PRP Records

Probable Primes Top 10000

(293016 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 ?
5251(35*10^109888-89)/9109889Robert Price02/2022
525218^87533-11109878Lelio R Paula04/2017
52532^364982-5109871Henri Lifchitz04/2006
52543*10^109861+59109862Robert Price08/2018
52555*10^109860-69109861Robert Price02/2021
52562^364936-1867979109857Enzo Doria04/2016
525727013^11652+11652^27013109846Hans Havermann10/2020
52582^364867-112087109836Enzo Doria06/2014
52594^182415-85061109825Mike Oakes06/2011
5260(2^364809+1034)/2109819Stefano Morozzi09/2020
5261(53*10^109809-287)/9109810Robert Price02/2022
5262(52*10^109807-133)/9109808Robert Price09/2021
526325708^18675+18675^25708109806Hans Havermann10/2020
5264(17^89227+16^89227)/33109788Robert Price08/2013
52652^364687-187109782Lelio R Paula01/2012
52662^364644+67109769Lelio R Paula01/2012
5267(9787*2^364625-1)/24947109763Lelio R Paula05/2015
5268(2^364616+5)/9109760Lelio R Paula01/2014
5269(55*10^109759+89)/9109760Robert Price03/2019
5270(14*32^72921+4171)/31109757Eric Chen04/2023
527112^101694+73109747Lelio R Paula03/2017
527213^98518-66109744Lelio R Paula03/2017
5273(8*10^109721-269)/9109721Robert Price09/2021
52742^364478-113261109719Enzo Doria07/2014
5275(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
5276(24737*2^364454+1)/3109716Lelio R Paula07/2014
527727814^8777+8777^27814109681Hans Havermann10/2020
5278(62*10^109673+1)/9109674Serge Batalov11/2010
52793^229824+340109654Lelio R Paula03/2017
5280(16623*33^72206-8095)/16109649Eric Chen05/2023
5281(2*10^109645-71)/3109645Robert Price12/2017
52822^364169-112813109626Enzo Doria06/2014
528328822^6359+6359^28822109622Hans Havermann11/2020
528410^109615+21109616Lelio R Paula03/2017
528510^109615-456267109615Patrick De Geest03/2017
52862^364094-113109604Lelio R Paula01/2012
528725251^21898+21898^25251109600Hans Havermann11/2020
5288(4^182026+11)/3109591Robert Price02/2017
52892^364041-6883109588Lelio R Paula09/2011
529012^101545+11109586Lelio R Paula03/2017
529126536^13475+13475^26536109582Hans Havermann11/2020
52922^363842-2787101109528Enzo Doria03/2016
5293(2^363812+3570)/2109519Stefano Morozzi09/2020
5294(22699*2^363782+1)/763109511Lelio R Paula07/2014
52952^363769+5711109506Lelio R Paula04/2017
5296(31*2^363748+1)/49109499Lelio R Paula03/2014
5297(2^363670+100280245065)109476Paul Bourdelais05/2022
5298p(22245)#/2-8109462Robert Price01/2017
52992^363556+55109442Lelio R Paula01/2012
5300(509*10^109414+31)/9109416Robert Price08/2022
5301(2^363437+1682)/2109406Stefano Morozzi09/2020
5302(55459*2^363411+1)/81109401Lelio R Paula07/2014
53032^363406+1871569109397Enzo Doria05/2016
5304(2^363370+1338)/2109385Stefano Morozzi02/2021
5305(2^363349+7)/9109378Lelio R Paula01/2014
53063^229236+100109374Lelio R Paula03/2017
5307(2^363315+3258)/2109369Stefano Morozzi02/2021
53082^363268-58695109355Lelio R Paula04/2017
53092^363191-112321109332Enzo Doria06/2014
531026231^14718+14718^26231109327Hans Havermann10/2020
531125461^19672+19672^25461109326Hans Havermann10/2020
53124*10^109316-63109317Robert Price10/2018
53132^363120+3109311Donovan Johnson04/2006
5314(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
53152^363042-114641109287Enzo Doria04/2015
53162^363020-112793109280Enzo Doria06/2014
5317(85*10^109253+203)/9109254Robert Price09/2020
531824990^23431+23431^24990109202Hans Havermann10/2020
5319(2^362746+3738)/2109198Stefano Morozzi09/2020
5320(2^362716+1282)/2109189Stefano Morozzi01/2021
5321(67607*2^362695+1)/70499109183Lelio R Paula07/2014
532225060^22737+22737^25060109180Hans Havermann10/2020
5323(9*2^362644+1)/5109167Lelio R Paula03/2014
53245^156181+38109166Lelio R Paula02/2017
5325(2^362623+3618)/2109161Stefano Morozzi09/2020
532625138^21993+21993^25138109157Hans Havermann10/2020
53274*10^109142+91109143Robert Price08/2018
53283^228750+68109142Lelio R Paula03/2017
5329(2^362561+786)/2109142Stefano Morozzi09/2020
5330(23*10^109113+61)/3109114Robert Price01/2022
53312*10^109100-49109101Robert Price09/2020
