PRP Records

Probable Primes Top 10000

(301901 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 ?
475131803^25670+25670^31803140233Hans Havermann05/2021
47522^465803-114817140221Enzo Doria05/2015
4753floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
47542^465503-112735140131Enzo Doria07/2014
4755(16*10^140091+167)/3140092Robert Price06/2019
4756(8*10^140087-137)/3140088Robert Price03/2022
47576^179964+179964^6-1140040Robert Price04/2014
4758(89*10^140008-179)/9140009Robert Price12/2019
4759(29*2^465077-1)/9140003Lelio R Paula08/2015
47602^465072-344789140001Enzo Doria07/2015
476134742^10683+10683^34742139965Hans Havermann05/2021
47625*10^139945+81139946Robert Price03/2019
476332648^19335+19335^32648139941Hans Havermann05/2021
47642^464864-17139939Lelio R Paula09/2017
47658*10^139920+51139921Robert Price08/2019
4766(85*10^139913-1)/3139915Robert Price02/2020
476731203^30436+30436^31203139896Hans Havermann04/2021
47682^464642+22189139872Enzo Doria09/2023
476926138^31663-31663^26138139865Frank Doornink03/2024
4770(16^116139+619)/5139845Anonymous08/2022
4771(2^464556+619)/5139845Eric Chen10/2023
47724*10^139839-27139840Robert Price08/2021
477333582^14573+14573^33582139821Hans Havermann05/2021
4774(17^113621+1)/18139804Paul Bourdelais09/2011
47762*10^139800-21139801Robert Price09/2020
477532628^19261+19261^32628139801Hans Havermann04/2021
4777(13*10^139782+191)/3139783Robert Price11/2018
4778(64*10^139776+791)/9139777Robert Price01/2022
4779(695*10^139772+7)/9139774Robert Price12/2021
4780(19*2^464312-1)/3139773Lelio R Paula08/2015
4781(74*10^139723+133)/9139724Robert Price06/2019
47823*10^139722+13139723Robert Price07/2018
478331577^26592+26592^31577139721Hans Havermann05/2021
478477*10^139692+3139694Robert Price06/2020
4785(31*2^463970+1)/5139670Lelio R Paula08/2015
4786(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
478739640^3321+3321^39640139584Hans Havermann05/2021
478836663^6410+6410^36663139571Hans Havermann05/2021
47892^463633-2788423139568Enzo Doria11/2015
479033659^13978+13978^33659139532Hans Havermann05/2021
479131811^24318+24318^31811139521Hans Havermann04/2021
479234149^12172+12172^34149139512Hans Havermann04/2021
4793(29*10^139476+313)/9139477Robert Price04/2021
479431721^24940+24940^31721139474Hans Havermann05/2021
479532833^17698+17698^32833139473Hans Havermann05/2021
47962^463271-109501139459Enzo Doria04/2014
4797(5*10^139457+79)/3139458Robert Price03/2018
47982^463237-99139449Lelio R Paula09/2017
4799(49*10^139442+383)/9139443Robert Price04/2019
480031155^29902+29902^31155139441Hans Havermann05/2021
4801(7*10^139417-547)/9139417Robert Price01/2018
480229636^31175-31175^29636139409Frank Doornink05/2024
4803(10^139398+191)/3139398Robert Price02/2018
480423*10^139386-3139388Robert Price10/2021
48052^463019+79463139383Enzo Doria06/2016
48063^292129-112756139381Enzo Doria07/2014
4807(15*2^462951+1)/527139361Lelio R Paula08/2015
480831922^23205+23205^31922139359Hans Havermann05/2021
4809(19*10^139336+503)/9139337Alfred Reich11/2023
48112^462855-1865707139334Enzo Doria02/2016
481031237^28876+28876^31237139334Hans Havermann05/2021
4812(86*10^139315+121)/9139316Robert Price08/2019
48132^462786-292043139313Enzo Doria08/2015
481438915^3798+3798^38915139299Hans Havermann05/2021
4816(26*10^139289+1)/9139290Serge Batalov05/2010
4815(17*10^139289+7)/3139290Robert Price06/2023
481734065^12248+12248^34065139260Hans Havermann05/2021
481836425^6654+6654^36425139256Hans Havermann05/2021
481939252^3527+3527^39252139243Hans Havermann05/2021
4820(17*10^139239+67)/3139240Robert Price01/2019
482131887^23248+23248^31887139231Hans Havermann05/2021
4822(25*10^139210-97)/9139211Robert Price01/2022
48232^462238-935139148Yves Minet02/2014
4824(29*10^139134-119)/9139135Robert Price12/2021
4825U(687859)/4127153139105Serge Batalov07/2024
4826(109*10^139100-7)/3139102Robert Price03/2021
482738744^3885+3885^38744139068Hans Havermann05/2021
482831112^29499+29499^31112139065Hans Havermann05/2021
48292*10^139043-63139044Robert Price01/2022
483036390^6613+6613^36390139025Hans Havermann04/2021
483130554^30989-30989^30554138988Frank Doornink05/2024
48322*10^138975+33138976Robert Price11/2021
483342437^1882+1882^42437138966Hans Havermann05/2021
