PRP Records

Probable Primes Top 10000

(294613 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 ?
475129901^14272+14272^29901124224Hans Havermann03/2021
47522^412645-112213124219Enzo Doria06/2014
475329837^14500+14500^29837124163Hans Havermann03/2021
475428074^26455+26455^28074124158Hans Havermann03/2021
47552^412285+213317124111Enzo Doria09/2023
47562^412248+74611124100Enzo Doria04/2016
4757(22*10^124096-13)/9124097Robert Price06/2018
4758(455*10^124093+31)/9124095Robert Price06/2021
47592^412192-3329124083Yves Minet12/2014
4760(25*2^412191-1)/23124082Lelio R Paula05/2014
4762(25*10^124076-67)/3124077Robert Price06/2019
476128132^25735+25735^28132124077Hans Havermann03/2021
4763F(593689)124074Henri Lifchitz01/2005
4764(11*2^412161+1)/19124073Lelio R Paula05/2014
476535364^3215+3215^35364124028Hans Havermann03/2021
4767(266*10^124022-11)/3124024Robert Price04/2020
476629987^13674+13674^29987124024Hans Havermann03/2021
47682^411932-111546435124004Paul Bourdelais10/2021
47692^411884-113279123990Enzo Doria07/2014
4770(2^411832+1)/257123972Lelio R Paula05/2014
4771(2^411833+2)/514123972Stefano Morozzi03/2020
4772(26*10^123970-89)/9123971Robert Price06/2018
47732^411790-1853531123962Enzo Doria08/2015
4774(5^177337+1)/6123953Paul Bourdelais11/2008
4775(101*10^123950+7)/9123952Robert Price02/2022
47762^411711-113257123938Enzo Doria07/2014
4777(23*2^411675-1)/3123928Lelio R Paula05/2014
477836289^2598+2598^36289123914Hans Havermann03/2021
4779(11*10^123899-179)/3123900Robert Price09/2018
478032276^6879+6879^32276123860Hans Havermann02/2021
47812^411325-351103123822Enzo Doria06/2015
4782(646*10^123817+11)/9123819Robert Price10/2021
478330738^10643+10643^30738123784Hans Havermann03/2021
478431074^9607+9607^31074123755Hans Havermann03/2021
47852^411052+1872481123739Enzo Doria05/2016
478634365^3986+3986^34365123733Hans Havermann03/2021
47872^410997+39123723Lelio R Paula05/2014
4788(649^43987-1)/648123700Michael Stocker05/2020
4789(148*10^123688-1)/3123690Robert Price03/2020
479036825^2284+2284^36825123684Hans Havermann03/2021
479129582^15171+15171^29582123683Hans Havermann03/2021
479210^123671+3593037123672Paul Bourdelais10/2021
47938*10^123657+87123658Robert Price10/2019
479430505^11302+11302^30505123642Hans Havermann03/2021
479529956^13401+13401^29956123633Hans Havermann03/2021
4796155^56438+154123618Norbert Schneider01/2019
47972^410596-39123602Lelio R Paula05/2014
4798(41*10^123600-221)/9123601Robert Price10/2021
479928995^18302+18302^28995123592Hans Havermann03/2021
480028302^23269+23269^28302123589Hans Havermann03/2021
48012^410540-115079123585Enzo Doria06/2015
4802(7*10^123563+107)/3123564Robert Price02/2018
48039*10^123549+89123550Robert Price11/2019
4804(197*10^123545+7)/3123547Robert Price12/2020
4805(3*2^410392-1)/9229123537Lelio R Paula05/2014
48062^410342+212449123526Enzo Doria08/2023
4807(29*10^123510+277)/9123511Robert Price11/2021
480828118^24687+24687^28118123508Hans Havermann03/2021
480939994^1225+1225^39994123507Hans Havermann03/2021
48102^410206-113081123485Enzo Doria07/2014
4811(25*2^410192+1)/10397123478Lelio R Paula04/2014
