PRP Records

Probable Primes Top 10000

(302575 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 ?
5001(29*10^139134-119)/9139135Robert Price12/2021
5002U(687859)/4127153139105Serge Batalov07/2024
5003(109*10^139100-7)/3139102Robert Price03/2021
500438744^3885+3885^38744139068Hans Havermann05/2021
500531112^29499+29499^31112139065Hans Havermann05/2021
50062*10^139043-63139044Robert Price01/2022
500736390^6613+6613^36390139025Hans Havermann04/2021
500830554^30989-30989^30554138988Frank Doornink05/2024
50092*10^138975+33138976Robert Price11/2021
501042437^1882+1882^42437138966Hans Havermann05/2021
501132151^20990+20990^32151138958Hans Havermann05/2021
501232154^20933+20933^32154138933Hans Havermann04/2021
501331082^29499+29499^31082138931Hans Havermann04/2021
501430573^30962-30962^30573138876Frank Doornink05/2024
50152^461228+1870441138844Enzo Doria05/2016
50162^461204-113675138837Enzo Doria08/2014
5017(397227*29^94935-19)/28138837Eric Chen06/2025
5018(2^461139-7)/47138815Lelio R Paula08/2015
5019(17*10^138812-521)/9138813Robert Price04/2018
50203*10^138811-11138812Robert Price07/2018
502129109^31088-31088^29109138778Frank Doornink05/2024
5022(28*10^138768+173)/3138769Robert Price12/2019
5023(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5024(379*10^138737-1)/9138739Robert Price02/2020
5025(43*10^138648+101)/9138649Robert Price11/2018
50262^460567-113541138645Enzo Doria08/2014
50272^460539+224789138637Enzo Doria07/2024
5028(10^138622+161)/9138622Robert Price09/2021
50297*10^138604+3138605Robert Price08/2015
5030(133*10^138600+17)/3138602Robert Price11/2021
503133912^12203+12203^33912138581Hans Havermann05/2021
50322^460330+69138574Lelio R Paula09/2017
5033(17*10^138569-77)/3138570Robert Price08/2019
503431186^27725+27725^31186138556Hans Havermann05/2021
5035(41^85909-3^85909)/38138552Robert Price09/2025
5036(16*10^138545+89)/3138546Robert Price03/2021
503739753^3056+3056^39753138546Hans Havermann05/2021
503831282^26847+26847^31282138545Hans Havermann05/2021
50396*10^138520-37138521Robert Price02/2021
50422^460078-69581138498Enzo Doria12/2015
504031830^22447+22447^31830138498Hans Havermann05/2021
5041Phi(237987,2^3)138498Henri Lifchitz12/2025
504337384^5065+5065^37384138492Hans Havermann05/2021
504428736^31055-31055^28736138457Frank Doornink05/2024
504534774^9585+9585^34774138456Hans Havermann05/2021
504610^138444-5001138444Robert Price12/2021
50472^459768+1531138404Lelio R Paula06/2012
5048(266*10^138328-17)/3138330Robert Price07/2020
504927200^31193-31193^27200138328Frank Doornink01/2024
50502024^41836+2025138319Henri Lifchitz01/2025
505128782^31019-31019^28782138318Frank Doornink05/2024
505232963^15696+15696^32963138306Hans Havermann05/2021
50532^459343-113611138277Enzo Doria08/2014
5054(28*10^138240+113)/3138241Robert Price03/2020
50552^459199+1874393138233Enzo Doria06/2016
505633339^14002+14002^33339138230Hans Havermann05/2021
505730137^30860-30860^30137138226Frank Doornink05/2024
50582^459063-345307138192Enzo Doria06/2015
50592*10^138162-43138163Robert Price04/2018
50602^458927-112747138151Enzo Doria06/2014
50612^458927-69217138151Enzo Doria11/2015
506230907^29458+29458^30907138130Hans Havermann05/2021
506332882^15837+15837^32882138094Hans Havermann05/2021
506439252^3295+3295^39252138083Hans Havermann05/2021
506533789^12190+12190^33789138062Hans Havermann06/2021
5066555555*2^458524+1513138036Darren Bedwell08/2009
506728095^31028-31028^28095138033Frank Doornink05/2024
506830931^29002+29002^30931138028Hans Havermann05/2021
50692^458465+2^32+1138012T. D. Noe06/2007
507032206^19275+19275^32206138003Hans Havermann05/2021
50712^458321-113053137969Enzo Doria07/2014
50726^177298+323137965Riley Fisher03/2023
50732^458298+79459137962Enzo Doria06/2016
507430254^30789-30789^30254137959Frank Doornink05/2024
50752^458248-21815137947Enzo Doria07/2013
50762^458194+1876549137931Enzo Doria07/2016
5077(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5078(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5079(793*10^137887+53)/9137889Robert Price01/2022
50802^457937+57137853Lelio R Paula09/2017
508128714^30921-30921^28714137849Frank Doornink05/2024
5082(8*10^137845+13)/3137846Robert Price06/2018