483432151^20990+20990^32151138958Hans Havermann05/2021
483532154^20933+20933^32154138933Hans Havermann04/2021
483631082^29499+29499^31082138931Hans Havermann04/2021
483730573^30962-30962^30573138876Frank Doornink05/2024
48382^461228+1870441138844Enzo Doria05/2016
48392^461204-113675138837Enzo Doria08/2014
4840(397227*29^94935-19)/28138837Eric Chen06/2025
4841(2^461139-7)/47138815Lelio R Paula08/2015
4842(17*10^138812-521)/9138813Robert Price04/2018
48433*10^138811-11138812Robert Price07/2018
484429109^31088-31088^29109138778Frank Doornink05/2024
4845(28*10^138768+173)/3138769Robert Price12/2019
4846(17*2^460963+1)/124051613138757Lelio R Paula08/2015
4847(379*10^138737-1)/9138739Robert Price02/2020
4848(43*10^138648+101)/9138649Robert Price11/2018
48492^460567-113541138645Enzo Doria08/2014
48502^460539+224789138637Enzo Doria07/2024
4851(10^138622+161)/9138622Robert Price09/2021
48527*10^138604+3138605Robert Price08/2015
4853(133*10^138600+17)/3138602Robert Price11/2021
485433912^12203+12203^33912138581Hans Havermann05/2021
48552^460330+69138574Lelio R Paula09/2017
4856(17*10^138569-77)/3138570Robert Price08/2019
485731186^27725+27725^31186138556Hans Havermann05/2021
4858(16*10^138545+89)/3138546Robert Price03/2021
485939753^3056+3056^39753138546Hans Havermann05/2021
486031282^26847+26847^31282138545Hans Havermann05/2021
48616*10^138520-37138521Robert Price02/2021
48632^460078-69581138498Enzo Doria12/2015
486231830^22447+22447^31830138498Hans Havermann05/2021
486437384^5065+5065^37384138492Hans Havermann05/2021
486528736^31055-31055^28736138457Frank Doornink05/2024
486634774^9585+9585^34774138456Hans Havermann05/2021
486710^138444-5001138444Robert Price12/2021
48682^459768+1531138404Lelio R Paula06/2012
4869(266*10^138328-17)/3138330Robert Price07/2020
487027200^31193-31193^27200138328Frank Doornink01/2024
48712024^41836+2025138319Henri Lifchitz01/2025
487228782^31019-31019^28782138318Frank Doornink05/2024
487332963^15696+15696^32963138306Hans Havermann05/2021
48742^459343-113611138277Enzo Doria08/2014
4875(28*10^138240+113)/3138241Robert Price03/2020
48762^459199+1874393138233Enzo Doria06/2016
487733339^14002+14002^33339138230Hans Havermann05/2021
487830137^30860-30860^30137138226Frank Doornink05/2024
48792^459063-345307138192Enzo Doria06/2015
48802*10^138162-43138163Robert Price04/2018
48812^458927-112747138151Enzo Doria06/2014
48822^458927-69217138151Enzo Doria11/2015
488330907^29458+29458^30907138130Hans Havermann05/2021
488432882^15837+15837^32882138094Hans Havermann05/2021
488539252^3295+3295^39252138083Hans Havermann05/2021
488633789^12190+12190^33789138062Hans Havermann06/2021
4887555555*2^458524+1513138036Darren Bedwell08/2009
488828095^31028-31028^28095138033Frank Doornink05/2024
488930931^29002+29002^30931138028Hans Havermann05/2021
48902^458465+2^32+1138012T. D. Noe06/2007
489132206^19275+19275^32206138003Hans Havermann05/2021
48922^458321-113053137969Enzo Doria07/2014
48936^177298+323137965Riley Fisher03/2023
48942^458298+79459137962Enzo Doria06/2016
489530254^30789-30789^30254137959Frank Doornink05/2024
48962^458248-21815137947Enzo Doria07/2013
48972^458194+1876549137931Enzo Doria07/2016
4898(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
4899(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
4900(793*10^137887+53)/9137889Robert Price01/2022
49012^457937+57137853Lelio R Paula09/2017
490228714^30921-30921^28714137849Frank Doornink05/2024
4903(8*10^137845+13)/3137846Robert Price06/2018
49042^457822+105137819Donovan Johnson06/2006
49052^457754-113711137798Enzo Doria09/2014
490611^132315-360137792Enzo Doria09/2012
4907(2^659318)%L(659318)137787Henri Lifchitz05/2025
490832072^19689+19689^32072137725Hans Havermann06/2021
490926529^31132-31132^26529137720Frank Doornink03/2024
491044592^1225+1225^44592137707Hans Havermann05/2021
491128986^30857-30857^28986137690Frank Doornink05/2024
49122^457347-37137676Lelio R Paula09/2017
49132^457322-2786393137668Enzo Doria10/2015
4914gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
4915Phi(699340M,10)137664Anonymous03/2025
491634015^11134+11134^34015137647Hans Havermann06/2021
49172^457240-59939137643Enzo Doria10/2015
4918(856*10^137633-1)/9137635Robert Price03/2020
