PRP Records

Probable Primes Top 10000

(302978 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 ?
500130323^31322-31322^30323140379Frank Doornink06/2024
5002(112*10^140357-1)/3140359Serge Batalov12/2014
5003(29*10^140337-17)/3140338Robert Price09/2019
50042^466181-112735140335Enzo Doria07/2014
5005(16*10^140290-37)/3140291Robert Price05/2021
5006(5*10^140281-119)/3140282Robert Price03/2018
500734568^11415+11415^34568140259Hans Havermann05/2021
5008(27*2^465872+1)/691140241Lelio R Paula08/2015
500933632^14781+14781^33632140236Hans Havermann05/2021
501031803^25670+25670^31803140233Hans Havermann05/2021
50112^465803-114817140221Enzo Doria05/2015
5012Phi(213305,-7)140192Henri Lifchitz12/2025
5013floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
50142^465503-112735140131Enzo Doria07/2014
5015(16*10^140091+167)/3140092Robert Price06/2019
5016(8*10^140087-137)/3140088Robert Price03/2022
50176^179964+179964^6-1140040Robert Price04/2014
5018(89*10^140008-179)/9140009Robert Price12/2019
5019(29*2^465077-1)/9140003Lelio R Paula08/2015
50202^465072-344789140001Enzo Doria07/2015
502134742^10683+10683^34742139965Hans Havermann05/2021
50225*10^139945+81139946Robert Price03/2019
502332648^19335+19335^32648139941Hans Havermann05/2021
50242^464864-17139939Lelio R Paula09/2017
50258*10^139920+51139921Robert Price08/2019
5026(85*10^139913-1)/3139915Robert Price02/2020
502731203^30436+30436^31203139896Hans Havermann04/2021
50282^464642+22189139872Enzo Doria09/2023
502926138^31663-31663^26138139865Frank Doornink03/2024
5030(16^116139+619)/5139845Anonymous08/2022
5031(2^464556+619)/5139845Eric Chen10/2023
50324*10^139839-27139840Robert Price08/2021
503333582^14573+14573^33582139821Hans Havermann05/2021
5034(17^113621+1)/18139804Paul Bourdelais09/2011
50362*10^139800-21139801Robert Price09/2020
503532628^19261+19261^32628139801Hans Havermann04/2021
5037(13*10^139782+191)/3139783Robert Price11/2018
5038(64*10^139776+791)/9139777Robert Price01/2022
5039(695*10^139772+7)/9139774Robert Price12/2021
5040(19*2^464312-1)/3139773Lelio R Paula08/2015
5041(74*10^139723+133)/9139724Robert Price06/2019
50423*10^139722+13139723Robert Price07/2018
504331577^26592+26592^31577139721Hans Havermann05/2021
504477*10^139692+3139694Robert Price06/2020
5045(31*2^463970+1)/5139670Lelio R Paula08/2015
5046(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
504739640^3321+3321^39640139584Hans Havermann05/2021
504836663^6410+6410^36663139571Hans Havermann05/2021
50492^463633-2788423139568Enzo Doria11/2015
505033659^13978+13978^33659139532Hans Havermann05/2021
505131811^24318+24318^31811139521Hans Havermann04/2021
505234149^12172+12172^34149139512Hans Havermann04/2021
5053(29*10^139476+313)/9139477Robert Price04/2021
505431721^24940+24940^31721139474Hans Havermann05/2021
505532833^17698+17698^32833139473Hans Havermann05/2021
50562^463271-109501139459Enzo Doria04/2014
5057(5*10^139457+79)/3139458Robert Price03/2018
50582^463237-99139449Lelio R Paula09/2017
5059(49*10^139442+383)/9139443Robert Price04/2019
506031155^29902+29902^31155139441Hans Havermann05/2021
5061(7*10^139417-547)/9139417Robert Price01/2018
506229636^31175-31175^29636139409Frank Doornink05/2024
5063(10^139398+191)/3139398Robert Price02/2018
506423*10^139386-3139388Robert Price10/2021
50652^463019+79463139383Enzo Doria06/2016
50663^292129-112756139381Enzo Doria07/2014
5067(15*2^462951+1)/527139361Lelio R Paula08/2015
506831922^23205+23205^31922139359Hans Havermann05/2021
5069(19*10^139336+503)/9139337Alfred Reich11/2023
50712^462855-1865707139334Enzo Doria02/2016
507031237^28876+28876^31237139334Hans Havermann05/2021
5072(86*10^139315+121)/9139316Robert Price08/2019
50732^462786-292043139313Enzo Doria08/2015
507438915^3798+3798^38915139299Hans Havermann05/2021
5076(26*10^139289+1)/9139290Serge Batalov05/2010
5075(17*10^139289+7)/3139290Robert Price06/2023
507734065^12248+12248^34065139260Hans Havermann05/2021
507836425^6654+6654^36425139256Hans Havermann05/2021
507939252^3527+3527^39252139243Hans Havermann05/2021
5080(17*10^139239+67)/3139240Robert Price01/2019
508131887^23248+23248^31887139231Hans Havermann05/2021
5082(25*10^139210-97)/9139211Robert Price01/2022
50832^462238-935139148Yves Minet02/2014