481228974^18215+18215^28974123442Hans Havermann03/2021
481328901^18618+18618^28901123406Hans Havermann03/2021
48142^409909-189123395Enzo Doria05/2014
48152^409896-109043123391Enzo Doria04/2014
48162^409890+75409123390Enzo Doria04/2016
481781254^33+33^81254123386Hans Havermann03/2021
481833463^4854+4854^33463123348Hans Havermann03/2021
481934061^4182+4182^34061123348Hans Havermann03/2021
4820133^58076-2123345Lelio R Paula10/2017
4821F(590041)123311Henri Lifchitz01/2005
4822(82*10^123299+377)/9123300Robert Price03/2022
48232^409566-113501123292Enzo Doria08/2014
48242^409533+77747123282Enzo Doria05/2016
48252^409436-112799123253Enzo Doria06/2014
482628212^23321+23321^28212123223Hans Havermann03/2021
48272^409225+1873787123189Enzo Doria06/2016
48282^409174+73009123174Enzo Doria04/2016
48292^409058-112685123139Enzo Doria06/2014
4830(13*10^123137-61)/3123138Robert Price11/2018
48314*10^123113+21123114Robert Price12/2018
48322^408778+77689123055Enzo Doria05/2016
48332^408690-75123028Lelio R Paula11/2013
483428327^22032+22032^28327123026Hans Havermann03/2021
4835(29*10^122996+673)/9122997Robert Price12/2018
4836(65*10^122994-101)/9122995Robert Price01/2022
48372^408574-2787341122994Enzo Doria03/2016
48383*10^122977+37122978Robert Price08/2018
4839(7*10^122976-67)/3122977Robert Price10/2021
4840Phi(157825,10)122961Maksym Voznyy06/2015
484125493^27902-27902^25493122948Frank Doornink02/2024
4842(68*10^122933-419)/9122934Robert Price07/2019
484329712^13721+13721^29712122931Hans Havermann03/2021
4844(13*2^408283+1)/1665122904Lelio R Paula05/2014
4845(266*10^122872-17)/3122874Robert Price07/2020
4846(16*10^122871+77)/3122872Robert Price03/2019
484730395^11022+11022^30395122865Hans Havermann03/2021
48484*10^122859-69122860Robert Price01/2022
4849(10^122857+167)/3122857Robert Price05/2021
485033331^4852+4852^33331122856Hans Havermann03/2021
4851(11*2^408100-1)/35122850Lelio R Paula04/2014
4852(19*10^122836-43)/3122837Robert Price05/2019
485328420^20969+20969^28420122820Hans Havermann03/2021
4854(16*10^122818+179)/3122819Robert Price11/2021
485529865^12934+12934^29865122797Hans Havermann03/2021
4856(2^407821-lucasV(1,2,407821)+1)/2122767Mike Oakes11/2016
4857(32*10^122733-77)/9122734Robert Price06/2018
4858(21*2^407604-1)/215122701Lelio R Paula04/2014
4860(22*10^122681+161)/3122682Robert Price05/2019
485929513^14350+14350^29513122682Hans Havermann03/2021
4861(21*2^407433-1)/13122650Lelio R Paula04/2014
4863(26*10^122625-131)/3122626Robert Price10/2019
4862(643*33^80753+3709)/32122626Eric Chen12/2023
486427925^24562+24562^27925122599Hans Havermann03/2021
4865(73*10^122592-1)/9122593Robert Price01/2015
4866(5*10^122592+91)/3122593Robert Price04/2018
486736751^2166+2166^36751122589Hans Havermann03/2021
4868(85*10^122585-1)/3122587Robert Price02/2020
486929368^14931+14931^29368122585Hans Havermann03/2021
48702^407179-112075122574Enzo Doria06/2014
4871(21*2^407131+1)/207517523122552Lelio R Paula04/2014
4872(66^67349+1)/67122543Paul Bourdelais09/2017
4873(646*10^122533+11)/9122535Robert Price10/2021
48742^407008-1867919122522Enzo Doria04/2016
