PRP Records

Probable Primes Top 10000

(301737 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 ?
57512^412248+74611124100Enzo Doria04/2016
5752(22*10^124096-13)/9124097Robert Price06/2018
5753(455*10^124093+31)/9124095Robert Price06/2021
57542^412192-3329124083Yves Minet12/2014
5755(25*2^412191-1)/23124082Lelio R Paula05/2014
5757(25*10^124076-67)/3124077Robert Price06/2019
575628132^25735+25735^28132124077Hans Havermann03/2021
5758F(593689)124074Henri Lifchitz01/2005
5759(11*2^412161+1)/19124073Lelio R Paula05/2014
57601232^40143-40143^1232124067Norman Luhn10/2024
576126372^28057-28057^26372124045Frank Doornink03/2024
576227528^27937-27937^27528124034Frank Doornink03/2024
576335364^3215+3215^35364124028Hans Havermann03/2021
5765(266*10^124022-11)/3124024Robert Price04/2020
576429987^13674+13674^29987124024Hans Havermann03/2021
57662^411932-111546435124004Paul Bourdelais10/2021
57672^411884-113279123990Enzo Doria07/2014
5768(2^411832+1)/257123972Lelio R Paula05/2014
5769(2^411833+2)/514123972Stefano Morozzi03/2020
5770(26*10^123970-89)/9123971Robert Price06/2018
57712^411790-1853531123962Enzo Doria08/2015
5772(5^177337+1)/6123953Paul Bourdelais11/2008
5773(101*10^123950+7)/9123952Robert Price02/2022
57742^411711-113257123938Enzo Doria07/2014
5775(23*2^411675-1)/3123928Lelio R Paula05/2014
577636289^2598+2598^36289123914Hans Havermann03/2021
5777(11*10^123899-179)/3123900Robert Price09/2018
577832276^6879+6879^32276123860Hans Havermann02/2021
57792^411325-351103123822Enzo Doria06/2015
5780(646*10^123817+11)/9123819Robert Price10/2021
578130738^10643+10643^30738123784Hans Havermann03/2021
578231074^9607+9607^31074123755Hans Havermann03/2021
57832^411052+1872481123739Enzo Doria05/2016
578434365^3986+3986^34365123733Hans Havermann03/2021
57852^410997+39123723Lelio R Paula05/2014
5786(649^43987-1)/648123700Michael Stocker05/2020
5787(148*10^123688-1)/3123690Robert Price03/2020
578836825^2284+2284^36825123684Hans Havermann03/2021
578929582^15171+15171^29582123683Hans Havermann03/2021
579010^123671+3593037123672Paul Bourdelais10/2021
57918*10^123657+87123658Robert Price10/2019
579230505^11302+11302^30505123642Hans Havermann03/2021
579329956^13401+13401^29956123633Hans Havermann03/2021
579419*35^80065+19442123628Eric Chen05/2025
5795155^56438+154123618Norbert Schneider01/2019
57962^410596-39123602Lelio R Paula05/2014
5797(41*10^123600-221)/9123601Robert Price10/2021
579828995^18302+18302^28995123592Hans Havermann03/2021
579928302^23269+23269^28302123589Hans Havermann03/2021
5800(41^76630+40)/37123587Alfred Reich06/2024
58012^410540-115079123585Enzo Doria06/2015
5802(7*10^123563+107)/3123564Robert Price02/2018
58039*10^123549+89123550Robert Price11/2019
5804(197*10^123545+7)/3123547Robert Price12/2020
5805(3*2^410392-1)/9229123537Lelio R Paula05/2014
58062^410342+212449123526Enzo Doria08/2023
5807(29*10^123510+277)/9123511Robert Price11/2021
580828118^24687+24687^28118123508Hans Havermann03/2021
580939994^1225+1225^39994123507Hans Havermann03/2021
58102^410206-113081123485Enzo Doria07/2014
5811(25*2^410192+1)/10397123478Lelio R Paula04/2014
