PRP Records

Probable Primes Top 10000

(303103 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 ?
575137832^2709+2709^37832129871Hans Havermann04/2021
575231055^15184+15184^31055129853Hans Havermann04/2021
5754(3^272141-3^136071+1)/7129844Serge Batalov03/2014
5753Phi(1632846L,3)129844Anonymous03/2025
575531385^13702+13702^31385129833Hans Havermann04/2021
5756(13*10^129826+41)/9129827Tyler Busby02/2023
575728901^29102-29102^28901129822Norbert Schneider03/2022
5758(47*10^129789-119)/9129790Robert Price05/2019
5759(9*2^431141+1)/17129787Lelio R Paula06/2015
576025999^29384-29384^25999129730Frank Doornink03/2024
576125771^29408-29408^25771129723Frank Doornink02/2024
5762(166*10^129712+17)/3129714Robert Price07/2022
5763(29*2^430881-1)/21129709Lelio R Paula06/2015
57642^430807+1869563129686Enzo Doria05/2016
57652^430721-21429129660Enzo Doria07/2013
5766Phi(326081,3)129648Henri Lifchitz12/2025
5767(4*10^129618+89)/3129619Robert Price08/2021
5768(142^60223-1)/141129616Anonymous06/2024
5769(10^129587-7^129587)/3129587Jon Grantham07/2023
57702^430415-276271129568Enzo Doria07/2015
577132282^10311+10311^32282129558Hans Havermann04/2021
577229486^24741+24741^29486129545Hans Havermann04/2021
5773(29*10^129543+313)/9129544Robert Price04/2021
577437095^3104+3104^37095129533Hans Havermann04/2021
577531132^14459+14459^31132129514Hans Havermann04/2021
577632582^9435+9435^32582129506Hans Havermann03/2021
577730442^17953+17953^30442129505Hans Havermann03/2021
5778(199*10^129487-7)/3129489Robert Price05/2020
57792^430142-2791721129486Enzo Doria03/2016
5780(7*10^129472-13)/3129473Robert Price07/2018
5781(8*10^129469+79)/3129470Robert Price10/2020
578231678^12213+12213^31678129463Hans Havermann04/2021
578310620^32143-10619^32143129412Norbert Schneider08/2023
5784(772*10^129406-7)/9129408Robert Price06/2022
5785(535^47431-1)/534129406Tom Wu09/2024
5786((3*20425-8193)*F(618977)-(20425-8193)*L(618977))/2129363Yaroslav Berezhko03/2025
578731100^14439+14439^31100129362Hans Havermann04/2021
578833009^8288+8288^33009129345Hans Havermann04/2021
578925895^29306-29306^25895129334Frank Doornink03/2024
5790(44^78697+43^78697)/87129333Aurel Gibier11/2023
579129675^22804+22804^29675129324Hans Havermann04/2021
579229068^28099+28099^29068129315Hans Havermann04/2021
57932^429568-21017129313Enzo Doria07/2013
5794(10^129295+83)/3129295Robert Price08/2021
5795(853*10^129274-7)/9129276Robert Price07/2021
5796998^43100+997129263Alfred Reich03/2026
579730958^14961+14961^30958129249Hans Havermann04/2021
5798(11*10^129239-179)/3129240Robert Price09/2018
579928659^28988+28988^28659129208Norbert Schneider02/2021
580029423^24616+24616^29423129203Hans Havermann03/2021
58012^429194-112685129201Enzo Doria06/2014
580231*35^83672+17398129197Eric Chen05/2025
58032^429145-2780449129186Enzo Doria04/2016
580432500^9427+9427^32500129168Hans Havermann04/2021
580533577^7014+7014^33577129136Hans Havermann03/2021
58062^428892-113453129110Enzo Doria07/2014
5807(11*2^428881-7)/15129106Renaud Lifchitz03/2011
58082^428727-113959129060Enzo Doria10/2014
5809(7*2^428725-1)/13129059Lelio R Paula05/2014
5810(10^129051-31)/3129051Serge Batalov12/2014
