287)/9109810Robert Price02/2022
5757(52*10^109807-133)/9109808Robert Price09/2021
575825708^18675+18675^25708109806Hans Havermann10/2020
5759(17^89227+16^89227)/33109788Robert Price08/2013
57602^364687-187109782Lelio R Paula01/2012
57612^364644+67109769Lelio R Paula01/2012
5762(9787*2^364625-1)/24947109763Lelio R Paula05/2015
5763(2^364616+5)/9109760Lelio R Paula01/2014
5764(55*10^109759+89)/9109760Robert Price03/2019
5765(14*32^72921+4171)/31109757Eric Chen04/2023
576612^101694+73109747Lelio R Paula03/2017
576713^98518-66109744Lelio R Paula03/2017
5768(8*10^109721-269)/9109721Robert Price09/2021
57692^364478-113261109719Enzo Doria07/2014
5770(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
5771(24737*2^364454+1)/3109716Lelio R Paula07/2014
577227814^8777+8777^27814109681Hans Havermann10/2020
5773(62*10^109673+1)/9109674Serge Batalov11/2010
57743^229824+340109654Lelio R Paula03/2017
5775(16623*33^72206-8095)/16109649Eric Chen05/2023
5776(2*10^109645-71)/3109645Robert Price12/2017
57772^364169-112813109626Enzo Doria06/2014
577828822^6359+6359^28822109622Hans Havermann11/2020
577910^109615+21109616Lelio R Paula03/2017
578010^109615-456267109615Patrick De Geest03/2017
57812^364094-113109604Lelio R Paula01/2012
578225251^21898+21898^25251109600Hans Havermann11/2020
5783(4^182026+11)/3109591Robert Price02/2017
57842^364041-6883109588Lelio R Paula09/2011
578512^101545+11109586Lelio R Paula03/2017
578626536^13475+13475^26536109582Hans Havermann11/2020
57872^363842-2787101109528Enzo Doria03/2016
5788(2^363812+3570)/2109519Stefano Morozzi09/2020
5789(22699*2^363782+1)/763109511Lelio R Paula07/2014
57902^363769+5711109506Lelio R Paula04/2017
5791(31*2^363748+1)/49109499Lelio R Paula03/2014
5792(2^363670+100280245065)109476Paul Bourdelais05/2022
5793p(22245)#/2-8109462Robert Price01/2017
57942^363556+55109442Lelio R Paula01/2012
5795(509*10^109414+31)/9109416Robert Price08/2022
5796(2^363437+1682)/2109406Stefano Morozzi09/2020
5797(55459*2^363411+1)/81109401Lelio R Paula07/2014
57982^363406+1871569109397Enzo Doria05/2016
5799(2^363370+1338)/2109385Stefano Morozzi02/2021
5800(2^363349+7)/9109378Lelio R Paula01/2014
5801(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
58023^229236+100109374Lelio R Paula03/2017
5803(2^363315+3258)/2109369Stefano Morozzi02/2021
58042^363268-58695109355Lelio R Paula04/2017
58052^363191-112321109332Enzo Doria06/2014
580626231^14718+14718^26231109327Hans Havermann10/2020
580725461^19672+19672^25461109326Hans Havermann10/2020
58084*10^109316-63109317Robert Price10/2018
58092^363120+3109311Donovan Johnson04/2006
5810(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
58112^363042-114641109287Enzo Doria04/2015
58122^363020-112793109280Enzo Doria06/2014
5813(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
5814(85*10^109253+203)/9109254Robert Price09/2020
581524990^23431+23431^24990109202Hans Havermann10/2020
5816(2^362746+3738)/2109198Stefano Morozzi09/2020
5817(2^362716+1282)/2109189Stefano Morozzi01/2021
5818(67607*2^362695+1)/70499109183Lelio R Paula07/2014
581925060^22737+22737^25060109180Hans Havermann10/2020
5820(9*2^362644+1)/5109167Lelio R Paula03/2014
58215^156181+38109166Lelio R Paula02/2017
5822(2^362623+3618)/2109161Stefano Morozzi09/2020
582325138^21993+21993^25138109157Hans Havermann10/2020
58244*10^109142+91109143Robert Price08/2018
58253^228750+68109142Lelio R Paula03/2017
5826(2^362561+786)/2109142Stefano Morozzi09/2020
5827(23*10^109113+61)/3109114Robert Price01/2022
58282*10^109100-49109101Robert Price09/2020
5829(10223*2^362376+1)/9109090Lelio R Paula07/2014
583065^60167-64^60167109078Robert Price08/2013
58317*3^228589-2109066Lelio R Paula09/2014
583224874^24243+24243^24874109063Hans Havermann11/2020
5833(17*10^109059-161)/9109060Robert Price02/2021
583429158^5495+5495^29158109050Hans Havermann11/2020
5835(78557*2^362188+1)/189109033Lelio R Paula07/2014
