PRP Records

Probable Primes Top 10000

(271067 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 ?
575112^84606+4791306Lelio R Paula06/2016
57522^303288+187431191299Enzo Doria06/2016
5753197^39788-291293Lelio R Paula10/2017
575411^87663-171091292Enzo Doria12/2012
57552^303224+253391280Henri Lifchitz05/2005
57566^117302+14391279Lelio R Paula05/2016
57573^191306-11288091277Enzo Doria07/2014
5758(10052^22807-1)/1005191276Serge Batalov08/2020
57592^303207+1291591275Lelio R Paula02/2016
57602^303191-11125991270Enzo Doria05/2014
576181539!4+3291267Robert Price09/2019
5762(2^303116+3570)/291247Stefano Morozzi09/2020
576310^91230+9^(91230+1)91231Robert Price08/2016
576410^91230+792191231Patrick De Geest11/2016
576510^91230-91114191230Patrick De Geest11/2016
576610^91229+34879391230Patrick De Geest07/2019
576710^91229-247191229Patrick De Geest01/2019
57682996^26241+26241^299691228Norbert Schneider01/2020
577010^91225+527191226Patrick De Geest01/2019
57692816^26445+26445^281691226Norbert Schneider02/2020
57726^117232-1742391225Enzo Doria02/2013
577110^91225-14721991225Patrick De Geest07/2019
57737*10^91215+391216Erik Branger11/2009
577410^91215+23061191216Patrick De Geest07/2019
577510^91215-453991215Patrick De Geest01/2019
5776(2^303007+606)/291214Stefano Morozzi09/2020
5777(2^302998+3102)/291212Stefano Morozzi09/2020
577810^91210+242191211Patrick De Geest01/2019
577910^91210-173791210Patrick De Geest01/2019
578097*10^91205-391207Robert Price01/2017
57812^302979-16118191206Enzo Doria04/2013
57822^302949+8191197Henri Lifchitz02/2007
578310^91194+20036191195Patrick De Geest07/2019
57854*6^117192-591194Lelio R Paula10/2014
578410^91194-866391194Patrick De Geest01/2019
57862^302918+9991188Lelio R Paula11/2012
578710^91186+26811191187Patrick De Geest07/2019
578810^91186-776391186Patrick De Geest01/2019
578910^91181+55047191182Patrick De Geest07/2019
579010^91181-136791181Patrick De Geest01/2019
579110^91178+7188391179Patrick De Geest07/2019
579210^91178-471991178Patrick De Geest01/2019
579324686^4935+4935^2468691173Hans Havermann08/2020
579410^91165+304391166Patrick De Geest01/2019
579510^91165-39941391165Patrick De Geest07/2019
579610^91156+386191157Patrick De Geest01/2019
579710^91156-23149791156Patrick De Geest07/2019
57982^302797+186958791151Enzo Doria05/2016
5799265^37614+37614^26591148Norbert Schneider01/2015
58007^107852+8291146Lelio R Paula04/2016
5801(38*10^91144-11)/991145Robert Price05/2015
5802(55*10^91142+377)/991143Robert Price10/2017
580310^91128+996191129Patrick De Geest01/2019
5805249^38030+38030^24991128Norbert Schneider01/2015
580410^91128-18915391128Patrick De Geest07/2019
58066^117094-21104991117Mike Oakes05/2011
580721353^18472+18472^2135391103Hans Havermann05/2020
58092^302602-186718191093Enzo Doria03/2016
580810^91092+5612791093Patrick De Geest07/2019
581010^91092-910791092Patrick De Geest01/2019
5811(1017*2^302592-1)/5391091Lelio R Paula04/2015
581215^77445-1691083Lelio R Paula07/2016
581321656^16053+16053^2165691076Hans Havermann05/2020
58142^302505+8191064Henri Lifchitz02/2007
58152^302496-11234991061Enzo Doria06/2014
581617^73999-7291052Lelio R Paula07/2016
581710^91047+933191048Patrick De Geest01/2019
581810^91047-67116991047Patrick De Geest07/2019
581910^91044+207791045Patrick De Geest01/2019
582010^91044-13635991044Patrick De Geest07/2019
582110^91041+934991042Patrick De Geest01/2019
582210^91041-782391041Patrick De Geest01/2019
582310^91040+407791041Patrick De Geest01/2019
582410^91040-11942191040Patrick De Geest07/2019
582510^91037+276991038Patrick De Geest01/2019
582610^91037-2264991037Patrick De Geest07/2019
5827(16*10^91032+41)/391033Robert Price10/2017
582810^91023+5803991024Patrick De Geest07/2019
582910^91023-647191023Patrick De Geest01/2019
583010^91018+787391019Patrick De Geest01/2019
583110^91018-33317791018Patrick De Geest07/2019
583210^91017+6876791018Patrick De Geest07/2019
583310^91017-42832791017Patrick De Geest07/2019