491936232^6289+6289^36232137631Hans Havermann05/2021
49202^457120-21575137607Enzo Doria07/2013
4922(11*2^456978+1)/15137564Lelio R Paula07/2015
492130963^27722+27722^30963137564Hans Havermann04/2021
492333722^12003+12003^33722137562Hans Havermann06/2021
4924(7*25^98399+10613)/12137556Curtis Bright05/2015
492541901^1918+1918^41901137555Hans Havermann06/2021
4926(7*10^137551-1)/3137552Robert Price08/2022
492732930^15021+15021^32930137539Hans Havermann05/2021
492831178^25785+25785^31178137538Hans Havermann05/2021
4929419^52446+52446^419137525Norbert Schneider11/2020
49302^456813+214175137515Enzo Doria10/2023
49312^456796-113513137510Enzo Doria08/2014
493231788^21137+21137^31788137485Hans Havermann04/2021
4933(7*2^456655+1)/39137467Lelio R Paula07/2015
493427151^31004-31004^27151137466Frank Doornink01/2024
49352^456503-114361137422Enzo Doria01/2015
4936(11*2^456387+1)/19137386Lelio R Paula07/2015
493730618^30618-5^5137352Serge Batalov04/2024
493836248^6147+6147^36248137332Hans Havermann05/2021
493931986^19651+19651^31986137329Hans Havermann05/2021
49402^456167+22313137320Enzo Doria09/2023
494131817^20656+20656^31817137292Hans Havermann05/2021
4942(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
4943(71*10^137250+1)/9137251Serge Batalov05/2010
49442^455922+76249137247Enzo Doria05/2016
494531310^24171+24171^31310137241Hans Havermann05/2021
494614^119741-119741^14137239Serge Batalov04/2016
494735014^8297+8297^35014137218Hans Havermann05/2021
4948(19*2^455760+1)/3455137196Lelio R Paula07/2015
4950124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
4949124^65536+57^65536137195Serge Batalov03/2018
49512^455689+72677137177Enzo Doria04/2016
4952(17948!)^2+Prime(17948)137118Robert Price08/2014
495331287^24128+24128^31287137116Hans Havermann05/2021
4954(37^87421-1)/36137093Robert Price03/2012
495536233^6070+6070^36233137077Hans Havermann05/2021
4956(8*10^137073-17)/9137073Serge Batalov11/2022
495738418^3697+3697^38418137070Hans Havermann04/2021
49582^455323-57137066Lelio R Paula09/2017
4959(56*10^137019+583)/9137020Robert Price08/2021
496025017^31148-31148^25017136997Frank Doornink12/2023
4961(73*17^111333-9)/16136991Curtis Bright05/2015
49622^455025-112723136977Enzo Doria06/2014
496333876^11039+11039^33876136959Hans Havermann05/2021
4964(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
4965(251^57059-1)/250136921Anonymous04/2024
496635142^7873+7873^35142136919Hans Havermann05/2021
4967(4997*31^91805-1)/2136918Eric Chen05/2024
496866*10^136894+7136896Robert Price07/2020
496928766^30697-30697^28766136875Frank Doornink05/2024
49702^454675-1777136871Yves Minet10/2011
497131676^20931+20931^31676136866Hans Havermann05/2021
49723*10^136829+29136830Robert Price05/2018
49734*10^136813-57136814Robert Price10/2018
4974(6092*28^94536-143)/9136812Curtis Bright05/2015
4975fibonacci(654572)-2136798Jon Grantham08/2023
497637359^4588+4588^37359136795Hans Havermann05/2021
49772^454348-53136773Lelio R Paula09/2017
497831^91680-2136729Lelio R Paula05/2017
49792^454199-113697136728Enzo Doria09/2014
498030785^27622+27622^30785136725Hans Havermann05/2021
498132973^14014+14014^32973136725Hans Havermann05/2021
49837*10^136716+69136717Robert Price07/2019
498236002^6273+6273^36002136717Hans Havermann05/2021
49846*10^136692+53136693Robert Price05/2020
4985(13*10^136687+47)/3136688Robert Price10/2018
4986F(2*453976)%(2^453976)136661Henri Lifchitz06/2025
49872^453935-2791357136649Enzo Doria01/2016
49882^453906-69131136640Enzo Doria11/2015
498933232^12915+12915^33232136620Hans Havermann05/2021
49902^453791+1873913136605Enzo Doria06/2016
499134166^9951+9951^34166136592Hans Havermann05/2021
4992(21*2^453740-1)/2735136588Lelio R Paula07/2015
499331102^24635+24635^31102136587Hans Havermann05/2021
4994580^49413+49413^580136550Norbert Schneider02/2019
49952^453503-2788297136519Enzo Doria11/2015
499634989^7958+7958^34989136486Hans Havermann12/2020
4997(2*10^136484+187)/9136484Robert Price06/2022
4998(5^653025)%L(653025)136475Henri Lifchitz06/2025
499931007^25158+25158^31007136452Hans Havermann11/2020
50002^453267-113827136447Enzo Doria09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 13 2025 16:29 (Time in France)

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