PRP Records

Probable Primes Top 10000

(302984 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 ?
500131335^30364+30364^31335140455Hans Havermann05/2021
500228511^31524-31524^28511140440Frank Doornink06/2024
500332795^19126+19126^32795140416Hans Havermann05/2021
5004(44*10^140410-503)/9140411Robert Price12/2018
500528332^31535-31535^28332140403Frank Doornink06/2024
5006153^64265-2140400Lelio R Paula11/2017
500730323^31322-31322^30323140379Frank Doornink06/2024
5008(112*10^140357-1)/3140359Serge Batalov12/2014
5009(29*10^140337-17)/3140338Robert Price09/2019
50102^466181-112735140335Enzo Doria07/2014
5011(16*10^140290-37)/3140291Robert Price05/2021
5012(5*10^140281-119)/3140282Robert Price03/2018
501334568^11415+11415^34568140259Hans Havermann05/2021
5014(27*2^465872+1)/691140241Lelio R Paula08/2015
501533632^14781+14781^33632140236Hans Havermann05/2021
501631803^25670+25670^31803140233Hans Havermann05/2021
50172^465803-114817140221Enzo Doria05/2015
5018Phi(213305,-7)140192Henri Lifchitz12/2025
5019floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
50202^465503-112735140131Enzo Doria07/2014
5021(16*10^140091+167)/3140092Robert Price06/2019
5022(8*10^140087-137)/3140088Robert Price03/2022
50236^179964+179964^6-1140040Robert Price04/2014
5024(89*10^140008-179)/9140009Robert Price12/2019
5025(29*2^465077-1)/9140003Lelio R Paula08/2015
50262^465072-344789140001Enzo Doria07/2015
502734742^10683+10683^34742139965Hans Havermann05/2021
50285*10^139945+81139946Robert Price03/2019
502932648^19335+19335^32648139941Hans Havermann05/2021
50302^464864-17139939Lelio R Paula09/2017
50318*10^139920+51139921Robert Price08/2019
5032(85*10^139913-1)/3139915Robert Price02/2020
503331203^30436+30436^31203139896Hans Havermann04/2021
50342^464642+22189139872Enzo Doria09/2023
503526138^31663-31663^26138139865Frank Doornink03/2024
5036(16^116139+619)/5139845Anonymous08/2022
5037(2^464556+619)/5139845Eric Chen10/2023
50384*10^139839-27139840Robert Price08/2021
503933582^14573+14573^33582139821Hans Havermann05/2021
5040(17^113621+1)/18139804Paul Bourdelais09/2011
50422*10^139800-21139801Robert Price09/2020
504132628^19261+19261^32628139801Hans Havermann04/2021
5043(13*10^139782+191)/3139783Robert Price11/2018
5044(64*10^139776+791)/9139777Robert Price01/2022
5045(695*10^139772+7)/9139774Robert Price12/2021
5046(19*2^464312-1)/3139773Lelio R Paula08/2015
5047(74*10^139723+133)/9139724Robert Price06/2019
50483*10^139722+13139723Robert Price07/2018
504931577^26592+26592^31577139721Hans Havermann05/2021
505077*10^139692+3139694Robert Price06/2020
5051(31*2^463970+1)/5139670Lelio R Paula08/2015
5052(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
505339640^3321+3321^39640139584Hans Havermann05/2021
505436663^6410+6410^36663139571Hans Havermann05/2021
50552^463633-2788423139568Enzo Doria11/2015
505633659^13978+13978^33659139532Hans Havermann05/2021
505731811^24318+24318^31811139521Hans Havermann04/2021
505834149^12172+12172^34149139512Hans Havermann04/2021
5059(29*10^139476+313)/9139477Robert Price04/2021
506031721^24940+24940^31721139474Hans Havermann05/2021
506132833^17698+17698^32833139473Hans Havermann05/2021
50622^463271-109501139459Enzo Doria04/2014
5063(5*10^139457+79)/3139458Robert Price03/2018
50642^463237-99139449Lelio R Paula09/2017
5065(49*10^139442+383)/9139443Robert Price04/2019
506631155^29902+29902^31155139441Hans Havermann05/2021
5067(7*10^139417-547)/9139417Robert Price01/2018
506829636^31175-31175^29636139409Frank Doornink05/2024
5069(10^139398+191)/3139398Robert Price02/2018
507023*10^139386-3139388Robert Price10/2021
50712^463019+79463139383Enzo Doria06/2016
50723^292129-112756139381Enzo Doria07/2014
5073(15*2^462951+1)/527139361Lelio R Paula08/2015
507431922^23205+23205^31922139359Hans Havermann05/2021
5075(19*10^139336+503)/9139337Alfred Reich11/2023
50772^462855-1865707139334Enzo Doria02/2016
507631237^28876+28876^31237139334Hans Havermann05/2021
5078(86*10^139315+121)/9139316Robert Price08/2019
50792^462786-292043139313Enzo Doria08/2015
508038915^3798+3798^38915139299Hans Havermann05/2021
5082(26*10^139289+1)/9139290Serge Batalov05/2010
5081(17*10^139289+7)/3139290Robert Price06/2023
508334065^12248+12248^34065139260Hans Havermann05/2021
