PRP Records

Probable Primes Top 10000

(302907 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 ?
500133582^14573+14573^33582139821Hans Havermann05/2021
5002(17^113621+1)/18139804Paul Bourdelais09/2011
50042*10^139800-21139801Robert Price09/2020
500332628^19261+19261^32628139801Hans Havermann04/2021
5005(13*10^139782+191)/3139783Robert Price11/2018
5006(64*10^139776+791)/9139777Robert Price01/2022
5007(695*10^139772+7)/9139774Robert Price12/2021
5008(19*2^464312-1)/3139773Lelio R Paula08/2015
5009(74*10^139723+133)/9139724Robert Price06/2019
50103*10^139722+13139723Robert Price07/2018
501131577^26592+26592^31577139721Hans Havermann05/2021
501277*10^139692+3139694Robert Price06/2020
5013(31*2^463970+1)/5139670Lelio R Paula08/2015
5014(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
501539640^3321+3321^39640139584Hans Havermann05/2021
501636663^6410+6410^36663139571Hans Havermann05/2021
50172^463633-2788423139568Enzo Doria11/2015
501833659^13978+13978^33659139532Hans Havermann05/2021
501931811^24318+24318^31811139521Hans Havermann04/2021
502034149^12172+12172^34149139512Hans Havermann04/2021
5021(29*10^139476+313)/9139477Robert Price04/2021
502231721^24940+24940^31721139474Hans Havermann05/2021
502332833^17698+17698^32833139473Hans Havermann05/2021
50242^463271-109501139459Enzo Doria04/2014
5025(5*10^139457+79)/3139458Robert Price03/2018
50262^463237-99139449Lelio R Paula09/2017
5027(49*10^139442+383)/9139443Robert Price04/2019
502831155^29902+29902^31155139441Hans Havermann05/2021
5029(7*10^139417-547)/9139417Robert Price01/2018
503029636^31175-31175^29636139409Frank Doornink05/2024
5031(10^139398+191)/3139398Robert Price02/2018
503223*10^139386-3139388Robert Price10/2021
50332^463019+79463139383Enzo Doria06/2016
50343^292129-112756139381Enzo Doria07/2014
5035(15*2^462951+1)/527139361Lelio R Paula08/2015
503631922^23205+23205^31922139359Hans Havermann05/2021
5037(19*10^139336+503)/9139337Alfred Reich11/2023
50392^462855-1865707139334Enzo Doria02/2016
503831237^28876+28876^31237139334Hans Havermann05/2021
5040(86*10^139315+121)/9139316Robert Price08/2019
50412^462786-292043139313Enzo Doria08/2015
504238915^3798+3798^38915139299Hans Havermann05/2021
5044(26*10^139289+1)/9139290Serge Batalov05/2010
5043(17*10^139289+7)/3139290Robert Price06/2023
504534065^12248+12248^34065139260Hans Havermann05/2021
504636425^6654+6654^36425139256Hans Havermann05/2021
504739252^3527+3527^39252139243Hans Havermann05/2021
5048(17*10^139239+67)/3139240Robert Price01/2019
504931887^23248+23248^31887139231Hans Havermann05/2021
5050(25*10^139210-97)/9139211Robert Price01/2022
50512^462238-935139148Yves Minet02/2014
5052(29*10^139134-119)/9139135Robert Price12/2021
5053U(687859)/4127153139105Serge Batalov07/2024
5054(109*10^139100-7)/3139102Robert Price03/2021
505538744^3885+3885^38744139068Hans Havermann05/2021
505631112^29499+29499^31112139065Hans Havermann05/2021
50572*10^139043-63139044Robert Price01/2022
505836390^6613+6613^36390139025Hans Havermann04/2021
505930554^30989-30989^30554138988Frank Doornink05/2024
50602*10^138975+33138976Robert Price11/2021
506142437^1882+1882^42437138966Hans Havermann05/2021
506232151^20990+20990^32151138958Hans Havermann05/2021
506332154^20933+20933^32154138933Hans Havermann04/2021
506431082^29499+29499^31082138931Hans Havermann04/2021
506530573^30962-30962^30573138876Frank Doornink05/2024
50662^461228+1870441138844Enzo Doria05/2016
50672^461204-113675138837Enzo Doria08/2014
5068(397227*29^94935-19)/28138837Eric Chen06/2025
5069(2^461139-7)/47138815Lelio R Paula08/2015
5070(17*10^138812-521)/9138813Robert Price04/2018
50713*10^138811-11138812Robert Price07/2018
507229109^31088-31088^29109138778Frank Doornink05/2024
5073(28*10^138768+173)/3138769Robert Price12/2019
5074(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5075(379*10^138737-1)/9138739Robert Price02/2020
5076(43*10^138648+101)/9138649Robert Price11/2018
50772^460567-113541138645Enzo Doria08/2014
50782^460539+224789138637Enzo Doria07/2024
5079(10^138622+161)/9138622Robert Price09/2021
50807*10^138604+3138605Robert Price08/2015
5081(133*10^138600+17)/3138602Robert Price11/2021
508233912^12203+12203^33912138581Hans Havermann05/2021
50832^460330+69138574Lelio R Paula09/2017
