PRP Records

Probable Primes Top 10000

(303242 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 ?
575131903^12168+12168^31903130331Hans Havermann04/2021
57522^432917+22217130322Enzo Doria09/2023
575329387^27112+27112^29387130278Hans Havermann04/2021
57542^432768+213181130277Enzo Doria09/2023
575529577^25370+25370^29577130267Hans Havermann04/2021
575631738^12685+12685^31738130231Hans Havermann03/2021
575744235^878+878^44235130206Hans Havermann04/2021
575832160^11171+11171^32160130187Hans Havermann04/2021
575929489^25956+25956^29489130172Hans Havermann04/2021
5760(2^432457-1)/1672739247834685086279697130159Tony Prest / Never Odd Or Even09/2013
576133005^8766+8766^33005130133Hans Havermann04/2021
5762(35*10^130132-611)/9130133Robert Price02/2022
5763(444^49408+1)/(444^256+1)130125Martin Hopf12/2023
57642^432217+41130111Lelio R Paula06/2017
5765(2^216089*(2^216091-1)-339)/25130098Makoto Morimoto03/2017
5766((2^216091+1066)^2+(2^216091+1066)+41)/47/2069130095Makoto Morimoto05/2016
576797^65480-2130094Lelio R Paula05/2017
576836007^4102+4102^36007130094Hans Havermann04/2021
57694*10^130088-89130089Robert Price11/2018
57702^432117-113215130081Enzo Doria07/2014
5771(4*10^130080+41)/9130080Serge Batalov11/2022
57729583*29^88890+736129997Eric Chen06/2025
57732^431804+72511129986Enzo Doria04/2016
577427902^29237-29237^27902129978Frank Doornink03/2024
577533^85579+32129953Alfred Reich10/2025
5776(2313^38809-1)/(2313^197-1)129898Ryan Propper11/2023
5777(13*10^129896+137)/3129897Robert Price06/2021
5778(13*10^129890+71)/3129891Robert Price06/2021
5779128^61638+127129885Alfred Reich06/2026
578029048^29101-29101^29048129882Norbert Schneider03/2022
578137832^2709+2709^37832129871Hans Havermann04/2021
578231055^15184+15184^31055129853Hans Havermann04/2021
5784(3^272141-3^136071+1)/7129844Serge Batalov03/2014
5783Phi(1632846L,3)129844Anonymous03/2025
578531385^13702+13702^31385129833Hans Havermann04/2021
5786(13*10^129826+41)/9129827Tyler Busby02/2023
578728901^29102-29102^28901129822Norbert Schneider03/2022
5788(47*10^129789-119)/9129790Robert Price05/2019
5789(9*2^431141+1)/17129787Lelio R Paula06/2015
579025999^29384-29384^25999129730Frank Doornink03/2024
579125771^29408-29408^25771129723Frank Doornink02/2024
5792(166*10^129712+17)/3129714Robert Price07/2022
5793(29*2^430881-1)/21129709Lelio R Paula06/2015
57942^430807+1869563129686Enzo Doria05/2016
57952^430721-21429129660Enzo Doria07/2013
5796Phi(326081,3)129648Henri Lifchitz12/2025
5797(4*10^129618+89)/3129619Robert Price08/2021
5798(142^60223-1)/141129616Anonymous06/2024
5799(10^129587-7^129587)/3129587Jon Grantham07/2023
58002^430415-276271129568Enzo Doria07/2015
580132282^10311+10311^32282129558Hans Havermann04/2021
580229486^24741+24741^29486129545Hans Havermann04/2021
5803(29*10^129543+313)/9129544Robert Price04/2021
580437095^3104+3104^37095129533Hans Havermann04/2021
580531132^14459+14459^31132129514Hans Havermann04/2021
580632582^9435+9435^32582129506Hans Havermann03/2021
580730442^17953+17953^30442129505Hans Havermann03/2021
5808(199*10^129487-7)/3129489Robert Price05/2020
58092^430142-2791721129486Enzo Doria03/2016