508436425^6654+6654^36425139256Hans Havermann05/2021
508539252^3527+3527^39252139243Hans Havermann05/2021
5086(17*10^139239+67)/3139240Robert Price01/2019
508731887^23248+23248^31887139231Hans Havermann05/2021
5088(25*10^139210-97)/9139211Robert Price01/2022
50892^462238-935139148Yves Minet02/2014
5090(29*10^139134-119)/9139135Robert Price12/2021
5091U(687859)/4127153139105Serge Batalov07/2024
5092(109*10^139100-7)/3139102Robert Price03/2021
509338744^3885+3885^38744139068Hans Havermann05/2021
509431112^29499+29499^31112139065Hans Havermann05/2021
50952*10^139043-63139044Robert Price01/2022
509636390^6613+6613^36390139025Hans Havermann04/2021
509730554^30989-30989^30554138988Frank Doornink05/2024
50982*10^138975+33138976Robert Price11/2021
509942437^1882+1882^42437138966Hans Havermann05/2021
510032151^20990+20990^32151138958Hans Havermann05/2021
510132154^20933+20933^32154138933Hans Havermann04/2021
510231082^29499+29499^31082138931Hans Havermann04/2021
510330573^30962-30962^30573138876Frank Doornink05/2024
51042^461228+1870441138844Enzo Doria05/2016
51052^461204-113675138837Enzo Doria08/2014
5106(397227*29^94935-19)/28138837Eric Chen06/2025
5107(2^461139-7)/47138815Lelio R Paula08/2015
5108(17*10^138812-521)/9138813Robert Price04/2018
51093*10^138811-11138812Robert Price07/2018
511029109^31088-31088^29109138778Frank Doornink05/2024
5111(28*10^138768+173)/3138769Robert Price12/2019
5112(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5113(379*10^138737-1)/9138739Robert Price02/2020
5114(43*10^138648+101)/9138649Robert Price11/2018
51152^460567-113541138645Enzo Doria08/2014
51162^460539+224789138637Enzo Doria07/2024
5117(10^138622+161)/9138622Robert Price09/2021
51187*10^138604+3138605Robert Price08/2015
5119(133*10^138600+17)/3138602Robert Price11/2021
512033912^12203+12203^33912138581Hans Havermann05/2021
51212^460330+69138574Lelio R Paula09/2017
5122(17*10^138569-77)/3138570Robert Price08/2019
512331186^27725+27725^31186138556Hans Havermann05/2021
5124(41^85909-3^85909)/38138552Robert Price09/2025
5125(16*10^138545+89)/3138546Robert Price03/2021
512639753^3056+3056^39753138546Hans Havermann05/2021
512731282^26847+26847^31282138545Hans Havermann05/2021
51286*10^138520-37138521Robert Price02/2021
51312^460078-69581138498Enzo Doria12/2015
512931830^22447+22447^31830138498Hans Havermann05/2021
5130Phi(237987,2^3)138498Henri Lifchitz12/2025
513237384^5065+5065^37384138492Hans Havermann05/2021
513328736^31055-31055^28736138457Frank Doornink05/2024
513434774^9585+9585^34774138456Hans Havermann05/2021
513510^138444-5001138444Robert Price12/2021
51362^459768+1531138404Lelio R Paula06/2012
5137(266*10^138328-17)/3138330Robert Price07/2020
513827200^31193-31193^27200138328Frank Doornink01/2024
51392024^41836+2025138319Henri Lifchitz01/2025
514028782^31019-31019^28782138318Frank Doornink05/2024
514132963^15696+15696^32963138306Hans Havermann05/2021
51422^459343-113611138277Enzo Doria08/2014
5143(28*10^138240+113)/3138241Robert Price03/2020
51442^459199+1874393138233Enzo Doria06/2016
514533339^14002+14002^33339138230Hans Havermann05/2021
514630137^30860-30860^30137138226Frank Doornink05/2024
51472^459063-345307138192Enzo Doria06/2015
51482*10^138162-43138163Robert Price04/2018
51492^458927-112747138151Enzo Doria06/2014
51502^458927-69217138151Enzo Doria11/2015
515130907^29458+29458^30907138130Hans Havermann05/2021
515232882^15837+15837^32882138094Hans Havermann05/2021
515339252^3295+3295^39252138083Hans Havermann05/2021
515433789^12190+12190^33789138062Hans Havermann06/2021
5155555555*2^458524+1513138036Darren Bedwell08/2009
515628095^31028-31028^28095138033Frank Doornink05/2024
515730931^29002+29002^30931138028Hans Havermann05/2021
51582^458465+2^32+1138012T. D. Noe06/2007
515932206^19275+19275^32206138003Hans Havermann05/2021
51602^458321-113053137969Enzo Doria07/2014
51616^177298+323137965Riley Fisher03/2023
51622^458298+79459137962Enzo Doria06/2016
516330254^30789-30789^30254137959Frank Doornink05/2024
51642^458248-21815137947Enzo Doria07/2013
51652^458194+1876549137931Enzo Doria07/2016
5166(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5167(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5168(793*10^137887+53)/9137889Robert Price01/2022