5084(17*10^138569-77)/3138570Robert Price08/2019
508531186^27725+27725^31186138556Hans Havermann05/2021
5086(41^85909-3^85909)/38138552Robert Price09/2025
5087(16*10^138545+89)/3138546Robert Price03/2021
508839753^3056+3056^39753138546Hans Havermann05/2021
508931282^26847+26847^31282138545Hans Havermann05/2021
50906*10^138520-37138521Robert Price02/2021
50932^460078-69581138498Enzo Doria12/2015
509131830^22447+22447^31830138498Hans Havermann05/2021
5092Phi(237987,2^3)138498Henri Lifchitz12/2025
509437384^5065+5065^37384138492Hans Havermann05/2021
509528736^31055-31055^28736138457Frank Doornink05/2024
509634774^9585+9585^34774138456Hans Havermann05/2021
509710^138444-5001138444Robert Price12/2021
50982^459768+1531138404Lelio R Paula06/2012
5099(266*10^138328-17)/3138330Robert Price07/2020
510027200^31193-31193^27200138328Frank Doornink01/2024
51012024^41836+2025138319Henri Lifchitz01/2025
510228782^31019-31019^28782138318Frank Doornink05/2024
510332963^15696+15696^32963138306Hans Havermann05/2021
51042^459343-113611138277Enzo Doria08/2014
5105(28*10^138240+113)/3138241Robert Price03/2020
51062^459199+1874393138233Enzo Doria06/2016
510733339^14002+14002^33339138230Hans Havermann05/2021
510830137^30860-30860^30137138226Frank Doornink05/2024
51092^459063-345307138192Enzo Doria06/2015
51102*10^138162-43138163Robert Price04/2018
51112^458927-112747138151Enzo Doria06/2014
51122^458927-69217138151Enzo Doria11/2015
511330907^29458+29458^30907138130Hans Havermann05/2021
511432882^15837+15837^32882138094Hans Havermann05/2021
511539252^3295+3295^39252138083Hans Havermann05/2021
511633789^12190+12190^33789138062Hans Havermann06/2021
5117555555*2^458524+1513138036Darren Bedwell08/2009
511828095^31028-31028^28095138033Frank Doornink05/2024
511930931^29002+29002^30931138028Hans Havermann05/2021
51202^458465+2^32+1138012T. D. Noe06/2007
512132206^19275+19275^32206138003Hans Havermann05/2021
51222^458321-113053137969Enzo Doria07/2014
51236^177298+323137965Riley Fisher03/2023
51242^458298+79459137962Enzo Doria06/2016
512530254^30789-30789^30254137959Frank Doornink05/2024
51262^458248-21815137947Enzo Doria07/2013
51272^458194+1876549137931Enzo Doria07/2016
5128(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5129(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5130(793*10^137887+53)/9137889Robert Price01/2022
51312^457937+57137853Lelio R Paula09/2017
513228714^30921-30921^28714137849Frank Doornink05/2024
5133(8*10^137845+13)/3137846Robert Price06/2018
51342^457822+105137819Donovan Johnson06/2006
51352^457754-113711137798Enzo Doria09/2014
513611^132315-360137792Enzo Doria09/2012
5137(2^659318)%L(659318)137787Henri Lifchitz05/2025
513832072^19689+19689^32072137725Hans Havermann06/2021
513926529^31132-31132^26529137720Frank Doornink03/2024
514044592^1225+1225^44592137707Hans Havermann05/2021
514128986^30857-30857^28986137690Frank Doornink05/2024
51422^457347-37137676Lelio R Paula09/2017
51432^457322-2786393137668Enzo Doria10/2015
5144gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5145Phi(699340M,10)137664Anonymous03/2025
514634015^11134+11134^34015137647Hans Havermann06/2021
51472^457240-59939137643Enzo Doria10/2015
5148(856*10^137633-1)/9137635Robert Price03/2020
514936232^6289+6289^36232137631Hans Havermann05/2021
51502^457120-21575137607Enzo Doria07/2013
5151(11*2^456978+1)/15137564Lelio R Paula07/2015
515230963^27722+27722^30963137564Hans Havermann04/2021
515333722^12003+12003^33722137562Hans Havermann06/2021
5154(7*25^98399+10613)/12137556Curtis Bright05/2015
515541901^1918+1918^41901137555Hans Havermann06/2021
5156(7*10^137551-1)/3137552Robert Price08/2022
515732930^15021+15021^32930137539Hans Havermann05/2021
515831178^25785+25785^31178137538Hans Havermann05/2021
5159419^52446+52446^419137525Norbert Schneider11/2020
51602^456813+214175137515Enzo Doria10/2023
51612^456796-113513137510Enzo Doria08/2014
516231788^21137+21137^31788137485Hans Havermann04/2021
5163(7*2^456655+1)/39137467Lelio R Paula07/2015
516427151^31004-31004^27151137466Frank Doornink01/2024
51652^456503-114361137422Enzo Doria01/2015
5166(11*2^456387+1)/19137386Lelio R Paula07/2015
516730618^30618-5^5137352Serge Batalov04/2024
516836248^6147+6147^36248137332Hans Havermann05/2021