5084(29*10^139134-119)/9139135Robert Price12/2021
5085U(687859)/4127153139105Serge Batalov07/2024
5086(109*10^139100-7)/3139102Robert Price03/2021
508738744^3885+3885^38744139068Hans Havermann05/2021
508831112^29499+29499^31112139065Hans Havermann05/2021
50892*10^139043-63139044Robert Price01/2022
509036390^6613+6613^36390139025Hans Havermann04/2021
509130554^30989-30989^30554138988Frank Doornink05/2024
50922*10^138975+33138976Robert Price11/2021
509342437^1882+1882^42437138966Hans Havermann05/2021
509432151^20990+20990^32151138958Hans Havermann05/2021
509532154^20933+20933^32154138933Hans Havermann04/2021
509631082^29499+29499^31082138931Hans Havermann04/2021
509730573^30962-30962^30573138876Frank Doornink05/2024
50982^461228+1870441138844Enzo Doria05/2016
50992^461204-113675138837Enzo Doria08/2014
5100(397227*29^94935-19)/28138837Eric Chen06/2025
5101(2^461139-7)/47138815Lelio R Paula08/2015
5102(17*10^138812-521)/9138813Robert Price04/2018
51033*10^138811-11138812Robert Price07/2018
510429109^31088-31088^29109138778Frank Doornink05/2024
5105(28*10^138768+173)/3138769Robert Price12/2019
5106(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5107(379*10^138737-1)/9138739Robert Price02/2020
5108(43*10^138648+101)/9138649Robert Price11/2018
51092^460567-113541138645Enzo Doria08/2014
51102^460539+224789138637Enzo Doria07/2024
5111(10^138622+161)/9138622Robert Price09/2021
51127*10^138604+3138605Robert Price08/2015
5113(133*10^138600+17)/3138602Robert Price11/2021
511433912^12203+12203^33912138581Hans Havermann05/2021
51152^460330+69138574Lelio R Paula09/2017
5116(17*10^138569-77)/3138570Robert Price08/2019
511731186^27725+27725^31186138556Hans Havermann05/2021
5118(41^85909-3^85909)/38138552Robert Price09/2025
5119(16*10^138545+89)/3138546Robert Price03/2021
512039753^3056+3056^39753138546Hans Havermann05/2021
512131282^26847+26847^31282138545Hans Havermann05/2021
51226*10^138520-37138521Robert Price02/2021
51252^460078-69581138498Enzo Doria12/2015
512331830^22447+22447^31830138498Hans Havermann05/2021
5124Phi(237987,2^3)138498Henri Lifchitz12/2025
512637384^5065+5065^37384138492Hans Havermann05/2021
512728736^31055-31055^28736138457Frank Doornink05/2024
512834774^9585+9585^34774138456Hans Havermann05/2021
512910^138444-5001138444Robert Price12/2021
51302^459768+1531138404Lelio R Paula06/2012
5131(266*10^138328-17)/3138330Robert Price07/2020
513227200^31193-31193^27200138328Frank Doornink01/2024
51332024^41836+2025138319Henri Lifchitz01/2025
513428782^31019-31019^28782138318Frank Doornink05/2024
513532963^15696+15696^32963138306Hans Havermann05/2021
51362^459343-113611138277Enzo Doria08/2014
5137(28*10^138240+113)/3138241Robert Price03/2020
51382^459199+1874393138233Enzo Doria06/2016
513933339^14002+14002^33339138230Hans Havermann05/2021
514030137^30860-30860^30137138226Frank Doornink05/2024
51412^459063-345307138192Enzo Doria06/2015
51422*10^138162-43138163Robert Price04/2018
51432^458927-112747138151Enzo Doria06/2014
51442^458927-69217138151Enzo Doria11/2015
514530907^29458+29458^30907138130Hans Havermann05/2021
514632882^15837+15837^32882138094Hans Havermann05/2021
514739252^3295+3295^39252138083Hans Havermann05/2021
514833789^12190+12190^33789138062Hans Havermann06/2021
5149555555*2^458524+1513138036Darren Bedwell08/2009
515028095^31028-31028^28095138033Frank Doornink05/2024
515130931^29002+29002^30931138028Hans Havermann05/2021
51522^458465+2^32+1138012T. D. Noe06/2007
515332206^19275+19275^32206138003Hans Havermann05/2021
51542^458321-113053137969Enzo Doria07/2014
51556^177298+323137965Riley Fisher03/2023
51562^458298+79459137962Enzo Doria06/2016
515730254^30789-30789^30254137959Frank Doornink05/2024
51582^458248-21815137947Enzo Doria07/2013
51592^458194+1876549137931Enzo Doria07/2016
5160(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5161(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5162(793*10^137887+53)/9137889Robert Price01/2022
51632^457937+57137853Lelio R Paula09/2017
516428714^30921-30921^28714137849Frank Doornink05/2024
5165(8*10^137845+13)/3137846Robert Price06/2018
51662^457822+105137819Donovan Johnson06/2006
51672^457754-113711137798Enzo Doria09/2014
516811^132315-360137792Enzo Doria09/2012