583410^91016+7311191017Patrick De Geest07/2019
583510^91016-797391016Patrick De Geest01/2019
58361949^27666+27666^194991016Norbert Schneider04/2020
58372^302332+57729457591012Lelio R Paula08/2016
583810^91004+907391005Patrick De Geest01/2019
583910^91004-49151991004Patrick De Geest07/2019
584010^91003+7426991004Patrick De Geest07/2019
584110^91003-390391003Patrick De Geest01/2019
58422^302274+7420990994Enzo Doria04/2016
584310^90991+8114790992Patrick De Geest07/2019
584410^90991-627990991Patrick De Geest01/2019
584510^90983+139390984Patrick De Geest01/2019
584611*10^90982+990984Robert Price08/2020
584710^90983-56238390983Patrick De Geest07/2019
5848(311^36497-1)/31090976Eric Chen09/2017
5849(2^302210+1014)/290974Stefano Morozzi09/2020
5850(3^190668+2)/8990970Lelio R Paula04/2013
58512^302188+9019590968Lelio R Paula02/2016
5852(53*10^90965-71)/990966Robert Price09/2015
585310^90965+57398790966Patrick De Geest07/2019
585410^90965-683390965Patrick De Geest01/2019
585510^90964+4878990965Patrick De Geest07/2019
585610^90964-5210390964Patrick De Geest07/2019
585710^90963+19188990964Patrick De Geest07/2019
585810^90963-365990963Patrick De Geest01/2019
585910^90962+765790963Patrick De Geest01/2019
586010^90962-21563390962Patrick De Geest07/2019
586110^90961+6747190962Patrick De Geest07/2019
586210^90961-21104390961Patrick De Geest07/2019
586310^90960+107211790961Patrick De Geest07/2019
586410^90959+879190960Patrick De Geest01/2019
586510^90960-61065990960Patrick De Geest07/2019
586610^90959-27521390959Patrick De Geest07/2019
5867(2^302129+3110)/290950Stefano Morozzi09/2020
586910^90948+986790949Patrick De Geest01/2019
586821665^15774+15774^2166590949Hans Havermann04/2020
587010^90948-10923990948Patrick De Geest07/2019
58712^302113+7410590946Enzo Doria04/2016
58722^302102-655590942Lelio R Paula02/2016
587310^90930+9522390931Patrick De Geest07/2019
587410^90930-362390930Patrick De Geest01/2019
5875156*(10^(4*22731)-1)/101-190925Robert Price05/2014
58763^190568+3890925Lelio R Paula04/2016
587710^90917+17986390918Patrick De Geest07/2019
587810^90917-669390917Patrick De Geest01/2019
58792^302009-1644990914Enzo Doria04/2013
588010^90908+318190909Patrick De Geest01/2019
588110^90908-13951190908Patrick De Geest07/2019
588210^90904+10694790905Patrick De Geest07/2019
588310^90904-516990904Patrick De Geest01/2019
588410^90903+12096390904Patrick De Geest07/2019
588510^90902+261390903Patrick De Geest01/2019
588610^90903-19073790903Patrick De Geest07/2019
588725174^4083+4083^2517490903Hans Havermann08/2020
588810^90902-95232990902Patrick De Geest07/2019
5889(17*2^301951-1)/16590896Lelio R Paula02/2014
58903^190497+7490891Lelio R Paula04/2016
5891(24737*2^301896+1)/39990882Lelio R Paula06/2014
589210^90880+570790881Patrick De Geest01/2019
589310^90880-15299390880Patrick De Geest07/2019
589418^72397+8990878Lelio R Paula06/2016
5895(2^301876+762)/290874Stefano Morozzi09/2020
5896134^42719-13390868Norbert Schneider03/2019
58976^116769-4790864Lelio R Paula05/2016
589810^90858+23343390859Patrick De Geest07/2019
589910^90858-830190858Patrick De Geest01/2019
590024298^5483+5483^2429890851Hans Havermann08/2020
590110^90849+4014190850Patrick De Geest07/2019
590210^90849-472190849Patrick De Geest01/2019
59032^301712-46590825Lelio R Paula02/2016
59042^301693-6990819Lelio R Paula11/2012
59052^301683-301683^290816Henri Lifchitz05/2005
590610^90807+727990808Patrick De Geest01/2019
590710^90807-16226390807Patrick De Geest07/2019
59086*10^90803+7990804Robert Price09/2020
590910^90800-645390800Patrick De Geest11/2018
591011^87187-171090796Enzo Doria12/2012
59115*10^90793+2190794Robert Price01/2017
5912(22*10^90792-13)/990793Robert Price03/2015
59132^301591-161590788Lelio R Paula02/2016
5914(52^52901+1)/5390777Paul Bourdelais08/2017
59152^301546-10903790775Enzo Doria04/2014
591610^90772+402990773Patrick De Geest11/2018
591710^90772-3662790772Patrick De Geest07/2019