58362*7^129008+9109025Lelio R Paula11/2014
583788*10^109022+7109024Robert Price03/2020
583828194^7337+7337^28194108985Hans Havermann10/2020
5839(5*10^108960+91)/3108961Robert Price04/2018
58402^361957+76367108960Enzo Doria05/2016
58412^361873-1411108935Yves Minet01/2013
5842(24737*2^361857+1)/35108933Lelio R Paula07/2014
5843115^52842-114108892Norbert Schneider07/2018
584413^97745-24108883Lelio R Paula03/2017
5845(2^361696+2562)/2108882Stefano Morozzi09/2020
584617^88475+8108864Lelio R Paula04/2017
58472^361567+51108843Lelio R Paula01/2012
58482^361563-109501108842Enzo Doria04/2014
584912^100852+83108838Lelio R Paula03/2017
58502^361497+767108822Lelio R Paula01/2012
585128019^7630+7630^28019108785Hans Havermann10/2020
585224723^24758-24758^24723108765Norbert Schneider11/2020
58532^361280-112349108757Enzo Doria06/2014
58542^361271-5955108754Lelio R Paula04/2017
585512^100757+19108736Lelio R Paula03/2017
585625368^19333+19333^25368108735Hans Havermann11/2020
5857(2^361195+3618)/2108731Stefano Morozzi09/2020
58582^361153-111546435108718Paul Bourdelais10/2021
585914^94849-61108710Lelio R Paula05/2017
586027267^9700+9700^27267108708Hans Havermann11/2020
5861(19^85009-5^85009)/14108705Robert Price07/2013
586224832^23853+23853^24832108704Hans Havermann11/2020
586327502^8963+8963^27502108701Hans Havermann11/2020
586425807^16278+16278^25807108689Hans Havermann11/2020
5865(11*2^361027+1)/40463108677Lelio R Paula03/2014
58662^360973+1299108664Lelio R Paula04/2017
58672^360959-109101108660Enzo Doria04/2014
58686*5^155454+7108659Lelio R Paula11/2014
586910^108656+79108657Lelio R Paula02/2017
587010^108656-50001108656Patrick De Geest03/2017
58712^360918-35108648Lelio R Paula01/2012
58724*10^108646-47108647Robert Price10/2021
5873(11*2^360886-1)/7108638Lelio R Paula03/2014
58743*10^108624-49108625Robert Price07/2018
5875(2^360831+666)/2108621Stefano Morozzi09/2020
5876(134*10^108610+7)/3108612Robert Price02/2020
58772*10^108609+29108610Robert Price02/2021
5878(10^108604+7)/71/191108600Alfred Reich06/2021
5879(2^360742+3222)/2108594Stefano Morozzi09/2020
58802^360706-458903108584Enzo Doria04/2015
588131112^3087+3087^31112108567Hans Havermann11/2020
58822^360641-113185108564Enzo Doria07/2014
5883(29*10^108559-71)/3108560Robert Price07/2021
58842^360618+75019108557Enzo Doria04/2016
58852^360607-216367108554Harrison Mesh06/2022
5886(14*10^108545-221)/9108546Robert Price04/2018
5887(44*10^108544-233)/9108545Robert Price01/2019
58883*5^155286+2108541Lelio R Paula11/2014
58897^128422+4108530Lelio R Paula11/2014
58907^128421-80108529Lelio R Paula03/2017
58912^360497+53807108521Yves Minet07/2010
58922^360468-4559108512Yves Minet03/2019
5893(2^360451+578)/2108507Stefano Morozzi09/2020
58942^360366+1459108481Lelio R Paula09/2011
58952^360364-1499108481Yves Minet05/2013
589625662^16871+16871^25662108477Hans Havermann10/2020
589725009^21748+21748^25009108475Hans Havermann10/2020
589814^94642-23108472Lelio R Paula05/2017
5899(197*10^108446-11)/3108448Robert Price03/2020
5900(2^360229+1290)/2108440Stefano Morozzi01/2021
59014*10^108412+9108413Robert Price05/2015
5902(259*10^108409-1)/3108411Robert Price12/2020
5903(2^360122+1194)/2108408Stefano Morozzi09/2020
5904133^51042-132108406Norbert Schneider02/2019
59052^360093-351103108399Enzo Doria06/2015
59062^360042+723108384Lelio R Paula01/2012
590785^56164-2108364Lelio R Paula10/2013
59082^359937-29323108352Enzo Doria07/2015
5909(2^359922+1762)/2108348Stefano Morozzi09/2020
5910(2^359903+758)/2108342Stefano Morozzi09/2020
59112^359898-19997108341Enzo Doria06/2013
5912(2^359886+2122)/2108337Stefano Morozzi09/2020
59132*5^154948-7108305Lelio R Paula11/2014
591410^108303+13108304Lelio R Paula02/2017
591510^108303-207959108303Patrick De Geest03/2017
59167*10^108300+69108301Robert Price07/2019
59172^359730+753108290Lelio R Paula12/2011
5918(8*10^108273+13)/3108274Robert Price06/2018
59192^359650-19797108266Enzo Doria06/2013