5811(3^732836)/(2^732836)129047Henri Lifchitz05/2025
5812(134*10^129038+7)/3129040Robert Price02/2020
58132^428564+71161129011Enzo Doria04/2016
581428781^28930+28930^28781129002Norbert Schneider02/2021
581529065^27424+27424^29065128995Hans Havermann04/2021
58162^428502-113285128992Enzo Doria07/2014
58172^428421-21373128968Enzo Doria06/2013
5818L(616787)128901Henri Lifchitz09/2008
5819(765^44701-1)/764128900Tom Wu07/2024
582020^99055-3128874Paul Bourdelais12/2020
582191^65772-2128851Lelio R Paula05/2017
58222^428022+43128848Lelio R Paula05/2017
58232^427999-459397128841Enzo Doria05/2015
58242^427993+76847128839Enzo Doria05/2016
582531059^14060+14060^31059128833Hans Havermann03/2021
582610^128805+152871128806Patrick De Geest05/2021
582710^128805-10001128805Robert Price02/2021
58282^427824-1851507128788Enzo Doria08/2015
58292^427807-21469128783Enzo Doria07/2013
583029082^26783+26783^29082128772Hans Havermann04/2021
583140055^1638+1638^40055128750Hans Havermann04/2021
5832(923^43411-1)/922128720Tom Wu07/2024
583311^123594-240128710Enzo Doria09/2012
58342^427504-21503128692Enzo Doria07/2013
583537727^2574+2574^37727128673Hans Havermann04/2021
583629686^21591+21591^29686128668Hans Havermann04/2021
583710^128668-70000000001128668Robert Price08/2021
583810^128668-350729128668Alfred Reich08/2024
5839Phi(57476,13#)128668Henri Lifchitz12/2025
58402^427420+91128667Lelio R Paula05/2017
58418*10^128651-37128652Robert Price03/2022
5842(68*10^128645-257)/9128646Robert Price07/2019
5843Phi(236553,7)128631Henri Lifchitz12/2025
58442^427269-113635128621Enzo Doria08/2014
5845136^60270+135128589Alfred Reich03/2026
58462^427130+1877569128579Enzo Doria08/2016
58472^427068+20011128561Enzo Doria06/2023
58482^427016-115349128545Enzo Doria07/2015
58492^427001+1334025128541Henri Lifchitz11/2024
5850(4*10^128510+137)/3128511Robert Price03/2018
58512^426889-112879128507Enzo Doria06/2014
58522^426804+1869931128481Enzo Doria05/2016
58532^426750+77635128465Enzo Doria05/2016
585427708^28913-28913^27708128450Frank Doornink03/2024
585536988^2969+2969^36988128445Hans Havermann03/2021
585636664^3185+3185^36664128439Hans Havermann03/2021
585732618^8649+8649^32618128416Hans Havermann04/2021
585828883^27874+27874^28883128391Hans Havermann04/2021
58592^426425-91128367Lelio R Paula05/2017
5860(15*2^426398-1)/11128359Lelio R Paula05/2014
58612^426352+74971128345Enzo Doria04/2016
5862(199*10^128343-7)/3128345Robert Price05/2020
58634*10^128343-21128344Robert Price09/2018
5864(65*10^128338+493)/9128339Robert Price08/2021
586535632^3997+3997^35632128337Hans Havermann04/2021
58662^426300-1863689128330Enzo Doria03/2016
58672^426293+1881017128327Enzo Doria11/2016
5868(88*10^128324-637)/9128325Robert Price11/2020
5869Phi(161347,7)128320Henri Lifchitz12/2025
5870Phi(135199,-9)128312Henri Lifchitz12/2025
5871(491*10^128285+31)/9128287Robert Price04/2022
587239103^1908+1908^39103128281Hans Havermann04/2021
58732^426043+35128252Robert Price11/2015
5874(4*10^128244-19)/3128245Robert Price03/2018
587526220^29021-29021^26220128234Frank Doornink03/2024
587635489^4102+4102^35489128222Hans Havermann04/2021
587734721^4926+4926^34721128208Hans Havermann04/2021
