PRP Records

Probable Primes Top 10000

(302940 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 ?
50012^464642+22189139872Enzo Doria09/2023
500226138^31663-31663^26138139865Frank Doornink03/2024
5003(16^116139+619)/5139845Anonymous08/2022
5004(2^464556+619)/5139845Eric Chen10/2023
50054*10^139839-27139840Robert Price08/2021
500633582^14573+14573^33582139821Hans Havermann05/2021
5007(17^113621+1)/18139804Paul Bourdelais09/2011
50092*10^139800-21139801Robert Price09/2020
500832628^19261+19261^32628139801Hans Havermann04/2021
5010(13*10^139782+191)/3139783Robert Price11/2018
5011(64*10^139776+791)/9139777Robert Price01/2022
5012(695*10^139772+7)/9139774Robert Price12/2021
5013(19*2^464312-1)/3139773Lelio R Paula08/2015
5014(74*10^139723+133)/9139724Robert Price06/2019
50153*10^139722+13139723Robert Price07/2018
501631577^26592+26592^31577139721Hans Havermann05/2021
501777*10^139692+3139694Robert Price06/2020
5018(31*2^463970+1)/5139670Lelio R Paula08/2015
5019(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
502039640^3321+3321^39640139584Hans Havermann05/2021
502136663^6410+6410^36663139571Hans Havermann05/2021
50222^463633-2788423139568Enzo Doria11/2015
502333659^13978+13978^33659139532Hans Havermann05/2021
502431811^24318+24318^31811139521Hans Havermann04/2021
502534149^12172+12172^34149139512Hans Havermann04/2021
5026(29*10^139476+313)/9139477Robert Price04/2021
502731721^24940+24940^31721139474Hans Havermann05/2021
502832833^17698+17698^32833139473Hans Havermann05/2021
50292^463271-109501139459Enzo Doria04/2014
5030(5*10^139457+79)/3139458Robert Price03/2018
50312^463237-99139449Lelio R Paula09/2017
5032(49*10^139442+383)/9139443Robert Price04/2019
503331155^29902+29902^31155139441Hans Havermann05/2021
5034(7*10^139417-547)/9139417Robert Price01/2018
503529636^31175-31175^29636139409Frank Doornink05/2024
5036(10^139398+191)/3139398Robert Price02/2018
503723*10^139386-3139388Robert Price10/2021
50382^463019+79463139383Enzo Doria06/2016
50393^292129-112756139381Enzo Doria07/2014
5040(15*2^462951+1)/527139361Lelio R Paula08/2015
504131922^23205+23205^31922139359Hans Havermann05/2021
5042(19*10^139336+503)/9139337Alfred Reich11/2023
50442^462855-1865707139334Enzo Doria02/2016
504331237^28876+28876^31237139334Hans Havermann05/2021
5045(86*10^139315+121)/9139316Robert Price08/2019
50462^462786-292043139313Enzo Doria08/2015
504738915^3798+3798^38915139299Hans Havermann05/2021
5049(26*10^139289+1)/9139290Serge Batalov05/2010
5048(17*10^139289+7)/3139290Robert Price06/2023
505034065^12248+12248^34065139260Hans Havermann05/2021
505136425^6654+6654^36425139256Hans Havermann05/2021
505239252^3527+3527^39252139243Hans Havermann05/2021
5053(17*10^139239+67)/3139240Robert Price01/2019
505431887^23248+23248^31887139231Hans Havermann05/2021
5055(25*10^139210-97)/9139211Robert Price01/2022
50562^462238-935139148Yves Minet02/2014
5057(29*10^139134-119)/9139135Robert Price12/2021
5058U(687859)/4127153139105Serge Batalov07/2024
5059(109*10^139100-7)/3139102Robert Price03/2021
506038744^3885+3885^38744139068Hans Havermann05/2021
506131112^29499+29499^31112139065Hans Havermann05/2021
50622*10^139043-63139044Robert Price01/2022
506336390^6613+6613^36390139025Hans Havermann04/2021
506430554^30989-30989^30554138988Frank Doornink05/2024
50652*10^138975+33138976Robert Price11/2021
506642437^1882+1882^42437138966Hans Havermann05/2021
506732151^20990+20990^32151138958Hans Havermann05/2021
506832154^20933+20933^32154138933Hans Havermann04/2021
506931082^29499+29499^31082138931Hans Havermann04/2021
507030573^30962-30962^30573138876Frank Doornink05/2024
50712^461228+1870441138844Enzo Doria05/2016
50722^461204-113675138837Enzo Doria08/2014
5073(397227*29^94935-19)/28138837Eric Chen06/2025
5074(2^461139-7)/47138815Lelio R Paula08/2015
5075(17*10^138812-521)/9138813Robert Price04/2018
50763*10^138811-11138812Robert Price07/2018
507729109^31088-31088^29109138778Frank Doornink05/2024
5078(28*10^138768+173)/3138769Robert Price12/2019
5079(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5080(379*10^138737-1)/9138739Robert Price02/2020
5081(43*10^138648+101)/9138649Robert Price11/2018
50822^460567-113541138645Enzo Doria08/2014
50832^460539+224789138637Enzo Doria07/2024