516931986^19651+19651^31986137329Hans Havermann05/2021
51702^456167+22313137320Enzo Doria09/2023
517131817^20656+20656^31817137292Hans Havermann05/2021
5172(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
5173(71*10^137250+1)/9137251Serge Batalov05/2010
51742^455922+76249137247Enzo Doria05/2016
517531310^24171+24171^31310137241Hans Havermann05/2021
517614^119741-119741^14137239Serge Batalov04/2016
517735014^8297+8297^35014137218Hans Havermann05/2021
5178(19*2^455760+1)/3455137196Lelio R Paula07/2015
5180124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
5179124^65536+57^65536137195Serge Batalov03/2018
51812^455689+72677137177Enzo Doria04/2016
5182(17948!)^2+Prime(17948)137118Robert Price08/2014
518331287^24128+24128^31287137116Hans Havermann05/2021
5184(37^87421-1)/36137093Robert Price03/2012
518536233^6070+6070^36233137077Hans Havermann05/2021
5186(8*10^137073-17)/9137073Serge Batalov11/2022
518738418^3697+3697^38418137070Hans Havermann04/2021
51882^455323-57137066Lelio R Paula09/2017
5189(56*10^137019+583)/9137020Robert Price08/2021
519025017^31148-31148^25017136997Frank Doornink12/2023
5191(73*17^111333-9)/16136991Curtis Bright05/2015
51922^455025-112723136977Enzo Doria06/2014
519333876^11039+11039^33876136959Hans Havermann05/2021
5194(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
5195(251^57059-1)/250136921Anonymous04/2024
519635142^7873+7873^35142136919Hans Havermann05/2021
5197(4997*31^91805-1)/2136918Eric Chen05/2024
519866*10^136894+7136896Robert Price07/2020
519928766^30697-30697^28766136875Frank Doornink05/2024
52002^454675-1777136871Yves Minet10/2011
520131676^20931+20931^31676136866Hans Havermann05/2021
52023*10^136829+29136830Robert Price05/2018
52034*10^136813-57136814Robert Price10/2018
5204(6092*28^94536-143)/9136812Curtis Bright05/2015
5205fibonacci(654572)-2136798Jon Grantham08/2023
520637359^4588+4588^37359136795Hans Havermann05/2021
52072^454348-53136773Lelio R Paula09/2017
520831^91680-2136729Lelio R Paula05/2017
52092^454199-113697136728Enzo Doria09/2014
521030785^27622+27622^30785136725Hans Havermann05/2021
521132973^14014+14014^32973136725Hans Havermann05/2021
52137*10^136716+69136717Robert Price07/2019
521236002^6273+6273^36002136717Hans Havermann05/2021
52146*10^136692+53136693Robert Price05/2020
5215Phi(568997,2)136692Henri Lifchitz02/2026
5216(13*10^136687+47)/3136688Robert Price10/2018
5217F(2*453976)%(2^453976)136661Henri Lifchitz06/2025
52182^453935-2791357136649Enzo Doria01/2016
52192^453906-69131136640Enzo Doria11/2015
522033232^12915+12915^33232136620Hans Havermann05/2021
52212^453791+1873913136605Enzo Doria06/2016
522234166^9951+9951^34166136592Hans Havermann05/2021
5223(21*2^453740-1)/2735136588Lelio R Paula07/2015
522431102^24635+24635^31102136587Hans Havermann05/2021
5225580^49413+49413^580136550Norbert Schneider02/2019
52262^453503-2788297136519Enzo Doria11/2015
522734989^7958+7958^34989136486Hans Havermann12/2020
5228(2*10^136484+187)/9136484Robert Price06/2022
5229(5^653025)%L(653025)136475Henri Lifchitz06/2025
523031007^25158+25158^31007136452Hans Havermann11/2020
52312^453267-113827136447Enzo Doria09/2014
523232234^17085+17085^32234136435Hans Havermann12/2020
52332^453102+1877629136398Enzo Doria08/2016
523431016^24981+24981^31016136397Hans Havermann12/2020
5235(62*10^136384-791)/9136385Robert Price06/2019
523634171^9798+9798^34171136382Hans Havermann12/2020
5237(17*10^136354-113)/3136355Robert Price06/2021
523832756^14541+14541^32756136350Hans Havermann11/2020
523932205^17086+17086^32205136313Hans Havermann12/2020
5240(25*10^136303+161)/3136304Robert Price09/2019
524135337^7196+7196^35337136299Hans Havermann12/2020
5242(182*10^136291+1)/3136293Robert Price02/2020
5243(88*10^136234+83)/9136235Robert Price03/2022
524423*10^136225-7136227Robert Price02/2020
5245L(651821)136223Henri Lifchitz09/2008
524625519^30908-30908^25519136208Frank Doornink02/2024
52472^452460+77701136205Enzo Doria05/2016
52482^452440-114755136199Enzo Doria04/2015
524928625^30558-30558^28625136190Frank Doornink05/2024
525032286^16489+16489^32286136157Hans Havermann11/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 05 2026 15:51 (Time in France)

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