5332(10223*2^362376+1)/9109090Lelio R Paula07/2014
533365^60167-64^60167109078Robert Price08/2013
53347*3^228589-2109066Lelio R Paula09/2014
533524874^24243+24243^24874109063Hans Havermann11/2020
5336(17*10^109059-161)/9109060Robert Price02/2021
533729158^5495+5495^29158109050Hans Havermann11/2020
5338(78557*2^362188+1)/189109033Lelio R Paula07/2014
53392*7^129008+9109025Lelio R Paula11/2014
534088*10^109022+7109024Robert Price03/2020
534128194^7337+7337^28194108985Hans Havermann10/2020
5342(5*10^108960+91)/3108961Robert Price04/2018
53432^361957+76367108960Enzo Doria05/2016
53442^361873-1411108935Yves Minet01/2013
5345(24737*2^361857+1)/35108933Lelio R Paula07/2014
5346115^52842-114108892Norbert Schneider07/2018
534713^97745-24108883Lelio R Paula03/2017
5348(2^361696+2562)/2108882Stefano Morozzi09/2020
534917^88475+8108864Lelio R Paula04/2017
53502^361567+51108843Lelio R Paula01/2012
53512^361563-109501108842Enzo Doria04/2014
535212^100852+83108838Lelio R Paula03/2017
53532^361497+767108822Lelio R Paula01/2012
535428019^7630+7630^28019108785Hans Havermann10/2020
535524723^24758-24758^24723108765Norbert Schneider11/2020
53562^361280-112349108757Enzo Doria06/2014
53572^361271-5955108754Lelio R Paula04/2017
535812^100757+19108736Lelio R Paula03/2017
535925368^19333+19333^25368108735Hans Havermann11/2020
5360(2^361195+3618)/2108731Stefano Morozzi09/2020
53612^361153-111546435108718Paul Bourdelais10/2021
536214^94849-61108710Lelio R Paula05/2017
536327267^9700+9700^27267108708Hans Havermann11/2020
5364(19^85009-5^85009)/14108705Robert Price07/2013
536524832^23853+23853^24832108704Hans Havermann11/2020
536627502^8963+8963^27502108701Hans Havermann11/2020
536725807^16278+16278^25807108689Hans Havermann11/2020
5368(11*2^361027+1)/40463108677Lelio R Paula03/2014
53692^360973+1299108664Lelio R Paula04/2017
53702^360959-109101108660Enzo Doria04/2014
53716*5^155454+7108659Lelio R Paula11/2014
537210^108656+79108657Lelio R Paula02/2017
537310^108656-50001108656Patrick De Geest03/2017
53742^360918-35108648Lelio R Paula01/2012
53754*10^108646-47108647Robert Price10/2021
5376(11*2^360886-1)/7108638Lelio R Paula03/2014
53773*10^108624-49108625Robert Price07/2018
5378(2^360831+666)/2108621Stefano Morozzi09/2020
5379(134*10^108610+7)/3108612Robert Price02/2020
53802*10^108609+29108610Robert Price02/2021
5381(10^108604+7)/71/191108600Alfred Reich06/2021
5382(2^360742+3222)/2108594Stefano Morozzi09/2020
53832^360706-458903108584Enzo Doria04/2015
538431112^3087+3087^31112108567Hans Havermann11/2020
53852^360641-113185108564Enzo Doria07/2014
5386(29*10^108559-71)/3108560Robert Price07/2021
53872^360618+75019108557Enzo Doria04/2016
53882^360607-216367108554Harrison Mesh06/2022
5389(14*10^108545-221)/9108546Robert Price04/2018
5390(44*10^108544-233)/9108545Robert Price01/2019
53913*5^155286+2108541Lelio R Paula11/2014
53927^128422+4108530Lelio R Paula11/2014
53937^128421-80108529Lelio R Paula03/2017
53942^360497+53807108521Yves Minet07/2010
53952^360468-4559108512Yves Minet03/2019
5396(2^360451+578)/2108507Stefano Morozzi09/2020
53972^360366+1459108481Lelio R Paula09/2011
53982^360364-1499108481Yves Minet05/2013
539925662^16871+16871^25662108477Hans Havermann10/2020
540025009^21748+21748^25009108475Hans Havermann10/2020
540114^94642-23108472Lelio R Paula05/2017
5402(197*10^108446-11)/3108448Robert Price03/2020
5403(2^360229+1290)/2108440Stefano Morozzi01/2021
54044*10^108412+9108413Robert Price05/2015
5405(259*10^108409-1)/3108411Robert Price12/2020
5406(2^360122+1194)/2108408Stefano Morozzi09/2020
5407133^51042-132108406Norbert Schneider02/2019
54082^360093-351103108399Enzo Doria06/2015
54092^360042+723108384Lelio R Paula01/2012
541085^56164-2108364Lelio R Paula10/2013
54112^359937-29323108352Enzo Doria07/2015
5412(2^359922+1762)/2108348Stefano Morozzi09/2020
5413(2^359903+758)/2108342Stefano Morozzi09/2020
54142^359898-19997108341Enzo Doria06/2013
5415(2^359886+2122)/2108337Stefano Morozzi09/2020
54162*5^154948-7108305Lelio R Paula11/2014