487511^117642-300122512Enzo Doria10/2012
4876(F(3*97700+1)^2+L(3*97700+1)^2)/2122509Henri Lifchitz10/2017
48772^406949+72197122504Enzo Doria04/2016
4878(19*10^122501+149)/3122502Robert Price05/2019
487928632^18977+18977^28632122495Hans Havermann03/2021
488031815^7076+7076^31815122481Hans Havermann03/2021
48812^406826-65122467Lelio R Paula11/2013
48822^406821-2797363122466Enzo Doria04/2016
4883(7*10^122456-331)/9122456Robert Price03/2022
48842^406758-17122447Lelio R Paula11/2013
488529941^12282+12282^29941122437Hans Havermann03/2021
4886(30^82883-1)/29122427Robert Price12/2011
488727496^27577+27577^27496122422Norbert Schneider12/2020
488828732^18215+18215^28732122411Hans Havermann03/2021
4889(2^406583-1)/813167122388Jens K. Andersen02/2009
48904*10^122377+19122378Robert Price10/2018
489128227^21634+21634^28227122368Hans Havermann03/2021
4892Phi(246362,10)122365Makoto Kamada09/2019
48933*10^122345-97122346Robert Price07/2018
489497^61575-2122336Lelio R Paula12/2014
48952*10^122319+47122320Robert Price12/2021
4896208^52765+52765^208122313Norbert Schneider11/2020
48982^406298+2799109122308Enzo Doria04/2016
48972^406296+213691122308Enzo Doria09/2023
48997*10^122294+57122295Robert Price06/2019
4900(27*2^406241-1)/10277122289Lelio R Paula04/2014
49012^406229-1849993122288Enzo Doria08/2015
49023*10^122274+7122275Robert Price07/2015
49032^406117+1876577122254Enzo Doria07/2016
490429308^14835+14835^29308122253Hans Havermann03/2021
490528119^22268+22268^28119122253Hans Havermann03/2021
490632167^6312+6312^32167122240Hans Havermann03/2021
49073^256199-2^256199122238Mike Oakes06/2005
490827678^26053+26053^27678122223Hans Havermann03/2021
49092^405992-78557122216Jorge Menendez03/2018
4910(8*10^122203+43)/3122204Robert Price06/2018
4911(58*10^122170+329)/9122171Robert Price05/2019
49122^405774+179149122151Enzo Doria06/2016
49132^405693+20417122126Enzo Doria07/2023
4914(218*10^122109+7)/9122111Robert Price06/2022
491529189^15246+15246^29189122103Hans Havermann03/2021
491734*10^122082-9122084Robert Price06/2020
491633442^4473+4473^33442122084Hans Havermann03/2021
49185*10^122082+41122083Robert Price03/2019
491931849^6808+6808^31849122078Hans Havermann03/2021
49212^405514-3311122072Yves Minet12/2014
49222^405514-115511122072Enzo Doria07/2015
492023*10^122070-7122072Robert Price02/2020
49232^405422-113261122045Enzo Doria07/2014
49242^405173+71237121970Enzo Doria04/2016
4925fibonacci(583574)+2121960Jon Grantham08/2023
4926(154*10^121953+17)/9121955Robert Price06/2022
4927(34*10^121924+191)/9121925Robert Price08/2021
4928(2^405016+1)/257121920Lelio R Paula04/2014
492928557^18590+18590^28557121918Hans Havermann03/2021
493028641^18002+18002^28641121877Hans Havermann03/2021
49312^404858+71329121875Enzo Doria04/2016
49322^404813-114703121861Enzo Doria04/2015
49332^404764+77791121847Enzo Doria05/2016
493428830^16841+16841^28830121847Hans Havermann03/2021
4935(4*10^121825+89)/3121826Robert Price08/2021
4936317^48694+48694^317121787Norbert Schneider08/2015
49372^404536-115259121778Enzo Doria06/2015
49382^404501-631121767Yves Minet07/2012