5878(305*10^128198+1)/9128200Robert Price02/2020
58792^425808-459959128181Enzo Doria06/2015
588030632^15291+15291^30632128178Hans Havermann04/2021
5881U(623603)128177Serge Batalov07/2024
588235981^3648+3648^35981128167Hans Havermann04/2021
58832^425627-113605128127Enzo Doria08/2014
5884(4*10^128109+119)/3128110Robert Price12/2021
5885(22*10^128094+53)/3128095Robert Price07/2019
5886(86*10^128086-221)/9128087Robert Price09/2019
588718565^30002-30002^18565128070Norbert Schneider01/2015
5888(2^425287-9)/2737128021Lelio R Paula05/2015
5889(3*2^425233-1)/25128007Lelio R Paula05/2014
5890Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
58912^425205+4911128000Marek Hubal02/2017
589229241^23836+23836^29241127995Hans Havermann04/2021
58932^425118-113663127974Enzo Doria08/2014
5894(86*10^127967-329)/9127968Robert Price01/2020
58952^425061+1869761127957Enzo Doria05/2016
5896746^44541+44541^746127955Norbert Schneider07/2019
589730236^17043+17043^30236127946Hans Havermann03/2021
58982^424938+212419127920Enzo Doria08/2023
58992^424918-21141127914Enzo Doria07/2013
5900Phi(274823,-3)127907Henri Lifchitz12/2025
5901(62*10^127903+91)/9127904Robert Price07/2021
59022^424864-29489127897Enzo Doria08/2015
590330438^15893+15893^30438127877Hans Havermann02/2021
5904(97*10^127858-1)/3127860Serge Batalov12/2014
590528929^26258+26258^28929127845Hans Havermann03/2021
590630563^15220+15220^30563127828Hans Havermann03/2021
59072^424632-2786639127827Enzo Doria03/2016
590810^127821-700001127821Robert Price08/2021
59092^424577-113755127811Enzo Doria09/2014
5910(7*2^424512-1)/3127792Lelio R Paula05/2014
5911(56*10^127752+691)/9127753Robert Price05/2019
591211^122629-720127705Enzo Doria11/2012
591322*10^127645+3127647Robert Price01/2020
591428715^27844+27844^28715127631Hans Havermann03/2021
5915(56*10^127612+187)/9127613Robert Price10/2021
5916(5*36^81995+821)/7127609Eric Chen01/2021
59174*10^127562-39127563Robert Price09/2020
591832595^8186+8186^32595127547Hans Havermann03/2021
59192^423696-21429127546Enzo Doria07/2013
59202^423664-1864559127536Enzo Doria03/2016
592137889^2322+2322^37889127530Hans Havermann03/2021
592237668^2429+2429^37668127523Hans Havermann03/2021
59233^267267-4127519Henri Lifchitz10/2014
5924fibonacci(610144)-2127513Jon Grantham08/2023
592526253^28852-28852^26253127503Frank Doornink03/2024
5926(103*10^127491+17)/3127493Robert Price08/2020
592729376^21869+21869^29376127487Hans Havermann03/2021
592831186^12241+12241^31186127483Hans Havermann02/2021
5929(19^99689+5^99689)/24127477Robert Price09/2013
59307239^33023-7238^33023127459Norbert Schneider02/2026
593127069^28754-28754^27069127452Frank Doornink01/2024
5932(21*2^423372+1)/101127447Lelio R Paula05/2014
593330594^14645+14645^30594127446Hans Havermann03/2021
59342^423328-21537127435Enzo Doria07/2013
5935(67*10^127413-7)/3127415Robert Price01/2020
5936(5*34^83193+700233)/11127408Eric Chen08/2023
5937(2*10^127407+73)/3127407Robert Price09/2020
5938(2^423165-7)/25127384Lelio R Paula05/2015
5939(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
5940(4*10^127349+17)/3127350Tyler Busby01/2023
594129512^20647+20647^29512127341Hans Havermann03/2021