541710^108303+13108304Lelio R Paula02/2017
541810^108303-207959108303Patrick De Geest03/2017
54197*10^108300+69108301Robert Price07/2019
54202^359730+753108290Lelio R Paula12/2011
5421(8*10^108273+13)/3108274Robert Price06/2018
54222^359650-19797108266Enzo Doria06/2013
5423(47*10^108261+259)/9108262Robert Price03/2022
542491^55259-90^55259108255Robert Price07/2015
542510^108251+85749108252Patrick De Geest02/2021
542610^108251-50000000001108251Robert Price12/2020
542710^108251-252081108251Patrick De Geest02/2021
54284*10^108238-71108239Robert Price12/2018
54293^226845+68108233Lelio R Paula03/2017
543031836^2509+2509^31836108227Hans Havermann10/2020
54315^154822-12866108216Enzo Doria05/2014
5432(9*2^359480+1)/5108215Lelio R Paula03/2014
54332^359454-177108207Lelio R Paula12/2011
5434(19*10^108184+191)/3108185Robert Price05/2019
54356^139022-59108181Lelio R Paula02/2017
5436(19*10^108176-43)/3108177Robert Price05/2019
54372^359352-179108176Lelio R Paula12/2011
54382^359338-1858781108172Enzo Doria04/2016
543912^100230-97108167Lelio R Paula03/2017
544027028^10043+10043^27028108163Hans Havermann11/2020
5441(25*2^359297-1)/137108159Lelio R Paula03/2014
5442(2^359262-509203)/9108148Lelio R Paula12/2013
544326583^11702+11702^26583108147Hans Havermann11/2020
5444(3^226648-8)/352715633108131Lelio R Paula12/2013
54456^138956-59108129Lelio R Paula02/2017
54462^359184+30285108126Lelio R Paula04/2017
544713^97059+10108119Lelio R Paula03/2017
54482^359137-81108112Lelio R Paula12/2011
5450(15185*2^359105-1)/567108103Lelio R Paula05/2015
54492^359110-11655108103Lelio R Paula04/2017
54512^359069-933075108091Paul Bourdelais06/2021
545226227^13222+13222^26227108090Hans Havermann10/2020
54538*6^138875+5108067Lelio R Paula11/2014
54542^358987-216919108066Enzo Doria05/2014
5455(2^358977+2714)/2108063Stefano Morozzi09/2020
545639^67918-67918^39108062Norbert Schneider02/2017
545724^78283-1*78283^24108048Dylan Delgado12/2019
545825282^18767+18767^25282108040Hans Havermann11/2020
54592^358785-16933108006Enzo Doria05/2013
5460(2^358783+5)/33383108000Lelio R Paula12/2013
54616^138770-77107985Lelio R Paula02/2017
5462(2^358727-1017)/94178479107980Lelio R Paula12/2013
546310^107976+19107977Lelio R Paula02/2017
546410^107976-202103107976Patrick De Geest03/2017
54652^358684+75781107975Enzo Doria04/2016
546624928^21411+21411^24928107955Hans Havermann10/2020
546799^54094+2107952Lelio R Paula06/2013
5468(2^358583-9)/391107942Lelio R Paula12/2013
5469(2^358562+838)/2107938Stefano Morozzi02/2021
54702^358538+55107931Lelio R Paula12/2011
54712^358517-109009107925Enzo Doria03/2014
547226395^12258+12258^26395107914Hans Havermann10/2020
54733^226159+104107906Lelio R Paula03/2017
54747*10^107870+39107871Robert Price01/2023
54752^358310-11655107863Lelio R Paula03/2017
5476(68*10^107852-329)/9107853Robert Price03/2021
54772^358275-112987107852Enzo Doria07/2014
54783^226038+4107848Tyler NeSmith01/2021
54792^358233-20005107839Enzo Doria06/2013
54802^358194+175107828Lelio R Paula12/2011
5481107^53125-106107812Norbert Schneider12/2016
5482(25*10^107804+161)/3107805Robert Price09/2019
54833^225922-2107793Lelio R Paula10/2013
548412^99874-95107783Lelio R Paula03/2017
5485(2^358042+3042)/2107782Stefano Morozzi09/2020
54862^358030-171107778Lelio R Paula12/2011
548711^103488-4170107772Enzo Doria12/2012
54882^357930-4547107748Yves Minet03/2019
54892^357911-20089107742Enzo Doria06/2013
54902^357885+12857107735Yves Minet07/2010
5491(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
54927^127473+40107728Lelio R Paula03/2017
54935*2^357850+9107725Lelio R Paula09/2014
54942^357786-291191107705Enzo Doria06/2015
549528907^5320+5320^28907107705Hans Havermann10/2020
549618^85798-23107700Lelio R Paula04/2017
54973*10^107697+61107698Robert Price09/2020
5498(14*10^107694-83)/3107695Robert Price12/2018
54992^357688-1854269107675Enzo Doria09/2015
55002^357671-112225107670Enzo Doria06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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