581228974^18215+18215^28974123442Hans Havermann03/2021
581328901^18618+18618^28901123406Hans Havermann03/2021
58142^409909-189123395Enzo Doria05/2014
5815135^57922-57922^135123394Norman Luhn10/2024
58162^409896-109043123391Enzo Doria04/2014
58172^409890+75409123390Enzo Doria04/2016
581881254^33+33^81254123386Hans Havermann03/2021
581933463^4854+4854^33463123348Hans Havermann03/2021
582034061^4182+4182^34061123348Hans Havermann03/2021
5821133^58076-2123345Lelio R Paula10/2017
5822L(2*409661)%(2^409661)123320Henri Lifchitz06/2025
5823F(590041)123311Henri Lifchitz01/2005
5824(82*10^123299+377)/9123300Robert Price03/2022
58252^409566-113501123292Enzo Doria08/2014
58262^409533+77747123282Enzo Doria05/2016
58272^409436-112799123253Enzo Doria06/2014
582828212^23321+23321^28212123223Hans Havermann03/2021
58292^409225+1873787123189Enzo Doria06/2016
58302^409174+73009123174Enzo Doria04/2016
5831(4893*35^79754-31)/34123148Eric Chen05/2025
58322^409058-112685123139Enzo Doria06/2014
5833(13*10^123137-61)/3123138Robert Price11/2018
58344*10^123113+21123114Robert Price12/2018
58352^408778+77689123055Enzo Doria05/2016
5836660^43643-43643^660123054Norman Luhn10/2024
58372^408690-75123028Lelio R Paula11/2013
583828327^22032+22032^28327123026Hans Havermann03/2021
5839(29*10^122996+673)/9122997Robert Price12/2018
5840(65*10^122994-101)/9122995Robert Price01/2022
58412^408574-2787341122994Enzo Doria03/2016
58423*10^122977+37122978Robert Price08/2018
5843(7*10^122976-67)/3122977Robert Price10/2021
5844Phi(157825,10)122961Maksym Voznyy06/2015
584525493^27902-27902^25493122948Frank Doornink02/2024
584626749^27768-27768^26749122938Frank Doornink03/2024
5847(68*10^122933-419)/9122934Robert Price07/2019
584829712^13721+13721^29712122931Hans Havermann03/2021
5849(13*2^408283+1)/1665122904Lelio R Paula05/2014
5850(266*10^122872-17)/3122874Robert Price07/2020
5851(16*10^122871+77)/3122872Robert Price03/2019
585230395^11022+11022^30395122865Hans Havermann03/2021
58534*10^122859-69122860Robert Price01/2022
5854(10^122857+167)/3122857Robert Price05/2021
585533331^4852+4852^33331122856Hans Havermann03/2021
5856(11*2^408100-1)/35122850Lelio R Paula04/2014
5857(19*10^122836-43)/3122837Robert Price05/2019
5858315^49162-49162^315122822Norman Luhn10/2024
585928420^20969+20969^28420122820Hans Havermann03/2021
5860(16*10^122818+179)/3122819Robert Price11/2021
586129865^12934+12934^29865122797Hans Havermann03/2021
5862(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
586317^99766+18122757Anonymous09/2024
5864(32*10^122733-77)/9122734Robert Price06/2018
5865(21*2^407604-1)/215122701Lelio R Paula04/2014
5867(22*10^122681+161)/3122682Robert Price05/2019
586629513^14350+14350^29513122682Hans Havermann03/2021
5868(21*2^407433-1)/13122650Lelio R Paula04/2014
5870(26*10^122625-131)/3122626Robert Price10/2019
5869(643*33^80753+3709)/32122626Eric Chen12/2023
587127925^24562+24562^27925122599Hans Havermann03/2021
5872(73*10^122592-1)/9122593Robert Price01/2015
5873(5*10^122592+91)/3122593Robert Price04/2018
587436751^2166+2166^36751122589Hans Havermann03/2021