59422^422987-3001935127332Paul Bourdelais07/2023
5943(112*10^127324+17)/3127326Robert Price03/2020
594529565^20252+20252^29565127321Hans Havermann03/2021
5944232^232^232+1831^1831127321Henri Lifchitz03/2025
5946fibonacci(609165)-3127308Jon Grantham08/2023
5948(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
5947(5^182099-3^182099)/2127282Kellen Shenton05/2022
5949(16*10^127259+197)/3127260Robert Price04/2019
5950(26*10^127240+61)/3127241Robert Price10/2019
5951(234483*27^88884-145)/26127230Curtis Bright05/2015
59522^422515-114997127190Enzo Doria06/2015
59535*10^127179-3127180Robert Price07/2015
595431678^10343+10343^31678127176Hans Havermann03/2021
5955(44*10^127169-233)/9127170Robert Price01/2019
595634947^4352+4352^34947127162Hans Havermann03/2021
59576*10^127158+19127159Robert Price11/2021
595830469^14902+14902^30469127155Hans Havermann03/2021
59595*10^127153+77127154Robert Price12/2018
596029941^17620+17620^29941127130Hans Havermann02/2021
596131607^10516+10516^31607127119Hans Havermann03/2021
5962(19*10^127118-97)/3127119Robert Price10/2021
5963(29*10^127111+691)/9127112Robert Price08/2021
5964736^44335+44335^736127104Norbert Schneider07/2019
596533040^7023+7023^33040127090Hans Havermann03/2021
5966(4*10^127081+167)/9127081Robert Price03/2022
596729748^18661+18661^29748127052Hans Havermann03/2021
596827905^28578-28578^27905127049Frank Doornink03/2024
5969-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
5970(78^67141-1)/77127036Paul Bourdelais09/2017
5971(14*10^127014-137)/3127015Robert Price04/2021
597231436^10965+10965^31436127002Hans Havermann03/2021
597328905^24758+24758^28905127001Hans Havermann03/2021
59742^421860-113285126993Enzo Doria07/2014
5975(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
5976(2^421827-7)/11126982Lelio R Paula05/2015
597726268^28729-28729^26268126966Frank Doornink03/2024
597811^121910-840126957Enzo Doria12/2012
5979(56*10^126935+187)/9126936Robert Price10/2021
598028915^24538+24538^28915126933Hans Havermann03/2021
5981(29*10^126928-77)/3126929Robert Price02/2020
5982(259*10^126919-1)/3126921Robert Price12/2020
598310^126919+204567126920Patrick De Geest05/2021
5984(2^421617+100280245065)126920Paul Bourdelais05/2022
598510^126919-100001126919Robert Price07/2020
598628340^28503+28503^28340126907Norbert Schneider02/2021
59872^421534-3001935126895Paul Bourdelais07/2023
5988(71^68539+1)/72126882Paul Bourdelais09/2017
5989(5*10^126871-119)/3126872Robert Price03/2018
5990Phi(47471,561)126871Henri Lifchitz12/2025
5991331^50339-10004126846Enzo Doria07/2012
59922^421363-2790757126843Enzo Doria03/2016
5993(106*10^126839-1)/3126841Serge Batalov12/2014
599437938^2203+2203^37938126828Hans Havermann03/2021
5995(13*10^126819+77)/9126820Robert Price07/2022
5996(7*2^421243+1)/39126807Lelio R Paula05/2014
5998(14*10^126784-83)/3126785Robert Price12/2018
59972^421169-3001935126785Paul Bourdelais07/2023
59992^421161-286183126783Enzo Doria06/2015
600026733^28628-28628^26733126738Frank Doornink03/2024


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 07 2026 13:22 (Time in France)

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