PRP Records

Probable Primes Top 10000

(295148 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 ?
40012^458248-21815137947Enzo Doria07/2013
40022^458194+1876549137931Enzo Doria07/2016
4003(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
4004(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
4005(793*10^137887+53)/9137889Robert Price01/2022
40062^457937+57137853Lelio R Paula09/2017
400728714^30921-30921^28714137849Frank Doornink05/2024
4008(8*10^137845+13)/3137846Robert Price06/2018
40092^457822+105137819Donovan Johnson06/2006
40102^457754-113711137798Enzo Doria09/2014
401111^132315-360137792Enzo Doria09/2012
401232072^19689+19689^32072137725Hans Havermann06/2021
401326529^31132-31132^26529137720Frank Doornink03/2024
401444592^1225+1225^44592137707Hans Havermann05/2021
401528986^30857-30857^28986137690Frank Doornink05/2024
40162^457347-37137676Lelio R Paula09/2017
40172^457322-2786393137668Enzo Doria10/2015
4018gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
401934015^11134+11134^34015137647Hans Havermann06/2021
40202^457240-59939137643Enzo Doria10/2015
4021(856*10^137633-1)/9137635Robert Price03/2020
402236232^6289+6289^36232137631Hans Havermann05/2021
40232^457120-21575137607Enzo Doria07/2013
4025(11*2^456978+1)/15137564Lelio R Paula07/2015
402430963^27722+27722^30963137564Hans Havermann04/2021
402633722^12003+12003^33722137562Hans Havermann06/2021
4027(7*25^98399+10613)/12137556Curtis Bright05/2015
402841901^1918+1918^41901137555Hans Havermann06/2021
4029(7*10^137551-1)/3137552Robert Price08/2022
403032930^15021+15021^32930137539Hans Havermann05/2021
403131178^25785+25785^31178137538Hans Havermann05/2021
4032419^52446+52446^419137525Norbert Schneider11/2020
40332^456813+214175137515Enzo Doria10/2023
40342^456796-113513137510Enzo Doria08/2014
403531788^21137+21137^31788137485Hans Havermann04/2021
4036(7*2^456655+1)/39137467Lelio R Paula07/2015
403727151^31004-31004^27151137466Frank Doornink01/2024
40382^456503-114361137422Enzo Doria01/2015
4039(11*2^456387+1)/19137386Lelio R Paula07/2015
404030618^30618-5^5137352Serge Batalov04/2024
404136248^6147+6147^36248137332Hans Havermann05/2021
404231986^19651+19651^31986137329Hans Havermann05/2021
40432^456167+22313137320Enzo Doria09/2023
404431817^20656+20656^31817137292Hans Havermann05/2021
4045(71*10^137250+1)/9137251Serge Batalov05/2010
40462^455922+76249137247Enzo Doria05/2016
404731310^24171+24171^31310137241Hans Havermann05/2021
404814^119741-119741^14137239Serge Batalov04/2016
404935014^8297+8297^35014137218Hans Havermann05/2021
4050(19*2^455760+1)/3455137196Lelio R Paula07/2015
4052124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
4051124^65536+57^65536137195Serge Batalov03/2018
40532^455689+72677137177Enzo Doria04/2016
4054(17948!)^2+Prime(17948)137118Robert Price08/2014
405531287^24128+24128^31287137116Hans Havermann05/2021
4056(37^87421-1)/36137093Robert Price03/2012
405736233^6070+6070^36233137077Hans Havermann05/2021
4058(8*10^137073-17)/9137073Serge Batalov11/2022
405938418^3697+3697^38418137070Hans Havermann04/2021
40602^455323-57137066Lelio R Paula09/2017
4061(56*10^137019+583)/9137020Robert Price08/2021
406225017^31148-31148^25017136997Frank Doornink12/2023
4063(73*17^111333-9)/16136991Curtis Bright05/2015
40642^455025-112723136977Enzo Doria06/2014
406533876^11039+11039^33876136959Hans Havermann05/2021
4066(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
4067(251^57059-1)/250136921Anonymous04/2024
406835142^7873+7873^35142136919Hans Havermann05/2021
4069(4997*31^91805-1)/2136918Eric Chen05/2024
407066*10^136894+7136896Robert Price07/2020
407128766^30697-30697^28766136875Frank Doornink05/2024
40722^454675-1777136871Yves Minet10/2011
407331676^20931+20931^31676136866Hans Havermann05/2021
40743*10^136829+29136830Robert Price05/2018
40754*10^136813-57136814Robert Price10/2018
4076(6092*28^94536-143)/9136812Curtis Bright05/2015
4077fibonacci(654572)-2136798Jon Grantham08/2023
407837359^4588+4588^37359136795Hans Havermann05/2021
40792^454348-53136773Lelio R Paula09/2017
408031^91680-2136729Lelio R Paula05/2017
40812^454199-113697136728Enzo Doria09/2014
408230785^27622+27622^30785136725Hans Havermann05/2021