5084(10^138622+161)/9138622Robert Price09/2021
50857*10^138604+3138605Robert Price08/2015
5086(133*10^138600+17)/3138602Robert Price11/2021
508733912^12203+12203^33912138581Hans Havermann05/2021
50882^460330+69138574Lelio R Paula09/2017
5089(17*10^138569-77)/3138570Robert Price08/2019
509031186^27725+27725^31186138556Hans Havermann05/2021
5091(41^85909-3^85909)/38138552Robert Price09/2025
5092(16*10^138545+89)/3138546Robert Price03/2021
509339753^3056+3056^39753138546Hans Havermann05/2021
509431282^26847+26847^31282138545Hans Havermann05/2021
50956*10^138520-37138521Robert Price02/2021
50982^460078-69581138498Enzo Doria12/2015
509631830^22447+22447^31830138498Hans Havermann05/2021
5097Phi(237987,2^3)138498Henri Lifchitz12/2025
509937384^5065+5065^37384138492Hans Havermann05/2021
510028736^31055-31055^28736138457Frank Doornink05/2024
510134774^9585+9585^34774138456Hans Havermann05/2021
510210^138444-5001138444Robert Price12/2021
51032^459768+1531138404Lelio R Paula06/2012
5104(266*10^138328-17)/3138330Robert Price07/2020
510527200^31193-31193^27200138328Frank Doornink01/2024
51062024^41836+2025138319Henri Lifchitz01/2025
510728782^31019-31019^28782138318Frank Doornink05/2024
510832963^15696+15696^32963138306Hans Havermann05/2021
51092^459343-113611138277Enzo Doria08/2014
5110(28*10^138240+113)/3138241Robert Price03/2020
51112^459199+1874393138233Enzo Doria06/2016
511233339^14002+14002^33339138230Hans Havermann05/2021
511330137^30860-30860^30137138226Frank Doornink05/2024
51142^459063-345307138192Enzo Doria06/2015
51152*10^138162-43138163Robert Price04/2018
51162^458927-112747138151Enzo Doria06/2014
51172^458927-69217138151Enzo Doria11/2015
511830907^29458+29458^30907138130Hans Havermann05/2021
511932882^15837+15837^32882138094Hans Havermann05/2021
512039252^3295+3295^39252138083Hans Havermann05/2021
512133789^12190+12190^33789138062Hans Havermann06/2021
5122555555*2^458524+1513138036Darren Bedwell08/2009
512328095^31028-31028^28095138033Frank Doornink05/2024
512430931^29002+29002^30931138028Hans Havermann05/2021
51252^458465+2^32+1138012T. D. Noe06/2007
512632206^19275+19275^32206138003Hans Havermann05/2021
51272^458321-113053137969Enzo Doria07/2014
51286^177298+323137965Riley Fisher03/2023
51292^458298+79459137962Enzo Doria06/2016
513030254^30789-30789^30254137959Frank Doornink05/2024
51312^458248-21815137947Enzo Doria07/2013
51322^458194+1876549137931Enzo Doria07/2016
5133(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5134(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5135(793*10^137887+53)/9137889Robert Price01/2022
51362^457937+57137853Lelio R Paula09/2017
513728714^30921-30921^28714137849Frank Doornink05/2024
5138(8*10^137845+13)/3137846Robert Price06/2018
51392^457822+105137819Donovan Johnson06/2006
51402^457754-113711137798Enzo Doria09/2014
514111^132315-360137792Enzo Doria09/2012
5142(2^659318)%L(659318)137787Henri Lifchitz05/2025
514332072^19689+19689^32072137725Hans Havermann06/2021
514426529^31132-31132^26529137720Frank Doornink03/2024
514544592^1225+1225^44592137707Hans Havermann05/2021
514628986^30857-30857^28986137690Frank Doornink05/2024
51472^457347-37137676Lelio R Paula09/2017
51482^457322-2786393137668Enzo Doria10/2015
5149gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5150Phi(699340M,10)137664Anonymous03/2025
515134015^11134+11134^34015137647Hans Havermann06/2021
51522^457240-59939137643Enzo Doria10/2015
5153(856*10^137633-1)/9137635Robert Price03/2020
515436232^6289+6289^36232137631Hans Havermann05/2021
51552^457120-21575137607Enzo Doria07/2013
5156(11*2^456978+1)/15137564Lelio R Paula07/2015
515730963^27722+27722^30963137564Hans Havermann04/2021
515833722^12003+12003^33722137562Hans Havermann06/2021
5159(7*25^98399+10613)/12137556Curtis Bright05/2015
516041901^1918+1918^41901137555Hans Havermann06/2021
5161(7*10^137551-1)/3137552Robert Price08/2022
516232930^15021+15021^32930137539Hans Havermann05/2021
516331178^25785+25785^31178137538Hans Havermann05/2021
5164419^52446+52446^419137525Norbert Schneider11/2020
51652^456813+214175137515Enzo Doria10/2023
51662^456796-113513137510Enzo Doria08/2014
516731788^21137+21137^31788137485Hans Havermann04/2021
5168(7*2^456655+1)/39137467Lelio R Paula07/2015
