PRP Records

Probable Primes Top 10000

(302601 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 ?
5751(15*2^426398-1)/11128359Lelio R Paula05/2014
57522^426352+74971128345Enzo Doria04/2016
5753(199*10^128343-7)/3128345Robert Price05/2020
57544*10^128343-21128344Robert Price09/2018
5755(65*10^128338+493)/9128339Robert Price08/2021
575635632^3997+3997^35632128337Hans Havermann04/2021
57572^426300-1863689128330Enzo Doria03/2016
57582^426293+1881017128327Enzo Doria11/2016
5759(88*10^128324-637)/9128325Robert Price11/2020
5760Phi(161347,7)128320Henri Lifchitz12/2025
5761Phi(135199,-9)128312Henri Lifchitz12/2025
5762(491*10^128285+31)/9128287Robert Price04/2022
576339103^1908+1908^39103128281Hans Havermann04/2021
57642^426043+35128252Robert Price11/2015
5765(4*10^128244-19)/3128245Robert Price03/2018
576626220^29021-29021^26220128234Frank Doornink03/2024
576735489^4102+4102^35489128222Hans Havermann04/2021
576834721^4926+4926^34721128208Hans Havermann04/2021
5769(305*10^128198+1)/9128200Robert Price02/2020
57702^425808-459959128181Enzo Doria06/2015
577130632^15291+15291^30632128178Hans Havermann04/2021
5772U(623603)128177Serge Batalov07/2024
577335981^3648+3648^35981128167Hans Havermann04/2021
57742^425627-113605128127Enzo Doria08/2014
5775(4*10^128109+119)/3128110Robert Price12/2021
5776(22*10^128094+53)/3128095Robert Price07/2019
5777(86*10^128086-221)/9128087Robert Price09/2019
577818565^30002-30002^18565128070Norbert Schneider01/2015
5779(2^425287-9)/2737128021Lelio R Paula05/2015
5780(3*2^425233-1)/25128007Lelio R Paula05/2014
5781Phi(149401,10)/30037901719561128003Makoto Kamada07/2022
57822^425205+4911128000Marek Hubal02/2017
578329241^23836+23836^29241127995Hans Havermann04/2021
57842^425118-113663127974Enzo Doria08/2014
5785(86*10^127967-329)/9127968Robert Price01/2020
57862^425061+1869761127957Enzo Doria05/2016
5787746^44541+44541^746127955Norbert Schneider07/2019
578830236^17043+17043^30236127946Hans Havermann03/2021
57892^424938+212419127920Enzo Doria08/2023
57902^424918-21141127914Enzo Doria07/2013
5791Phi(274823,-3)127907Henri Lifchitz12/2025
5792(62*10^127903+91)/9127904Robert Price07/2021
57932^424864-29489127897Enzo Doria08/2015
579430438^15893+15893^30438127877Hans Havermann02/2021
5795(97*10^127858-1)/3127860Serge Batalov12/2014
579628929^26258+26258^28929127845Hans Havermann03/2021
579730563^15220+15220^30563127828Hans Havermann03/2021
57982^424632-2786639127827Enzo Doria03/2016
579910^127821-700001127821Robert Price08/2021
58002^424577-113755127811Enzo Doria09/2014
5801(7*2^424512-1)/3127792Lelio R Paula05/2014
5802(56*10^127752+691)/9127753Robert Price05/2019
580311^122629-720127705Enzo Doria11/2012
580422*10^127645+3127647Robert Price01/2020
580528715^27844+27844^28715127631Hans Havermann03/2021
5806(56*10^127612+187)/9127613Robert Price10/2021
5807(5*36^81995+821)/7127609Eric Chen01/2021
58084*10^127562-39127563Robert Price09/2020
580932595^8186+8186^32595127547Hans Havermann03/2021
58102^423696-21429127546Enzo Doria07/2013
58112^423664-1864559127536Enzo Doria03/2016
581237889^2322+2322^37889127530Hans Havermann03/2021
581337668^2429+2429^37668127523Hans Havermann03/2021