51692^457937+57137853Lelio R Paula09/2017
517028714^30921-30921^28714137849Frank Doornink05/2024
5171(8*10^137845+13)/3137846Robert Price06/2018
51722^457822+105137819Donovan Johnson06/2006
51732^457754-113711137798Enzo Doria09/2014
517411^132315-360137792Enzo Doria09/2012
5175(2^659318)%L(659318)137787Henri Lifchitz05/2025
517632072^19689+19689^32072137725Hans Havermann06/2021
517726529^31132-31132^26529137720Frank Doornink03/2024
517844592^1225+1225^44592137707Hans Havermann05/2021
517928986^30857-30857^28986137690Frank Doornink05/2024
51802^457347-37137676Lelio R Paula09/2017
51812^457322-2786393137668Enzo Doria10/2015
5182gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5183Phi(699340M,10)137664Anonymous03/2025
518434015^11134+11134^34015137647Hans Havermann06/2021
51852^457240-59939137643Enzo Doria10/2015
5186(856*10^137633-1)/9137635Robert Price03/2020
518736232^6289+6289^36232137631Hans Havermann05/2021
51882^457120-21575137607Enzo Doria07/2013
5189(11*2^456978+1)/15137564Lelio R Paula07/2015
519030963^27722+27722^30963137564Hans Havermann04/2021
519133722^12003+12003^33722137562Hans Havermann06/2021
5192(7*25^98399+10613)/12137556Curtis Bright05/2015
519341901^1918+1918^41901137555Hans Havermann06/2021
5194(7*10^137551-1)/3137552Robert Price08/2022
519532930^15021+15021^32930137539Hans Havermann05/2021
519631178^25785+25785^31178137538Hans Havermann05/2021
5197419^52446+52446^419137525Norbert Schneider11/2020
51982^456813+214175137515Enzo Doria10/2023
51992^456796-113513137510Enzo Doria08/2014
520031788^21137+21137^31788137485Hans Havermann04/2021
5201(7*2^456655+1)/39137467Lelio R Paula07/2015
520227151^31004-31004^27151137466Frank Doornink01/2024
52032^456503-114361137422Enzo Doria01/2015
5204(11*2^456387+1)/19137386Lelio R Paula07/2015
520530618^30618-5^5137352Serge Batalov04/2024
520636248^6147+6147^36248137332Hans Havermann05/2021
520731986^19651+19651^31986137329Hans Havermann05/2021
52082^456167+22313137320Enzo Doria09/2023
520931817^20656+20656^31817137292Hans Havermann05/2021
5210(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
5211(71*10^137250+1)/9137251Serge Batalov05/2010
52122^455922+76249137247Enzo Doria05/2016
521331310^24171+24171^31310137241Hans Havermann05/2021
521414^119741-119741^14137239Serge Batalov04/2016
521535014^8297+8297^35014137218Hans Havermann05/2021
5216(19*2^455760+1)/3455137196Lelio R Paula07/2015
5218124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
5217124^65536+57^65536137195Serge Batalov03/2018
52192^455689+72677137177Enzo Doria04/2016
5220(17948!)^2+Prime(17948)137118Robert Price08/2014
522131287^24128+24128^31287137116Hans Havermann05/2021
5222(37^87421-1)/36137093Robert Price03/2012
522336233^6070+6070^36233137077Hans Havermann05/2021
5224(8*10^137073-17)/9137073Serge Batalov11/2022
522538418^3697+3697^38418137070Hans Havermann04/2021
52262^455323-57137066Lelio R Paula09/2017
5227(56*10^137019+583)/9137020Robert Price08/2021
522825017^31148-31148^25017136997Frank Doornink12/2023
5229(73*17^111333-9)/16136991Curtis Bright05/2015
52302^455025-112723136977Enzo Doria06/2014
523133876^11039+11039^33876136959Hans Havermann05/2021
5232(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
5233(251^57059-1)/250136921Anonymous04/2024
523435142^7873+7873^35142136919Hans Havermann05/2021
5235(4997*31^91805-1)/2136918Eric Chen05/2024
523666*10^136894+7136896Robert Price07/2020
523728766^30697-30697^28766136875Frank Doornink05/2024
52382^454675-1777136871Yves Minet10/2011
523931676^20931+20931^31676136866Hans Havermann05/2021
52403*10^136829+29136830Robert Price05/2018
52414*10^136813-57136814Robert Price10/2018
5242(6092*28^94536-143)/9136812Curtis Bright05/2015
5243fibonacci(654572)-2136798Jon Grantham08/2023
524437359^4588+4588^37359136795Hans Havermann05/2021
52452^454348-53136773Lelio R Paula09/2017
524631^91680-2136729Lelio R Paula05/2017
52472^454199-113697136728Enzo Doria09/2014
524830785^27622+27622^30785136725Hans Havermann05/2021
524932973^14014+14014^32973136725Hans Havermann05/2021
525036002^6273+6273^36002136717Hans Havermann05/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 02 2026 10:02 (Time in France)

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