50832^457822+105137819Donovan Johnson06/2006
50842^457754-113711137798Enzo Doria09/2014
508511^132315-360137792Enzo Doria09/2012
5086(2^659318)%L(659318)137787Henri Lifchitz05/2025
508732072^19689+19689^32072137725Hans Havermann06/2021
508826529^31132-31132^26529137720Frank Doornink03/2024
508944592^1225+1225^44592137707Hans Havermann05/2021
509028986^30857-30857^28986137690Frank Doornink05/2024
50912^457347-37137676Lelio R Paula09/2017
50922^457322-2786393137668Enzo Doria10/2015
5093gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5094Phi(699340M,10)137664Anonymous03/2025
509534015^11134+11134^34015137647Hans Havermann06/2021
50962^457240-59939137643Enzo Doria10/2015
5097(856*10^137633-1)/9137635Robert Price03/2020
509836232^6289+6289^36232137631Hans Havermann05/2021
50992^457120-21575137607Enzo Doria07/2013
5100(11*2^456978+1)/15137564Lelio R Paula07/2015
510130963^27722+27722^30963137564Hans Havermann04/2021
510233722^12003+12003^33722137562Hans Havermann06/2021
5103(7*25^98399+10613)/12137556Curtis Bright05/2015
510441901^1918+1918^41901137555Hans Havermann06/2021
5105(7*10^137551-1)/3137552Robert Price08/2022
510632930^15021+15021^32930137539Hans Havermann05/2021
510731178^25785+25785^31178137538Hans Havermann05/2021
5108419^52446+52446^419137525Norbert Schneider11/2020
51092^456813+214175137515Enzo Doria10/2023
51102^456796-113513137510Enzo Doria08/2014
511131788^21137+21137^31788137485Hans Havermann04/2021
5112(7*2^456655+1)/39137467Lelio R Paula07/2015
511327151^31004-31004^27151137466Frank Doornink01/2024
51142^456503-114361137422Enzo Doria01/2015
5115(11*2^456387+1)/19137386Lelio R Paula07/2015
511630618^30618-5^5137352Serge Batalov04/2024
511736248^6147+6147^36248137332Hans Havermann05/2021
511831986^19651+19651^31986137329Hans Havermann05/2021
51192^456167+22313137320Enzo Doria09/2023
512031817^20656+20656^31817137292Hans Havermann05/2021
5121(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
5122(71*10^137250+1)/9137251Serge Batalov05/2010
51232^455922+76249137247Enzo Doria05/2016
512431310^24171+24171^31310137241Hans Havermann05/2021
512514^119741-119741^14137239Serge Batalov04/2016
512635014^8297+8297^35014137218Hans Havermann05/2021
5127(19*2^455760+1)/3455137196Lelio R Paula07/2015
5129124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
5128124^65536+57^65536137195Serge Batalov03/2018
51302^455689+72677137177Enzo Doria04/2016
5131(17948!)^2+Prime(17948)137118Robert Price08/2014
513231287^24128+24128^31287137116Hans Havermann05/2021
5133(37^87421-1)/36137093Robert Price03/2012
513436233^6070+6070^36233137077Hans Havermann05/2021
5135(8*10^137073-17)/9137073Serge Batalov11/2022
513638418^3697+3697^38418137070Hans Havermann04/2021
51372^455323-57137066Lelio R Paula09/2017
5138(56*10^137019+583)/9137020Robert Price08/2021
513925017^31148-31148^25017136997Frank Doornink12/2023
5140(73*17^111333-9)/16136991Curtis Bright05/2015
51412^455025-112723136977Enzo Doria06/2014
514233876^11039+11039^33876136959Hans Havermann05/2021
5143(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
5144(251^57059-1)/250136921Anonymous04/2024
514535142^7873+7873^35142136919Hans Havermann05/2021
5146(4997*31^91805-1)/2136918Eric Chen05/2024
514766*10^136894+7136896Robert Price07/2020
514828766^30697-30697^28766136875Frank Doornink05/2024
51492^454675-1777136871Yves Minet10/2011
515031676^20931+20931^31676136866Hans Havermann05/2021
51513*10^136829+29136830Robert Price05/2018
51524*10^136813-57136814Robert Price10/2018
5153(6092*28^94536-143)/9136812Curtis Bright05/2015
5154fibonacci(654572)-2136798Jon Grantham08/2023
515537359^4588+4588^37359136795Hans Havermann05/2021
51562^454348-53136773Lelio R Paula09/2017
515731^91680-2136729Lelio R Paula05/2017
51582^454199-113697136728Enzo Doria09/2014
515930785^27622+27622^30785136725Hans Havermann05/2021
516032973^14014+14014^32973136725Hans Havermann05/2021
51627*10^136716+69136717Robert Price07/2019
516136002^6273+6273^36002136717Hans Havermann05/2021
51636*10^136692+53136693Robert Price05/2020
5164Phi(568997,2)136692Henri Lifchitz02/2026
5165(13*10^136687+47)/3136688Robert Price10/2018
5166F(2*453976)%(2^453976)136661Henri Lifchitz06/2025
51672^453935-2791357136649Enzo Doria01/2016