591810^90771+6773790772Patrick De Geest07/2019
591910^90771-44100390771Patrick De Geest07/2019
592010^90770+2894190771Patrick De Geest07/2019
592110^90770-43190770Patrick De Geest11/2018
592214^79195-390768Lelio R Paula06/2016
592310^90766+87790767Patrick De Geest11/2018
59242^301517-186169390766Enzo Doria11/2015
592510^90766-10924190766Patrick De Geest07/2019
592610^90765+48536190766Patrick De Geest07/2019
592710^90765-479790765Patrick De Geest11/2018
592810^90757+757390758Patrick De Geest11/2018
592910^90757-55497990757Patrick De Geest07/2019
593010^90756+43810990757Patrick De Geest07/2019
593110^90756-872790756Patrick De Geest11/2018
593210^90749+82390750Patrick De Geest11/2018
59352^301460-17390749Lelio R Paula11/2012
593310^90748+421390749Patrick De Geest11/2018
593410^90749-13041390749Patrick De Geest07/2019
593610^90748-7541190748Patrick De Geest07/2019
593710^90747+43847190748Patrick De Geest07/2019
593810^90747-927990747Patrick De Geest11/2018
5939(85*10^90745-103)/990746Robert Price10/2017
5940(2^301439+1206)/290742Stefano Morozzi09/2020
594110^90726+407790727Patrick De Geest11/2018
594210^90726-50495190726Patrick De Geest07/2019
594310^90721+18190722Patrick De Geest11/2018
5944(2^301372+2722)/290722Stefano Morozzi09/2020
594510^90721-17714990721Patrick De Geest07/2019
5946(2^301317+1146)/290706Stefano Morozzi09/2020
59472^301312-8990704Lelio R Paula11/2012
594810^90696+634990697Patrick De Geest11/2018
59502^301285-12990696Lelio R Paula11/2012
594910^90696-63504990696Patrick De Geest07/2019
59512^301282-10999190695Enzo Doria04/2014
595210^90690+887790691Patrick De Geest11/2018
595310^90690-22743390690Patrick De Geest07/2019
595410^90683+6141190684Patrick De Geest07/2019
5955(2^301244+1738)/290684Stefano Morozzi09/2020
595610^90683-257790683Patrick De Geest11/2018
59572^301228-185426990679Enzo Doria09/2015
5958(151*10^90669-1)/390671Robert Price04/2017
5959(2^301201+2046)/290671Stefano Morozzi09/2020
5960(32*10^90669+13)/990670Robert Price04/2015
596110^90669+979390670Patrick De Geest11/2018
596210^90669-22393190669Patrick De Geest07/2019
5963(2^301191+2510)/290668Stefano Morozzi09/2020
596410^90665+1098990666Patrick De Geest07/2019
596510^90665-308790665Patrick De Geest11/2018
596610^90662+8963790663Patrick De Geest07/2019
596710^90662-951990662Patrick De Geest11/2018
596810^90661+237390662Patrick De Geest11/2018
596910^90661-19478190661Patrick De Geest07/2019
59703*5^129698+890656Lelio R Paula10/2014
5971F(433781)90655Henri Lifchitz09/2003
597219^70891+8290653Lelio R Paula06/2016
5973(29*2^301124-1)/1390648Lelio R Paula02/2014
597410^90636+6415990637Patrick De Geest07/2019
597510^90636-310190636Patrick De Geest11/2018
59767*3^189953-890632Lelio R Paula08/2014
597710^90626+33928990627Patrick De Geest07/2019
597810^90626-113190626Patrick De Geest11/2018
597911^87022-180090625Enzo Doria12/2012
598010^90623+86190624Patrick De Geest11/2018
598110^90623-30584190623Patrick De Geest07/2019
5982(2^301042+47)/1203696990616Lelio R Paula06/2013
59842^301004-278693990612Enzo Doria03/2016
598310^90611+16997790612Patrick De Geest07/2019
598510^90611-973790611Patrick De Geest11/2018
598610^90610+3674790611Patrick De Geest07/2019
598810^90609+682390610Patrick De Geest11/2018
598710^90610-2657390610Patrick De Geest07/2019
598910^90609-22817390609Patrick De Geest07/2019
59902^300980-2790605Lelio R Paula11/2012
59912*10^90597-790598Dmitry Domanov11/2010
5992197^39485+290597Lelio R Paula06/2013
59937^107198+4890593Lelio R Paula04/2016
5994(86*10^90588+121)/990589Robert Price03/2017
59952^300923+5390587Lelio R Paula11/2012
59962^300874+790573Lelio R Paula10/2012
599710^90567+948990568Patrick De Geest11/2018
599810^90567-23135390567Patrick De Geest07/2019
5999(2^300857+2214)/290567Stefano Morozzi01/2020
60005^129568-5690565Lelio R Paula04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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