408332973^14014+14014^32973136725Hans Havermann05/2021
40857*10^136716+69136717Robert Price07/2019
408436002^6273+6273^36002136717Hans Havermann05/2021
40866*10^136692+53136693Robert Price05/2020
4087(13*10^136687+47)/3136688Robert Price10/2018
40882^453935-2791357136649Enzo Doria01/2016
40892^453906-69131136640Enzo Doria11/2015
409033232^12915+12915^33232136620Hans Havermann05/2021
40912^453791+1873913136605Enzo Doria06/2016
409234166^9951+9951^34166136592Hans Havermann05/2021
4093(21*2^453740-1)/2735136588Lelio R Paula07/2015
409431102^24635+24635^31102136587Hans Havermann05/2021
4095580^49413+49413^580136550Norbert Schneider02/2019
40962^453503-2788297136519Enzo Doria11/2015
409734989^7958+7958^34989136486Hans Havermann12/2020
4098(2*10^136484+187)/9136484Robert Price06/2022
409931007^25158+25158^31007136452Hans Havermann11/2020
41002^453267-113827136447Enzo Doria09/2014
410132234^17085+17085^32234136435Hans Havermann12/2020
41022^453102+1877629136398Enzo Doria08/2016
410331016^24981+24981^31016136397Hans Havermann12/2020
4104(62*10^136384-791)/9136385Robert Price06/2019
410534171^9798+9798^34171136382Hans Havermann12/2020
4106(17*10^136354-113)/3136355Robert Price06/2021
410732756^14541+14541^32756136350Hans Havermann11/2020
410832205^17086+17086^32205136313Hans Havermann12/2020
4109(25*10^136303+161)/3136304Robert Price09/2019
411035337^7196+7196^35337136299Hans Havermann12/2020
4111(182*10^136291+1)/3136293Robert Price02/2020
4112(88*10^136234+83)/9136235Robert Price03/2022
411323*10^136225-7136227Robert Price02/2020
4114L(651821)136223Henri Lifchitz09/2008
411525519^30908-30908^25519136208Frank Doornink02/2024
41162^452460+77701136205Enzo Doria05/2016
41172^452440-114755136199Enzo Doria04/2015
411828625^30558-30558^28625136190Frank Doornink05/2024
411932286^16489+16489^32286136157Hans Havermann11/2020
4120(47*10^136141+493)/9136142Robert Price03/2019
412127140^30699-30699^27140136108Frank Doornink01/2024
412240392^2339+2339^40392136082Hans Havermann12/2020
41232*10^136057-43136058Robert Price04/2018
41242^451971+21563136057Enzo Doria08/2023
4125(2^451956-5)/181136051Lelio R Paula07/2015
41262^451947-22165136050Enzo Doria07/2013
41272^451787-21805136002Enzo Doria07/2013
41282^451734-112817135986Enzo Doria06/2014
4129(11*2^451714+1)/75135979Lelio R Paula07/2015
41302^451705-21879135977Enzo Doria07/2013
4131(4666^37249-1)/(4666^193-1)135957Ryan Propper11/2023
41322^451560-112349135934Enzo Doria06/2014
41332^451530+45135925Lelio R Paula08/2017
413426594^30719-30719^26594135925Frank Doornink03/2024
413531622^19875+19875^31622135922Hans Havermann11/2020
4136(25*10^135906-73)/3135907Robert Price09/2019
41372^451450-21743135900Enzo Doria07/2013
4138(7*10^135879+11)/9135879Tyler Busby01/2023
413935218^7199+7199^35218135846Hans Havermann11/2020
414035661^6446+6446^35661135844Hans Havermann11/2020
4141(7*33^89453-4743239)/32135835Eric Chen12/2023
414231869^18248+18248^31869135801Hans Havermann12/2020
4143(77*10^135789+157)/9135790Robert Price05/2022
41442^450958+60529135752Enzo Doria08/2023
41452^450805+65135706Lelio R Paula08/2017
414630761^25728+25728^30761135669Hans Havermann12/2020
41472*10^135663+69135664Robert Price06/2020
414833962^9867+9867^33962135651Hans Havermann11/2020
414934474^8605+8605^34474135647Hans Havermann11/2020
415034501^8508+8508^34501135583Hans Havermann12/2020
415135487^6614+6614^35487135577Hans Havermann12/2020
4152(13725^32768+1)/131074135573Lelio R Paula03/2012
4153(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
4154(5^193939+1)/6135557Paul Bourdelais12/2008
4155(76*10^135553-49)/9135554Robert Price07/2022
41565*3^284077+2^284077135540Jon Grantham08/2023
4157(844*10^135527-7)/9135529Robert Price05/2021
415827191^30560-30560^27191135517Frank Doornink01/2024
415940387^2260+2260^40387135463Hans Havermann12/2020
41602^449944-113247135447Enzo Doria07/2014
41612^449770-113247135395Enzo Doria07/2014
41622^449637-21471135355Enzo Doria07/2013
416326061^30650-30650^26061135351Frank Doornink03/2024
41642^449571-75135335Lelio R Paula08/2017
4165(14*10^135301-53)/3135302Robert Price12/2018
4166(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
4167(13*10^135279+437)/9135280Robert Price04/2018