5875(85*10^122585-1)/3122587Robert Price02/2020
587629368^14931+14931^29368122585Hans Havermann03/2021
58772^407179-112075122574Enzo Doria06/2014
5878(21*2^407131+1)/207517523122552Lelio R Paula04/2014
5879(66^67349+1)/67122543Paul Bourdelais09/2017
5880(646*10^122533+11)/9122535Robert Price10/2021
58812^407008-1867919122522Enzo Doria04/2016
588211^117642-300122512Enzo Doria10/2012
5883(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
58842^406949+72197122504Enzo Doria04/2016
5885(19*10^122501+149)/3122502Robert Price05/2019
588628632^18977+18977^28632122495Hans Havermann03/2021
588731815^7076+7076^31815122481Hans Havermann03/2021
58882^406826-65122467Lelio R Paula11/2013
58892^406821-2797363122466Enzo Doria04/2016
5890(7*10^122456-331)/9122456Robert Price03/2022
58912^406758-17122447Lelio R Paula11/2013
589229941^12282+12282^29941122437Hans Havermann03/2021
5893(30^82883-1)/29122427Robert Price12/2011
589427496^27577+27577^27496122422Norbert Schneider12/2020
589528732^18215+18215^28732122411Hans Havermann03/2021
5896(2^406583-1)/813167122388Jens K. Andersen02/2009
58974*10^122377+19122378Robert Price10/2018
589828227^21634+21634^28227122368Hans Havermann03/2021
5899Phi(246362,10)122365Makoto Kamada09/2019
59003*10^122345-97122346Robert Price07/2018
590197^61575-2122336Lelio R Paula12/2014
59022*10^122319+47122320Robert Price12/2021
5903208^52765+52765^208122313Norbert Schneider11/2020
59052^406298+2799109122308Enzo Doria04/2016
59042^406296+213691122308Enzo Doria09/2023
59067*10^122294+57122295Robert Price06/2019
5907(27*2^406241-1)/10277122289Lelio R Paula04/2014
59082^406229-1849993122288Enzo Doria08/2015
59093*10^122274+7122275Robert Price07/2015
59102^406117+1876577122254Enzo Doria07/2016
591129308^14835+14835^29308122253Hans Havermann03/2021
591228119^22268+22268^28119122253Hans Havermann03/2021
591332167^6312+6312^32167122240Hans Havermann03/2021
59143^256199-2^256199122238Mike Oakes06/2005
591527678^26053+26053^27678122223Hans Havermann03/2021
59162^405992-78557122216Jorge Menendez03/2018
5917(8*10^122203+43)/3122204Robert Price06/2018
5918(58*10^122170+329)/9122171Robert Price05/2019
59192^405774+179149122151Enzo Doria06/2016
59202^405693+20417122126Enzo Doria07/2023
5921(218*10^122109+7)/9122111Robert Price06/2022
592229189^15246+15246^29189122103Hans Havermann03/2021
592434*10^122082-9122084Robert Price06/2020
592333442^4473+4473^33442122084Hans Havermann03/2021
59255*10^122082+41122083Robert Price03/2019
592631849^6808+6808^31849122078Hans Havermann03/2021
59282^405514-3311122072Yves Minet12/2014
59292^405514-115511122072Enzo Doria07/2015
592723*10^122070-7122072Robert Price02/2020
59302^405422-113261122045Enzo Doria07/2014
593195^61698-61698^95122022Norman Luhn10/2024
59322^405173+71237121970Enzo Doria04/2016
5933fibonacci(583574)+2121960Jon Grantham08/2023
5934(154*10^121953+17)/9121955Robert Price06/2022
5935(34*10^121924+191)/9121925Robert Price08/2021
5936(2^405016+1)/257121920Lelio R Paula04/2014
593728557^18590+18590^28557121918Hans Havermann03/2021
593828641^18002+18002^28641121877Hans Havermann03/2021
59392^404858+71329121875Enzo Doria04/2016