5920(47*10^108261+259)/9108262Robert Price03/2022
592191^55259-90^55259108255Robert Price07/2015
592210^108251+85749108252Patrick De Geest02/2021
592310^108251-50000000001108251Robert Price12/2020
592410^108251-252081108251Patrick De Geest02/2021
59254*10^108238-71108239Robert Price12/2018
59263^226845+68108233Lelio R Paula03/2017
592731836^2509+2509^31836108227Hans Havermann10/2020
59285^154822-12866108216Enzo Doria05/2014
5929(9*2^359480+1)/5108215Lelio R Paula03/2014
59302^359454-177108207Lelio R Paula12/2011
5931(19*10^108184+191)/3108185Robert Price05/2019
59326^139022-59108181Lelio R Paula02/2017
5933(19*10^108176-43)/3108177Robert Price05/2019
59342^359352-179108176Lelio R Paula12/2011
59352^359338-1858781108172Enzo Doria04/2016
593612^100230-97108167Lelio R Paula03/2017
593727028^10043+10043^27028108163Hans Havermann11/2020
5938(25*2^359297-1)/137108159Lelio R Paula03/2014
5939(2^359262-509203)/9108148Lelio R Paula12/2013
594026583^11702+11702^26583108147Hans Havermann11/2020
5941(3^226648-8)/352715633108131Lelio R Paula12/2013
59426^138956-59108129Lelio R Paula02/2017
59432^359184+30285108126Lelio R Paula04/2017
594413^97059+10108119Lelio R Paula03/2017
59452^359137-81108112Lelio R Paula12/2011
5947(15185*2^359105-1)/567108103Lelio R Paula05/2015
59462^359110-11655108103Lelio R Paula04/2017
59482^359069-933075108091Paul Bourdelais06/2021
594926227^13222+13222^26227108090Hans Havermann10/2020
59508*6^138875+5108067Lelio R Paula11/2014
59512^358987-216919108066Enzo Doria05/2014
5952(2^358977+2714)/2108063Stefano Morozzi09/2020
595339^67918-67918^39108062Norbert Schneider02/2017
595424^78283-1*78283^24108048Dylan Delgado12/2019
595525282^18767+18767^25282108040Hans Havermann11/2020
59562^358785-16933108006Enzo Doria05/2013
5957(2^358783+5)/33383108000Lelio R Paula12/2013
59586^138770-77107985Lelio R Paula02/2017
5959(2^358727-1017)/94178479107980Lelio R Paula12/2013
596010^107976+19107977Lelio R Paula02/2017
596110^107976-202103107976Patrick De Geest03/2017
59622^358684+75781107975Enzo Doria04/2016
596324928^21411+21411^24928107955Hans Havermann10/2020
596499^54094+2107952Lelio R Paula06/2013
5965(2^358583-9)/391107942Lelio R Paula12/2013
5966(2^358562+838)/2107938Stefano Morozzi02/2021
59672^358538+55107931Lelio R Paula12/2011
59682^358517-109009107925Enzo Doria03/2014
596926395^12258+12258^26395107914Hans Havermann10/2020
59703^226159+104107906Lelio R Paula03/2017
59717*10^107870+39107871Robert Price01/2023
59722^358310-11655107863Lelio R Paula03/2017
5973(68*10^107852-329)/9107853Robert Price03/2021
59742^358275-112987107852Enzo Doria07/2014
59753^226038+4107848Tyler NeSmith01/2021
59762^358233-20005107839Enzo Doria06/2013
59772^358194+175107828Lelio R Paula12/2011
5978107^53125-106107812Norbert Schneider12/2016
5979(25*10^107804+161)/3107805Robert Price09/2019
59803^225922-2107793Lelio R Paula10/2013
598112^99874-95107783Lelio R Paula03/2017
5982(2^358042+3042)/2107782Stefano Morozzi09/2020
59832^358030-171107778Lelio R Paula12/2011
598411^103488-4170107772Enzo Doria12/2012
59852^357930-4547107748Yves Minet03/2019
59862^357911-20089107742Enzo Doria06/2013
59872^357885+12857107735Yves Minet07/2010
5988(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
59897^127473+40107728Lelio R Paula03/2017
59905*2^357850+9107725Lelio R Paula09/2014
59912^357786-291191107705Enzo Doria06/2015
599228907^5320+5320^28907107705Hans Havermann10/2020
599318^85798-23107700Lelio R Paula04/2017
59943*10^107697+61107698Robert Price09/2020
5995(14*10^107694-83)/3107695Robert Price12/2018
59962^357688-1854269107675Enzo Doria09/2015
59972^357671-112225107670Enzo Doria06/2014
599834323^1370+1370^34323107662Hans Havermann11/2020
59992^357618-21005107654Enzo Doria06/2013
60002^357615-17505107653Enzo Doria05/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 05 2023 08:12 (Time in France)

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