58143^267267-4127519Henri Lifchitz10/2014
5815fibonacci(610144)-2127513Jon Grantham08/2023
581626253^28852-28852^26253127503Frank Doornink03/2024
5817(103*10^127491+17)/3127493Robert Price08/2020
581829376^21869+21869^29376127487Hans Havermann03/2021
581931186^12241+12241^31186127483Hans Havermann02/2021
5820(19^99689+5^99689)/24127477Robert Price09/2013
58217239^33023-7238^33023127459Norbert Schneider02/2026
582227069^28754-28754^27069127452Frank Doornink01/2024
5823(21*2^423372+1)/101127447Lelio R Paula05/2014
582430594^14645+14645^30594127446Hans Havermann03/2021
58252^423328-21537127435Enzo Doria07/2013
5826(67*10^127413-7)/3127415Robert Price01/2020
5827(5*34^83193+700233)/11127408Eric Chen08/2023
5828(2*10^127407+73)/3127407Robert Price09/2020
5829(2^423165-7)/25127384Lelio R Paula05/2015
5830(7726^32768+1)/13917994151414876602369127379Kellen Shenton04/2021
5831(4*10^127349+17)/3127350Tyler Busby01/2023
583229512^20647+20647^29512127341Hans Havermann03/2021
58332^422987-3001935127332Paul Bourdelais07/2023
5834(112*10^127324+17)/3127326Robert Price03/2020
583629565^20252+20252^29565127321Hans Havermann03/2021
5835232^232^232+1831^1831127321Henri Lifchitz03/2025
5837fibonacci(609165)-3127308Jon Grantham08/2023
5839(F(5)^182099-F(4)^182099)/F(3)127282Wayne Halsdorf08/2013
5838(5^182099-3^182099)/2127282Kellen Shenton05/2022
5840(16*10^127259+197)/3127260Robert Price04/2019
5841(26*10^127240+61)/3127241Robert Price10/2019
5842(234483*27^88884-145)/26127230Curtis Bright05/2015
58432^422515-114997127190Enzo Doria06/2015
58445*10^127179-3127180Robert Price07/2015
584531678^10343+10343^31678127176Hans Havermann03/2021
5846(44*10^127169-233)/9127170Robert Price01/2019
584734947^4352+4352^34947127162Hans Havermann03/2021
58486*10^127158+19127159Robert Price11/2021
584930469^14902+14902^30469127155Hans Havermann03/2021
58505*10^127153+77127154Robert Price12/2018
585129941^17620+17620^29941127130Hans Havermann02/2021
585231607^10516+10516^31607127119Hans Havermann03/2021
5853(19*10^127118-97)/3127119Robert Price10/2021
5854(29*10^127111+691)/9127112Robert Price08/2021
5855736^44335+44335^736127104Norbert Schneider07/2019
585633040^7023+7023^33040127090Hans Havermann03/2021
5857(4*10^127081+167)/9127081Robert Price03/2022
585829748^18661+18661^29748127052Hans Havermann03/2021
585927905^28578-28578^27905127049Frank Doornink03/2024
5860-516776642557847117490*Bern(37960)/34256837217082767928421792453127042Thomas Ritschel06/2017
5861(78^67141-1)/77127036Paul Bourdelais09/2017
5862(14*10^127014-137)/3127015Robert Price04/2021
586331436^10965+10965^31436127002Hans Havermann03/2021
586428905^24758+24758^28905127001Hans Havermann03/2021
58652^421860-113285126993Enzo Doria07/2014
5866(10^127030+7)/81234833/9230384921/6092460488946445358851126991Alfred Reich07/2021
5867(2^421827-7)/11126982Lelio R Paula05/2015
586826268^28729-28729^26268126966Frank Doornink03/2024
586911^121910-840126957Enzo Doria12/2012
5870(56*10^126935+187)/9126936Robert Price10/2021
587128915^24538+24538^28915126933Hans Havermann03/2021
5872(29*10^126928-77)/3126929Robert Price02/2020
5873(259*10^126919-1)/3126921Robert Price12/2020
587410^126919+204567126920Patrick De Geest05/2021