59402^404813-114703121861Enzo Doria04/2015
59412^404764+77791121847Enzo Doria05/2016
594228830^16841+16841^28830121847Hans Havermann03/2021
5943(4*10^121825+89)/3121826Robert Price08/2021
5944317^48694+48694^317121787Norbert Schneider08/2015
59452^404536-115259121778Enzo Doria06/2015
59462^404501-631121767Yves Minet07/2012
59475*10^121764-69121765Robert Price02/2021
594828236^20485+20485^28236121738Hans Havermann02/2021
5949(382*10^121694-31)/9121696Robert Price06/2022
595063^67620+2121672Lelio R Paula08/2015
5951(25*34^79445-28062367)/33121669Eric Chen08/2023
5952(13*33^80110-121453)/32121648Eric Chen12/2023
5953(16*10^121633+167)/3121634Robert Price06/2019
595429955^11494+11494^29955121632Hans Havermann02/2021
5955(17*10^121621+1)/9121622Serge Batalov05/2010
595631088^8163+8163^31088121612Hans Havermann02/2021
5957(15*2^403912+1)/271121589Lelio R Paula05/2014
5958(211^52301-1)/210121560Anonymous04/2024
5959(10^121543-79)/3121543Robert Price01/2018
5960801^41852-41852^801121523Norman Luhn10/2024
59612^403676+76831121519Enzo Doria05/2016
5962(41^75337-1)/98233421080121492Paul Vanderveen05/2025
5963715^42564-42564^715121491Norman Luhn10/2024
5964(7*10^121487+143)/3121488Robert Price03/2018
596527965^22086+22086^27965121484Hans Havermann02/2021
5966(893*10^121470+7)/9121472Robert Price06/2021
5967(206*10^121462-11)/3121464Robert Price02/2022
596826282^27481-27481^26282121457Frank Doornink03/2024
5969(77*10^121455+67)/9121456Robert Price12/2021
59702^403363-113635121425Enzo Doria08/2014
597125531^27552-27552^25531121424Frank Doornink02/2024
5972(17*10^121418-113)/3121419Robert Price06/2021
59732^403336-1861469121417Enzo Doria03/2016
597427929^22186+22186^27929121382Hans Havermann02/2021
5975p(24442)#/2-64121381Robert Price04/2017
597611^116555-720121380Enzo Doria11/2012
5977(873^41263+1)/874121353Jinyuan Wang12/2024
59782^403100-461267121346Enzo Doria07/2015
59792^403093-112213121344Enzo Doria06/2014
598029404^13385+13385^29404121340Hans Havermann02/2021
598128106^20745+20745^28106121332Hans Havermann02/2021
5982(316^48539+1)/317121330Eric Chen10/2017
5983(23*10^121320-71)/3121321Robert Price07/2020
59842^403004+1866361121317Enzo Doria03/2016
59852^402953+89121301Lelio R Paula10/2013
59862^402944-2788319121299Enzo Doria03/2016
5987(44*10^121297-719)/9121298Robert Price12/2018
5988(27*2^402865+1)/5121276Lelio R Paula04/2014
59892^402828-113183121264Enzo Doria07/2014
5990(17*10^121242+1)/9121243Serge Batalov05/2010
5991(15*2^402757+1)/101121242Lelio R Paula05/2014
5992282^49477-49477^282121231Norman Luhn10/2024
59942^402715+1874223121230Enzo Doria06/2016
5993(35*10^121229-593)/9121230Robert Price07/2018
5995(91^61879+1)/92121222Paul Bourdelais09/2017
5996291^49190-49190^291121199Norman Luhn10/2024
5997(10^121243)/(121243^10)121193Henri Lifchitz05/2025
599828719^16568+16568^28719121174Hans Havermann02/2021
59997*10^121144+9121145Robert Price09/2015
600027490^25467+25467^27490121121Hans Havermann02/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 13 2025 09:00 (Time in France)

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