49395*10^121764-69121765Robert Price02/2021
494028236^20485+20485^28236121738Hans Havermann02/2021
4941(382*10^121694-31)/9121696Robert Price06/2022
494263^67620+2121672Lelio R Paula08/2015
4943(25*34^79445-28062367)/33121669Eric Chen08/2023
4944(13*33^80110-121453)/32121648Eric Chen12/2023
4945(16*10^121633+167)/3121634Robert Price06/2019
494629955^11494+11494^29955121632Hans Havermann02/2021
4947(17*10^121621+1)/9121622Serge Batalov05/2010
494831088^8163+8163^31088121612Hans Havermann02/2021
4949(15*2^403912+1)/271121589Lelio R Paula05/2014
4950(10^121543-79)/3121543Robert Price01/2018
49512^403676+76831121519Enzo Doria05/2016
4952(7*10^121487+143)/3121488Robert Price03/2018
495327965^22086+22086^27965121484Hans Havermann02/2021
4954(893*10^121470+7)/9121472Robert Price06/2021
4955(206*10^121462-11)/3121464Robert Price02/2022
4956(77*10^121455+67)/9121456Robert Price12/2021
49572^403363-113635121425Enzo Doria08/2014
495825531^27552-27552^25531121424Frank Doornink02/2024
4959(17*10^121418-113)/3121419Robert Price06/2021
49602^403336-1861469121417Enzo Doria03/2016
496127929^22186+22186^27929121382Hans Havermann02/2021
4962p(24442)#/2-64121381Robert Price04/2017
496311^116555-720121380Enzo Doria11/2012
49642^403100-461267121346Enzo Doria07/2015
49652^403093-112213121344Enzo Doria06/2014
496629404^13385+13385^29404121340Hans Havermann02/2021
496728106^20745+20745^28106121332Hans Havermann02/2021
4968(316^48539+1)/317121330Eric Chen10/2017
4969(23*10^121320-71)/3121321Robert Price07/2020
49702^403004+1866361121317Enzo Doria03/2016
49712^402953+89121301Lelio R Paula10/2013
49722^402944-2788319121299Enzo Doria03/2016
4973(44*10^121297-719)/9121298Robert Price12/2018
4974(27*2^402865+1)/5121276Lelio R Paula04/2014
49752^402828-113183121264Enzo Doria07/2014
4976(17*10^121242+1)/9121243Serge Batalov05/2010
4977(15*2^402757+1)/101121242Lelio R Paula05/2014
49792^402715+1874223121230Enzo Doria06/2016
4978(35*10^121229-593)/9121230Robert Price07/2018
4980(91^61879+1)/92121222Paul Bourdelais09/2017
498128719^16568+16568^28719121174Hans Havermann02/2021
49827*10^121144+9121145Robert Price09/2015
498327490^25467+25467^27490121121Hans Havermann02/2021
498434575^3182+3182^34575121106Hans Havermann02/2021
49855*10^121100-37121101Robert Price11/2021
498625592^27467-27467^25592121078Frank Doornink02/2024
498729954^10935+10935^29954120979Hans Havermann02/2021
498833585^3992+3992^33585120946Hans Havermann02/2021
498940296^1003+1003^40296120941Hans Havermann02/2021
49902^401725-113251120932Enzo Doria07/2014
4991(15*2^401677-1)/19120917Lelio R Paula05/2014
49922^401652+73711120910Enzo Doria04/2016
4993(2^401632+3)/79120902Lelio R Paula04/2014
499440450^973+973^40450120870Hans Havermann01/2021
4995(8*10^120851-11)/3120852Robert Price07/2023
499610^120841+88417120842Patrick De Geest04/2020
499710^120841-123456789120841Robert Price02/2020
499810^120841-176853120841Patrick De Geest04/2020
49992^401406-2791331120836Enzo Doria03/2016
5000(28^83497+1)/29120832Robert Price07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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