5810(7*10^129472-13)/3129473Robert Price07/2018
5811(8*10^129469+79)/3129470Robert Price10/2020
581231678^12213+12213^31678129463Hans Havermann04/2021
581310620^32143-10619^32143129412Norbert Schneider08/2023
5814(772*10^129406-7)/9129408Robert Price06/2022
5815(535^47431-1)/534129406Tom Wu09/2024
5816((3*20425-8193)*F(618977)-(20425-8193)*L(618977))/2129363Yaroslav Berezhko03/2025
581731100^14439+14439^31100129362Hans Havermann04/2021
581833009^8288+8288^33009129345Hans Havermann04/2021
581925895^29306-29306^25895129334Frank Doornink03/2024
5820(44^78697+43^78697)/87129333Aurel Gibier11/2023
582129675^22804+22804^29675129324Hans Havermann04/2021
582229068^28099+28099^29068129315Hans Havermann04/2021
58232^429568-21017129313Enzo Doria07/2013
5824(10^129295+83)/3129295Robert Price08/2021
5825(853*10^129274-7)/9129276Robert Price07/2021
5826998^43100+997129263Alfred Reich03/2026
582730958^14961+14961^30958129249Hans Havermann04/2021
5828(11*10^129239-179)/3129240Robert Price09/2018
582928659^28988+28988^28659129208Norbert Schneider02/2021
583029423^24616+24616^29423129203Hans Havermann03/2021
58312^429194-112685129201Enzo Doria06/2014
583231*35^83672+17398129197Eric Chen05/2025
58332^429145-2780449129186Enzo Doria04/2016
583432500^9427+9427^32500129168Hans Havermann04/2021
583533577^7014+7014^33577129136Hans Havermann03/2021
58362^428892-113453129110Enzo Doria07/2014
5837(11*2^428881-7)/15129106Renaud Lifchitz03/2011
58382^428727-113959129060Enzo Doria10/2014
5839(7*2^428725-1)/13129059Lelio R Paula05/2014
5840(10^129051-31)/3129051Serge Batalov12/2014
5841(3^732836)/(2^732836)129047Henri Lifchitz05/2025
5842(134*10^129038+7)/3129040Robert Price02/2020
58432^428564+71161129011Enzo Doria04/2016
584428781^28930+28930^28781129002Norbert Schneider02/2021
584529065^27424+27424^29065128995Hans Havermann04/2021
58462^428502-113285128992Enzo Doria07/2014
58472^428421-21373128968Enzo Doria06/2013
5848L(616787)128901Henri Lifchitz09/2008
5849(765^44701-1)/764128900Tom Wu07/2024
585020^99055-3128874Paul Bourdelais12/2020
585191^65772-2128851Lelio R Paula05/2017
58522^428022+43128848Lelio R Paula05/2017
58532^427999-459397128841Enzo Doria05/2015
58542^427993+76847128839Enzo Doria05/2016
585531059^14060+14060^31059128833Hans Havermann03/2021
585610^128805+152871128806Patrick De Geest05/2021
585710^128805-10001128805Robert Price02/2021
58582^427824-1851507128788Enzo Doria08/2015
58592^427807-21469128783Enzo Doria07/2013
586029082^26783+26783^29082128772Hans Havermann04/2021
586140055^1638+1638^40055128750Hans Havermann04/2021
5862(923^43411-1)/922128720Tom Wu07/2024
586311^123594-240128710Enzo Doria09/2012
58642^427504-21503128692Enzo Doria07/2013
586537727^2574+2574^37727128673Hans Havermann04/2021
586629686^21591+21591^29686128668Hans Havermann04/2021
586710^128668-70000000001128668Robert Price08/2021
586810^128668-350729128668Alfred Reich08/2024
5869Phi(57476,13#)128668Henri Lifchitz12/2025
58702^427420+91128667Lelio R Paula05/2017
58718*10^128651-37128652Robert Price03/2022
5873(68*10^128645-257)/9128646Robert Price07/2019
5872128^61050+127128646Alfred Reich06/2026
5874Phi(236553,7)128631Henri Lifchitz12/2025