5875(2^421617+100280245065)126920Paul Bourdelais05/2022
587610^126919-100001126919Robert Price07/2020
587728340^28503+28503^28340126907Norbert Schneider02/2021
58782^421534-3001935126895Paul Bourdelais07/2023
5879(71^68539+1)/72126882Paul Bourdelais09/2017
5880(5*10^126871-119)/3126872Robert Price03/2018
5881Phi(47471,561)126871Henri Lifchitz12/2025
5882331^50339-10004126846Enzo Doria07/2012
58832^421363-2790757126843Enzo Doria03/2016
5884(106*10^126839-1)/3126841Serge Batalov12/2014
588537938^2203+2203^37938126828Hans Havermann03/2021
5886(13*10^126819+77)/9126820Robert Price07/2022
5887(7*2^421243+1)/39126807Lelio R Paula05/2014
5889(14*10^126784-83)/3126785Robert Price12/2018
58882^421169-3001935126785Paul Bourdelais07/2023
58902^421161-286183126783Enzo Doria06/2015
589126733^28628-28628^26733126738Frank Doornink03/2024
5892(106*10^126726+17)/3126728Robert Price04/2021
589330718^13347+13347^30718126724Hans Havermann03/2021
58942^420939-113935126716Enzo Doria10/2014
589511*23^93048+356126708Eric Chen08/2023
5896177^56363-2126703Lelio R Paula10/2017
58972^420741-113659126656Enzo Doria08/2014
58982^420694-21126642Lelio R Paula05/2017
5899(13*10^126638+437)/9126639Robert Price04/2018
5900(167*10^126637-17)/3126639Robert Price03/2020
59014*10^126625+87126626Robert Price08/2018
5902(31*2^420556+1)/7126601Lelio R Paula05/2014
59037*10^126600-99126601Robert Price06/2019
5904U(655247)/250330563881/206066063082749126596Serge Batalov07/2024
59052^420424-59189126561Enzo Doria10/2015
590628717^25534+25534^28717126560Hans Havermann03/2021
5907(86*10^126542+103)/9126543Robert Price12/2021
5908(19*10^126517-7)/3126518Robert Price12/2023
59092026^38261-2025^38261126516Henri Lifchitz12/2025
591028922^23655+23655^28922126503Hans Havermann03/2021
59112^420126+71893126471Enzo Doria04/2016
591225982^28643-28643^25982126450Frank Doornink03/2024
5913(43*10^126441+47)/9126442Robert Price12/2018
59148*10^126408+71126409Robert Price05/2022
59152^419866+1877059126393Enzo Doria07/2016
591629315^20484+20484^29315126390Hans Havermann03/2021
591729433^19676+19676^29433126384Hans Havermann03/2021
5918F(604711)126377Henri Lifchitz02/2005
59192^419757+72707126360Enzo Doria04/2016
59202^419720-21569126349Enzo Doria07/2013
59212^419637+29126324Henri Lifchitz02/2006
592231004^11865+11865^31004126319Hans Havermann03/2021
59232^419612+1876741126316Enzo Doria07/2016
59242^419520+2793271126289Enzo Doria03/2016
5925(2^419447-5)/369126264Lelio R Paula05/2014
59262^419328-1859939126231Enzo Doria03/2016
59272^419282-1851507126217Enzo Doria08/2015
5928(133*10^126212+17)/3126214Robert Price11/2021
59292^419251+1866143126208Enzo Doria03/2016
593011^121185+2126202Robert Price05/2014
593128203^28352+28352^28203126175Norbert Schneider01/2021
5932Phi(267889,3)126161Henri Lifchitz12/2025
5933(23*2^419036-1)/1393126141Lelio R Paula05/2014
59342^418851+23126087Robert Price09/2015
5935(2^418849-9)/2681126083Lelio R Paula05/2014
59362^418829+167126081Lelio R Paula01/2012
593731037^11530+11530^31037126067Hans Havermann03/2021
59384*10^126064-69126065Robert Price01/2022
5939(31*2^418782-1)/75891126063Lelio R Paula05/2014
5940(19*2^418754-1)/15126058Lelio R Paula05/2014