516927151^31004-31004^27151137466Frank Doornink01/2024
51702^456503-114361137422Enzo Doria01/2015
5171(11*2^456387+1)/19137386Lelio R Paula07/2015
517230618^30618-5^5137352Serge Batalov04/2024
517336248^6147+6147^36248137332Hans Havermann05/2021
517431986^19651+19651^31986137329Hans Havermann05/2021
51752^456167+22313137320Enzo Doria09/2023
517631817^20656+20656^31817137292Hans Havermann05/2021
5177(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
5178(71*10^137250+1)/9137251Serge Batalov05/2010
51792^455922+76249137247Enzo Doria05/2016
518031310^24171+24171^31310137241Hans Havermann05/2021
518114^119741-119741^14137239Serge Batalov04/2016
518235014^8297+8297^35014137218Hans Havermann05/2021
5183(19*2^455760+1)/3455137196Lelio R Paula07/2015
5185124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
5184124^65536+57^65536137195Serge Batalov03/2018
51862^455689+72677137177Enzo Doria04/2016
5187(17948!)^2+Prime(17948)137118Robert Price08/2014
518831287^24128+24128^31287137116Hans Havermann05/2021
5189(37^87421-1)/36137093Robert Price03/2012
519036233^6070+6070^36233137077Hans Havermann05/2021
5191(8*10^137073-17)/9137073Serge Batalov11/2022
519238418^3697+3697^38418137070Hans Havermann04/2021
51932^455323-57137066Lelio R Paula09/2017
5194(56*10^137019+583)/9137020Robert Price08/2021
519525017^31148-31148^25017136997Frank Doornink12/2023
5196(73*17^111333-9)/16136991Curtis Bright05/2015
51972^455025-112723136977Enzo Doria06/2014
519833876^11039+11039^33876136959Hans Havermann05/2021
5199(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
5200(251^57059-1)/250136921Anonymous04/2024
520135142^7873+7873^35142136919Hans Havermann05/2021
5202(4997*31^91805-1)/2136918Eric Chen05/2024
520366*10^136894+7136896Robert Price07/2020
520428766^30697-30697^28766136875Frank Doornink05/2024
52052^454675-1777136871Yves Minet10/2011
520631676^20931+20931^31676136866Hans Havermann05/2021
52073*10^136829+29136830Robert Price05/2018
52084*10^136813-57136814Robert Price10/2018
5209(6092*28^94536-143)/9136812Curtis Bright05/2015
5210fibonacci(654572)-2136798Jon Grantham08/2023
521137359^4588+4588^37359136795Hans Havermann05/2021
52122^454348-53136773Lelio R Paula09/2017
521331^91680-2136729Lelio R Paula05/2017
52142^454199-113697136728Enzo Doria09/2014
521530785^27622+27622^30785136725Hans Havermann05/2021
521632973^14014+14014^32973136725Hans Havermann05/2021
52187*10^136716+69136717Robert Price07/2019
521736002^6273+6273^36002136717Hans Havermann05/2021
52196*10^136692+53136693Robert Price05/2020
5220Phi(568997,2)136692Henri Lifchitz02/2026
5221(13*10^136687+47)/3136688Robert Price10/2018
5222F(2*453976)%(2^453976)136661Henri Lifchitz06/2025
52232^453935-2791357136649Enzo Doria01/2016
52242^453906-69131136640Enzo Doria11/2015
522533232^12915+12915^33232136620Hans Havermann05/2021
52262^453791+1873913136605Enzo Doria06/2016
522734166^9951+9951^34166136592Hans Havermann05/2021
5228(21*2^453740-1)/2735136588Lelio R Paula07/2015
522931102^24635+24635^31102136587Hans Havermann05/2021
5230580^49413+49413^580136550Norbert Schneider02/2019
52312^453503-2788297136519Enzo Doria11/2015
523234989^7958+7958^34989136486Hans Havermann12/2020
5233(2*10^136484+187)/9136484Robert Price06/2022
5234(5^653025)%L(653025)136475Henri Lifchitz06/2025
523531007^25158+25158^31007136452Hans Havermann11/2020
52362^453267-113827136447Enzo Doria09/2014
523732234^17085+17085^32234136435Hans Havermann12/2020
52382^453102+1877629136398Enzo Doria08/2016
523931016^24981+24981^31016136397Hans Havermann12/2020
5240(62*10^136384-791)/9136385Robert Price06/2019
524134171^9798+9798^34171136382Hans Havermann12/2020
5242(17*10^136354-113)/3136355Robert Price06/2021
524332756^14541+14541^32756136350Hans Havermann11/2020
524432205^17086+17086^32205136313Hans Havermann12/2020
5245(25*10^136303+161)/3136304Robert Price09/2019
524635337^7196+7196^35337136299Hans Havermann12/2020
5247(182*10^136291+1)/3136293Robert Price02/2020
5248(88*10^136234+83)/9136235Robert Price03/2022
524923*10^136225-7136227Robert Price02/2020
5250L(651821)136223Henri Lifchitz09/2008


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 15 2026 08:45 (Time in France)

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