58752^427269-113635128621Enzo Doria08/2014
5876136^60270+135128589Alfred Reich03/2026
58772^427130+1877569128579Enzo Doria08/2016
58782^427068+20011128561Enzo Doria06/2023
58792^427016-115349128545Enzo Doria07/2015
58802^427001+1334025128541Henri Lifchitz11/2024
5881(4*10^128510+137)/3128511Robert Price03/2018
58822^426889-112879128507Enzo Doria06/2014
58832^426804+1869931128481Enzo Doria05/2016
58842^426750+77635128465Enzo Doria05/2016
588527708^28913-28913^27708128450Frank Doornink03/2024
588636988^2969+2969^36988128445Hans Havermann03/2021
588736664^3185+3185^36664128439Hans Havermann03/2021
588832618^8649+8649^32618128416Hans Havermann04/2021
588928883^27874+27874^28883128391Hans Havermann04/2021
58902^426425-91128367Lelio R Paula05/2017
5891(15*2^426398-1)/11128359Lelio R Paula05/2014
58922^426352+74971128345Enzo Doria04/2016
5893(199*10^128343-7)/3128345Robert Price05/2020
58944*10^128343-21128344Robert Price09/2018
5895(65*10^128338+493)/9128339Robert Price08/2021
589635632^3997+3997^35632128337Hans Havermann04/2021
58972^426300-1863689128330Enzo Doria03/2016
58982^426293+1881017128327Enzo Doria11/2016
5899(88*10^128324-637)/9128325Robert Price11/2020
5900Phi(161347,7)128320Henri Lifchitz12/2025
5901Phi(135199,-9)128312Henri Lifchitz12/2025
5902(491*10^128285+31)/9128287Robert Price04/2022
590339103^1908+1908^39103128281Hans Havermann04/2021
59042^426043+35128252Robert Price11/2015
5905(4*10^128244-19)/3128245Robert Price03/2018
590626220^29021-29021^26220128234Frank Doornink03/2024
590735489^4102+4102^35489128222Hans Havermann04/2021
590834721^4926+4926^34721128208Hans Havermann04/2021
5909(305*10^128198+1)/9128200Robert Price02/2020
59102^425808-459959128181Enzo Doria06/2015
591130632^15291+15291^30632128178Hans Havermann04/2021
5912U(623603)128177Serge Batalov07/2024
591335981^3648+3648^35981128167Hans Havermann04/2021
59142^425627-113605128127Enzo Doria08/2014
5915(4*10^128109+119)/3128110Robert Price12/2021
5916(22*10^128094+53)/3128095Robert Price07/2019
5917(86*10^128086-221)/9128087Robert Price09/2019
591818565^30002-30002^18565128070Norbert Schneider01/2015
5919(2^425287-9)/2737128021Lelio R Paula05/2015
5920(3*2^425233-1)/25128007Lelio R Paula05/2014
5921Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
59222^425205+4911128000Marek Hubal02/2017
592329241^23836+23836^29241127995Hans Havermann04/2021
59242^425118-113663127974Enzo Doria08/2014
5925(86*10^127967-329)/9127968Robert Price01/2020
59262^425061+1869761127957Enzo Doria05/2016
5927746^44541+44541^746127955Norbert Schneider07/2019
592830236^17043+17043^30236127946Hans Havermann03/2021
59292^424938+212419127920Enzo Doria08/2023
59302^424918-21141127914Enzo Doria07/2013
5931Phi(274823,-3)127907Henri Lifchitz12/2025
5932(62*10^127903+91)/9127904Robert Price07/2021
59332^424864-29489127897Enzo Doria08/2015
593430438^15893+15893^30438127877Hans Havermann02/2021
5935(97*10^127858-1)/3127860Serge Batalov12/2014
593628929^26258+26258^28929127845Hans Havermann03/2021
593730563^15220+15220^30563127828Hans Havermann03/2021
59382^424632-2786639127827Enzo Doria03/2016
593910^127821-700001127821Robert Price08/2021