5941(35*10^126048-323)/9126049Robert Price10/2021
594233016^6551+6551^33016126000Hans Havermann03/2021
59432^418548-111546435125996Paul Bourdelais10/2021
594425134^28625-28625^25134125958Frank Doornink12/2023
594534736^4227+4227^34736125954Hans Havermann03/2021
5946(23*35^81566-144013)/34125944Eric Chen05/2025
594726197^28502-28502^26197125930Frank Doornink03/2024
59482^418319-109501125927Enzo Doria04/2014
59492^418316-112373125926Enzo Doria06/2014
595040398^1309+1309^40398125919Hans Havermann03/2021
5951(8*10^125894-29)/3125895Robert Price07/2018
5952(26*10^125886-413)/9125887Robert Price05/2018
595310^(2*62938+1)-7*10^62938-1125877Robert Price07/2023
595455*10^125847+9125849Robert Price03/2022
59554*10^125832+57125833Robert Price05/2022
59562^417968+1869811125821Enzo Doria06/2016
59572^417902+63125802Lelio R Paula09/2015
5958(10^125792-91)/9125792Serge Batalov12/2014
595930438^13573+13573^30438125791Hans Havermann03/2021
596032867^6714+6714^32867125782Hans Havermann03/2021
596131155^10892+10892^31155125777Hans Havermann03/2021
5962(35*10^125754-593)/9125755Robert Price07/2018
596330455^13464+13464^30455125754Hans Havermann03/2021
5964(32*10^125751-77)/9125752Robert Price06/2018
59652^417704+77011125742Enzo Doria05/2016
596629755^16816+16816^29755125737Hans Havermann03/2021
5967(22*10^125734+203)/9125735Robert Price10/2021
596829918^15915+15915^29918125710Hans Havermann03/2021
5969(10^125706+149)/3125706Serge Batalov12/2014
597028531^25368+25368^28531125659Hans Havermann03/2021
59712^417419-115309125656Enzo Doria07/2015
5972(46*10^125642+593)/9125643Robert Price04/2022
59732^417315+213953125625Enzo Doria10/2023
59742^417300+77281125620Enzo Doria05/2016
597530638^12537+12537^30638125561Hans Havermann03/2021
59762^417095-1657125559Yves Minet07/2014
597730162^14525+14525^30162125538Hans Havermann03/2021
5978(56*10^125535+583)/9125536Robert Price08/2021
5979(23*10^125517-179)/3125518Robert Price06/2022
59809*10^125516+29125517Robert Price03/2022
5981404*35^81280+23125505Eric Chen05/2025
5982(88*10^125492-637)/9125493Robert Price11/2020
598328958^21525+21525^28958125474Hans Havermann02/2021
59862^416773-25125462Lelio R Paula09/2015
5984(10^125482+7)/162685667/1639829194459125462Alfred Reich07/2021
598526078^28409-28409^26078125462Frank Doornink03/2024
598733889^5032+5032^33889125449Hans Havermann03/2021
5988(289511#+292834)/(2^3*146417)125444Makoto Morimoto10/2017
5989(2861^36481+1)/(2861^191+1)125438Martin Hopf12/2023
5990(11*2^416691+1)/43125436Lelio R Paula05/2014
5991(289511#+1896)/(2*3^3*79*780193*9911849)125434Makoto Morimoto06/2019
59922^416641-2*416641+1125422Robert Price05/2018
599333392^5697+5697^33392125409Hans Havermann03/2021
5994(21*2^416566-1)/17125399Lelio R Paula05/2014
59952^416530+1870429125389Enzo Doria05/2016
5996(56*10^125385+691)/9125386Robert Price05/2019
599727953^28198+28198^27953125381Norbert Schneider01/2021
599831074^10837+10837^31074125381Hans Havermann03/2021
599933745^5194+5194^33745125380Hans Havermann03/2021
60002^416490+1875109125376Enzo Doria09/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 01 2026 13:21 (Time in France)

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