41682^449330-35135262Lelio R Paula08/2017
4169(19*2^449325+1)/9135261Lelio R Paula07/2015
4170(2709^39601+1)/(2709^199+1)135260Martin Hopf12/2023
4171(13*10^135184-43)/3135185Robert Price11/2018
41722^449049-115309135178Enzo Doria07/2015
4173(10^135174+191)/3135174Robert Price02/2018
41742^449030-15135172Lelio R Paula08/2017
4175(157*10^135151-1)/3135153Robert Price01/2022
4176(2^448966+100280245065)135153Paul Bourdelais05/2022
4177(27*2^448936-1)/11135144Lelio R Paula07/2015
4178(37*10^135099+251)/9135100Robert Price09/2021
417932221^15586+15586^32221135095Hans Havermann12/2020
41802^448762-351401135091Enzo Doria07/2015
41812*10^135083-43135084Robert Price04/2018
418231357^20278+20278^31357135056Hans Havermann12/2020
418332242^15445+15445^32242135055Hans Havermann12/2020
4184k(198476)135054Robert Price07/2020
418532461^14470+14470^32461135053Hans Havermann12/2020
418631353^20288+20288^31353135045Hans Havermann12/2020
41875*10^135019+77135020Robert Price12/2018
4188(10^135011+719)/9135011Serge Batalov12/2014
4189(197*10^134978+7)/3134980Robert Price12/2020
41902^448386-2786261134978Enzo Doria03/2016
419126480^30517-30517^26480134975Frank Doornink03/2024
4192(73*10^134939+143)/9134940Robert Price07/2019
419333957^9392+9392^33957134903Hans Havermann12/2020
41942^448122+20809134899Enzo Doria08/2023
41952^448113-113949134896Enzo Doria11/2014
419630958^22755+22755^30958134887Hans Havermann12/2020
41972^447888-2786639134828Enzo Doria03/2016
41982^447870-396765134823Enzo Doria07/2013
419910^(2*67404+1)-10^67404-1134809Robert Price07/2023
42002^447766-21791134791Enzo Doria07/2013
4201(19*10^134786-49)/3134787Robert Price05/2019
4202Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
4203(23*2^447647+1)/155134755Lelio R Paula07/2015
42042^447552-1019134727Yves Minet02/2014
4205(2*10^134720-41)/3134720Robert Price02/2018
4206(25*10^134695-97)/9134696Robert Price01/2022
42072^447437-113569134692Enzo Doria08/2014
42082^447426-65134689Lelio R Paula08/2017
42092^447357-2797573134668Enzo Doria04/2016
42102^447278+93134645Lelio R Paula08/2017
421133193^11370+11370^33193134623Hans Havermann12/2020
421230736^23979+23979^30736134619Hans Havermann11/2020
42132^447094-113193134589Enzo Doria07/2014
42143^282041-9934134568Enzo Doria05/2014
42152^447019-109039134567Enzo Doria04/2014
421631376^19437+19437^31376134561Hans Havermann12/2020
42172^446990-22041134558Enzo Doria07/2013
4218123^64370+122134528Karsten Bonath04/2018
421930100^29461+29461^30100134525Hans Havermann11/2020
422031251^20158+20158^31251134519Hans Havermann11/2020
42212^446782-39701134495Enzo Doria09/2015
422231817^16858+16858^31817134485Hans Havermann12/2020
422332448^13937+13937^32448134471Hans Havermann12/2020
42245^192321+3^192321-1134427Jon Grantham08/2023
42252^446494-16485134409Enzo Doria04/2013
422630042^29785+29785^30042134408Hans Havermann12/2020
422729504^30069-30069^29504134405Norbert Schneider12/2014
42282^446441+65134393Lelio R Paula08/2017
4229(10^134385+719)/9134385Serge Batalov12/2014
423030043^29688+29688^30043134370Hans Havermann12/2020
4231(2*10^134364+529)/9134364Robert Price01/2018
423234657^7512+7512^34657134323Hans Havermann11/2020
4233(13*2^446187-1)/661134314Lelio R Paula07/2015
42345^192103+3^192103+2^192103+1134275Matthias Baur12/2019
423542035^1564+1564^42035134270Hans Havermann12/2020
4237(2^446022-7)/339134264Lelio R Paula07/2015
423630621^24248+24248^30621134264Hans Havermann12/2020
423830341^26562+26562^30341134237Hans Havermann11/2020
423910^134209+99867134210Patrick De Geest05/2021
424010^134209-80000001134209Robert Price04/2021
424110^134209-323283134209Patrick De Geest05/2021
424229976^29953+29953^29976134186Hans Havermann12/2020
424335038^6755+6755^35038134183Hans Havermann12/2020
424463^74568+2134174Lelio R Paula06/2017
42452^445671-22071134161Enzo Doria07/2013
4246532^49205+49205^532134129Norbert Schneider02/2019
424736453^4780+4780^36453134127Hans Havermann04/2021
4248(28*10^134122-1)/9134123Serge Batalov10/2014
42492^445515-113859134114Enzo Doria10/2014
425031083^20636+20636^31083134112Hans Havermann04/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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