59402^424577-113755127811Enzo Doria09/2014
5941(7*2^424512-1)/3127792Lelio R Paula05/2014
5942(56*10^127752+691)/9127753Robert Price05/2019
594311^122629-720127705Enzo Doria11/2012
594422*10^127645+3127647Robert Price01/2020
594528715^27844+27844^28715127631Hans Havermann03/2021
5946(56*10^127612+187)/9127613Robert Price10/2021
5947(5*36^81995+821)/7127609Eric Chen01/2021
59484*10^127562-39127563Robert Price09/2020
594932595^8186+8186^32595127547Hans Havermann03/2021
59502^423696-21429127546Enzo Doria07/2013
59512^423664-1864559127536Enzo Doria03/2016
595237889^2322+2322^37889127530Hans Havermann03/2021
595337668^2429+2429^37668127523Hans Havermann03/2021
59543^267267-4127519Henri Lifchitz10/2014
5955fibonacci(610144)-2127513Jon Grantham08/2023
595626253^28852-28852^26253127503Frank Doornink03/2024
5957(103*10^127491+17)/3127493Robert Price08/2020
595829376^21869+21869^29376127487Hans Havermann03/2021
595931186^12241+12241^31186127483Hans Havermann02/2021
5960(19^99689+5^99689)/24127477Robert Price09/2013
59617239^33023-7238^33023127459Norbert Schneider02/2026
596227069^28754-28754^27069127452Frank Doornink01/2024
5963(21*2^423372+1)/101127447Lelio R Paula05/2014
596430594^14645+14645^30594127446Hans Havermann03/2021
59652^423328-21537127435Enzo Doria07/2013
5966(67*10^127413-7)/3127415Robert Price01/2020
5967(5*34^83193+700233)/11127408Eric Chen08/2023
5968(2*10^127407+73)/3127407Robert Price09/2020
5969(2^423165-7)/25127384Lelio R Paula05/2015
5970(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
5971(4*10^127349+17)/3127350Tyler Busby01/2023
597229512^20647+20647^29512127341Hans Havermann03/2021
59732^422987-3001935127332Paul Bourdelais07/2023
5974(112*10^127324+17)/3127326Robert Price03/2020
597629565^20252+20252^29565127321Hans Havermann03/2021
5975232^232^232+1831^1831127321Henri Lifchitz03/2025
5977fibonacci(609165)-3127308Jon Grantham08/2023
5979(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
5978(5^182099-3^182099)/2127282Kellen Shenton05/2022
5980(16*10^127259+197)/3127260Robert Price04/2019
5981(26*10^127240+61)/3127241Robert Price10/2019
5982(234483*27^88884-145)/26127230Curtis Bright05/2015
59832^422515-114997127190Enzo Doria06/2015
59845*10^127179-3127180Robert Price07/2015
598531678^10343+10343^31678127176Hans Havermann03/2021
5986(44*10^127169-233)/9127170Robert Price01/2019
598734947^4352+4352^34947127162Hans Havermann03/2021
59886*10^127158+19127159Robert Price11/2021
598930469^14902+14902^30469127155Hans Havermann03/2021
59905*10^127153+77127154Robert Price12/2018
599129941^17620+17620^29941127130Hans Havermann02/2021
599231607^10516+10516^31607127119Hans Havermann03/2021
5993(19*10^127118-97)/3127119Robert Price10/2021
5994(29*10^127111+691)/9127112Robert Price08/2021
5995736^44335+44335^736127104Norbert Schneider07/2019
599633040^7023+7023^33040127090Hans Havermann03/2021
5997(4*10^127081+167)/9127081Robert Price03/2022
599829748^18661+18661^29748127052Hans Havermann03/2021
599927905^28578-28578^27905127049Frank Doornink03/2024
6000-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 03 2026 18:59 (Time in France)

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