51682^453906-69131136640Enzo Doria11/2015
516933232^12915+12915^33232136620Hans Havermann05/2021
51702^453791+1873913136605Enzo Doria06/2016
517134166^9951+9951^34166136592Hans Havermann05/2021
5172(21*2^453740-1)/2735136588Lelio R Paula07/2015
517331102^24635+24635^31102136587Hans Havermann05/2021
5174580^49413+49413^580136550Norbert Schneider02/2019
51752^453503-2788297136519Enzo Doria11/2015
517634989^7958+7958^34989136486Hans Havermann12/2020
5177(2*10^136484+187)/9136484Robert Price06/2022
5178(5^653025)%L(653025)136475Henri Lifchitz06/2025
517931007^25158+25158^31007136452Hans Havermann11/2020
51802^453267-113827136447Enzo Doria09/2014
518132234^17085+17085^32234136435Hans Havermann12/2020
51822^453102+1877629136398Enzo Doria08/2016
518331016^24981+24981^31016136397Hans Havermann12/2020
5184(62*10^136384-791)/9136385Robert Price06/2019
518534171^9798+9798^34171136382Hans Havermann12/2020
5186(17*10^136354-113)/3136355Robert Price06/2021
518732756^14541+14541^32756136350Hans Havermann11/2020
518832205^17086+17086^32205136313Hans Havermann12/2020
5189(25*10^136303+161)/3136304Robert Price09/2019
519035337^7196+7196^35337136299Hans Havermann12/2020
5191(182*10^136291+1)/3136293Robert Price02/2020
5192(88*10^136234+83)/9136235Robert Price03/2022
519323*10^136225-7136227Robert Price02/2020
5194L(651821)136223Henri Lifchitz09/2008
519525519^30908-30908^25519136208Frank Doornink02/2024
51962^452460+77701136205Enzo Doria05/2016
51972^452440-114755136199Enzo Doria04/2015
519828625^30558-30558^28625136190Frank Doornink05/2024
519932286^16489+16489^32286136157Hans Havermann11/2020
5200(47*10^136141+493)/9136142Robert Price03/2019
520127140^30699-30699^27140136108Frank Doornink01/2024
5202Phi(199391,-5)136098Henri Lifchitz12/2025
520340392^2339+2339^40392136082Hans Havermann12/2020
52042*10^136057-43136058Robert Price04/2018
52052^451971+21563136057Enzo Doria08/2023
5206(2^451956-5)/181136051Lelio R Paula07/2015
52072^451947-22165136050Enzo Doria07/2013
5208(3^451810)%(2^451810)136008Henri Lifchitz06/2025
52092^451787-21805136002Enzo Doria07/2013
52102^451734-112817135986Enzo Doria06/2014
5211(11*2^451714+1)/75135979Lelio R Paula07/2015
52122^451705-21879135977Enzo Doria07/2013
5213(4666^37249-1)/(4666^193-1)135957Ryan Propper11/2023
52142^451560-112349135934Enzo Doria06/2014
52152^451530+45135925Lelio R Paula08/2017
521626594^30719-30719^26594135925Frank Doornink03/2024
521731622^19875+19875^31622135922Hans Havermann11/2020
5218(25*10^135906-73)/3135907Robert Price09/2019
52192^451450-21743135900Enzo Doria07/2013
5220(7*10^135879+11)/9135879Tyler Busby01/2023
522135218^7199+7199^35218135846Hans Havermann11/2020
522235661^6446+6446^35661135844Hans Havermann11/2020
5223(7*33^89453-4743239)/32135835Eric Chen12/2023
522431869^18248+18248^31869135801Hans Havermann12/2020
5225(77*10^135789+157)/9135790Robert Price05/2022
5226Phi(286219,-3)135763Henri Lifchitz12/2025
52272^450958+60529135752Enzo Doria08/2023
52282^450805+65135706Lelio R Paula08/2017
522910^135669+21135670Boyan Hu12/2024
523030761^25728+25728^30761135669Hans Havermann12/2020
52312*10^135663+69135664Robert Price06/2020
523233962^9867+9867^33962135651Hans Havermann11/2020
523334474^8605+8605^34474135647Hans Havermann11/2020
523434501^8508+8508^34501135583Hans Havermann12/2020
523535487^6614+6614^35487135577Hans Havermann12/2020
5236(13725^32768+1)/131074135573Lelio R Paula03/2012
5237(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
5239(5^193939+1)/6135557Paul Bourdelais12/2008
5238Phi(193939,-5)135557Henri Lifchitz12/2025
5240(76*10^135553-49)/9135554Robert Price07/2022
52415*3^284077+2^284077135540Jon Grantham08/2023
5242(844*10^135527-7)/9135529Robert Price05/2021
524327191^30560-30560^27191135517Frank Doornink01/2024
524440387^2260+2260^40387135463Hans Havermann12/2020
52452^449944-113247135447Enzo Doria07/2014
5246Phi(70509,-1105)135418Henri Lifchitz12/2025
52472^449770-113247135395Enzo Doria07/2014
52482^449637-21471135355Enzo Doria07/2013
524926061^30650-30650^26061135351Frank Doornink03/2024
52502^449571-75135335Lelio R Paula08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 15 2026 14:19 (Time in France)

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