5169(2^659318)%L(659318)137787Henri Lifchitz05/2025
517032072^19689+19689^32072137725Hans Havermann06/2021
517126529^31132-31132^26529137720Frank Doornink03/2024
517244592^1225+1225^44592137707Hans Havermann05/2021
517328986^30857-30857^28986137690Frank Doornink05/2024
51742^457347-37137676Lelio R Paula09/2017
51752^457322-2786393137668Enzo Doria10/2015
5176gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5177Phi(699340M,10)137664Anonymous03/2025
517834015^11134+11134^34015137647Hans Havermann06/2021
51792^457240-59939137643Enzo Doria10/2015
5180(856*10^137633-1)/9137635Robert Price03/2020
518136232^6289+6289^36232137631Hans Havermann05/2021
51822^457120-21575137607Enzo Doria07/2013
5183(11*2^456978+1)/15137564Lelio R Paula07/2015
518430963^27722+27722^30963137564Hans Havermann04/2021
518533722^12003+12003^33722137562Hans Havermann06/2021
5186(7*25^98399+10613)/12137556Curtis Bright05/2015
518741901^1918+1918^41901137555Hans Havermann06/2021
5188(7*10^137551-1)/3137552Robert Price08/2022
518932930^15021+15021^32930137539Hans Havermann05/2021
519031178^25785+25785^31178137538Hans Havermann05/2021
5191419^52446+52446^419137525Norbert Schneider11/2020
51922^456813+214175137515Enzo Doria10/2023
51932^456796-113513137510Enzo Doria08/2014
519431788^21137+21137^31788137485Hans Havermann04/2021
5195(7*2^456655+1)/39137467Lelio R Paula07/2015
519627151^31004-31004^27151137466Frank Doornink01/2024
51972^456503-114361137422Enzo Doria01/2015
5198(11*2^456387+1)/19137386Lelio R Paula07/2015
519930618^30618-5^5137352Serge Batalov04/2024
520036248^6147+6147^36248137332Hans Havermann05/2021
520131986^19651+19651^31986137329Hans Havermann05/2021
52022^456167+22313137320Enzo Doria09/2023
520331817^20656+20656^31817137292Hans Havermann05/2021
5204(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
5205(71*10^137250+1)/9137251Serge Batalov05/2010
52062^455922+76249137247Enzo Doria05/2016
520731310^24171+24171^31310137241Hans Havermann05/2021
520814^119741-119741^14137239Serge Batalov04/2016
520935014^8297+8297^35014137218Hans Havermann05/2021
5210(19*2^455760+1)/3455137196Lelio R Paula07/2015
5212124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
5211124^65536+57^65536137195Serge Batalov03/2018
52132^455689+72677137177Enzo Doria04/2016
5214(17948!)^2+Prime(17948)137118Robert Price08/2014
521531287^24128+24128^31287137116Hans Havermann05/2021
5216(37^87421-1)/36137093Robert Price03/2012
521736233^6070+6070^36233137077Hans Havermann05/2021
5218(8*10^137073-17)/9137073Serge Batalov11/2022
521938418^3697+3697^38418137070Hans Havermann04/2021
52202^455323-57137066Lelio R Paula09/2017
5221(56*10^137019+583)/9137020Robert Price08/2021
522225017^31148-31148^25017136997Frank Doornink12/2023
5223(73*17^111333-9)/16136991Curtis Bright05/2015
52242^455025-112723136977Enzo Doria06/2014
522533876^11039+11039^33876136959Hans Havermann05/2021
5226(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
5227(251^57059-1)/250136921Anonymous04/2024
522835142^7873+7873^35142136919Hans Havermann05/2021
5229(4997*31^91805-1)/2136918Eric Chen05/2024
523066*10^136894+7136896Robert Price07/2020
523128766^30697-30697^28766136875Frank Doornink05/2024
52322^454675-1777136871Yves Minet10/2011
523331676^20931+20931^31676136866Hans Havermann05/2021
52343*10^136829+29136830Robert Price05/2018
52354*10^136813-57136814Robert Price10/2018
5236(6092*28^94536-143)/9136812Curtis Bright05/2015
5237fibonacci(654572)-2136798Jon Grantham08/2023
523837359^4588+4588^37359136795Hans Havermann05/2021
52392^454348-53136773Lelio R Paula09/2017
524031^91680-2136729Lelio R Paula05/2017
52412^454199-113697136728Enzo Doria09/2014
524230785^27622+27622^30785136725Hans Havermann05/2021
524332973^14014+14014^32973136725Hans Havermann05/2021
52457*10^136716+69136717Robert Price07/2019
524436002^6273+6273^36002136717Hans Havermann05/2021
52466*10^136692+53136693Robert Price05/2020
5247Phi(568997,2)136692Henri Lifchitz02/2026
5248(13*10^136687+47)/3136688Robert Price10/2018
5249F(2*453976)%(2^453976)136661Henri Lifchitz06/2025
52502^453935-2791357136649Enzo Doria01/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 01 2026 11:05 (Time in France)

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