PRP Records

Probable Primes Top 10000

(303214 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 ?
50022^469198+782569141243Enzo Doria10/2016
500138129^5062+5062^38129141243Hans Havermann05/2021
5003(41^87583-1)/192892799240141242Paul Vanderveen05/2025
50042^469076-2786939141206Enzo Doria11/2015
500538630^4521+4521^38630141202Hans Havermann05/2021
5006Phi(143337,-5#)141148Henri Lifchitz12/2025
500731755^27836+27836^31755141139Hans Havermann05/2021
500835554^9325+9325^35554141137Hans Havermann05/2021
50092^468804+1874941141125Enzo Doria06/2016
50102^468787+81353141119Enzo Doria08/2016
501130204^31493-31493^30204141091Frank Doornink06/2024
50122^468595-350407141062Enzo Doria06/2015
50132^468564+87855141052Lelio R Paula01/2016
50142^468551-21987141048Enzo Doria07/2013
50152^468523-7141040Lelio R Paula08/2015
5016(25*10^141019-13)/3141020Robert Price09/2019
50172^468405+87855141004Lelio R Paula01/2016
501839338^3831+3831^39338140961Hans Havermann05/2021
501931458^30239+30239^31458140950Hans Havermann05/2021
50208*10^140932+29140933Robert Price11/2021
502133166^17691+17691^33166140881Hans Havermann06/2021
50222^467978-113051140876Enzo Doria07/2014
50232^467780-344429140816Enzo Doria07/2015
50249*10^140802-89140803Robert Price04/2020
50252^467605-1855603140764Enzo Doria09/2015
5026(9^147503-5^147503)/4140754Jon Grantham07/2023
50275*10^140744-7140745Robert Price09/2015
5029(5^201359-1)/4140744Paul Bourdelais12/2008
5028Phi(201359,5)140744Henri Lifchitz12/2025
50302^467401-1850023140702Enzo Doria08/2015
5031(14*10^140693+13)/9140694Tyler Busby02/2023
5032(266*10^140681-17)/3140683Robert Price07/2020
5033(2^467270+78557)/23247140658Lelio R Paula07/2015
503432138^23781+23781^32138140644Hans Havermann05/2021
503531654^27735+27735^31654140640Hans Havermann05/2021
5036(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
50372^467166-1854941140631Enzo Doria09/2015
5038(203*10^140615-11)/3140617Robert Price12/2020
5039(85*10^140609+473)/9140610Robert Price01/2020
5040(3^672799)%L(672799)140607Henri Lifchitz06/2025
504139231^3836+3836^39231140600Hans Havermann06/2021
50425*3^294676+2^294676140597Jon Grantham08/2023
5043(5^672618)%L(672618)140569Henri Lifchitz07/2025
50442^466866-1840571140541Enzo Doria06/2015
50452^466829-459523140530Enzo Doria05/2015
50462^466692-113213140489Enzo Doria07/2014
504723*10^140464-3140466Robert Price10/2021
5048(2*10^140461-17)/3140461Serge Batalov11/2022
504929^96047-30140459Anonymous09/2024
505031335^30364+30364^31335140455Hans Havermann05/2021
505128511^31524-31524^28511140440Frank Doornink06/2024
505232795^19126+19126^32795140416Hans Havermann05/2021
5053(44*10^140410-503)/9140411Robert Price12/2018
505428332^31535-31535^28332140403Frank Doornink06/2024
5055153^64265-2140400Lelio R Paula11/2017
505630323^31322-31322^30323140379Frank Doornink06/2024
5057(112*10^140357-1)/3140359Serge Batalov12/2014
5058(29*10^140337-17)/3140338Robert Price09/2019
50592^466181-112735140335Enzo Doria07/2014
5060(16*10^140290-37)/3140291Robert Price05/2021
5061(5*10^140281-119)/3140282Robert Price03/2018
506234568^11415+11415^34568140259Hans Havermann05/2021
5063(27*2^465872+1)/691140241Lelio R Paula08/2015
506433632^14781+14781^33632140236Hans Havermann05/2021
506531803^25670+25670^31803140233Hans Havermann05/2021
50662^465803-114817140221Enzo Doria05/2015
5067Phi(213305,-7)140192Henri Lifchitz12/2025
5068floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
50692^465503-112735140131Enzo Doria07/2014
5070(16*10^140091+167)/3140092Robert Price06/2019
5071(8*10^140087-137)/3140088Robert Price03/2022
50726^179964+179964^6-1140040Robert Price04/2014
5073(89*10^140008-179)/9140009Robert Price12/2019
5074(29*2^465077-1)/9140003Lelio R Paula08/2015
50752^465072-344789140001Enzo Doria07/2015
507634742^10683+10683^34742139965Hans Havermann05/2021
50775*10^139945+81139946Robert Price03/2019
507832648^19335+19335^32648139941Hans Havermann05/2021
50792^464864-17139939Lelio R Paula09/2017
50808*10^139920+51139921Robert Price08/2019
5081(85*10^139913-1)/3139915Robert Price02/2020
508231203^30436+30436^31203139896Hans Havermann04/2021
50832^464642+22189139872Enzo Doria09/2023
508426138^31663-31663^26138139865Frank Doornink03/2024
5085(47^83641-5^83641)/42139855Robert Price05/2026
5086(16^116139+619)/5139845Anonymous08/2022
5087(2^464556+619)/5139845Eric Chen10/2023
50884*10^139839-27139840Robert Price08/2021
508933582^14573+14573^33582139821Hans Havermann05/2021
5090(17^113621+1)/18139804Paul Bourdelais09/2011
50922*10^139800-21139801Robert Price09/2020
509132628^19261+19261^32628139801Hans Havermann04/2021
5093(13*10^139782+191)/3139783Robert Price11/2018
5094(64*10^139776+791)/9139777Robert Price01/2022
5095(695*10^139772+7)/9139774Robert Price12/2021
5096(19*2^464312-1)/3139773Lelio R Paula08/2015
5097(74*10^139723+133)/9139724Robert Price06/2019
50983*10^139722+13139723Robert Price07/2018
509931577^26592+26592^31577139721Hans Havermann05/2021
510077*10^139692+3139694Robert Price06/2020
5101(31*2^463970+1)/5139670Lelio R Paula08/2015
5102(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
510339640^3321+3321^39640139584Hans Havermann05/2021
510436663^6410+6410^36663139571Hans Havermann05/2021
51052^463633-2788423139568Enzo Doria11/2015
510633659^13978+13978^33659139532Hans Havermann05/2021
510731811^24318+24318^31811139521Hans Havermann04/2021
510834149^12172+12172^34149139512Hans Havermann04/2021
5109(29*10^139476+313)/9139477Robert Price04/2021
511031721^24940+24940^31721139474Hans Havermann05/2021
511132833^17698+17698^32833139473Hans Havermann05/2021
51122^463271-109501139459Enzo Doria04/2014
5113(5*10^139457+79)/3139458Robert Price03/2018
51142^463237-99139449Lelio R Paula09/2017
5115(49*10^139442+383)/9139443Robert Price04/2019
511631155^29902+29902^31155139441Hans Havermann05/2021
5117(7*10^139417-547)/9139417Robert Price01/2018
511829636^31175-31175^29636139409Frank Doornink05/2024
5119(10^139398+191)/3139398Robert Price02/2018
512023*10^139386-3139388Robert Price10/2021
51212^463019+79463139383Enzo Doria06/2016
51223^292129-112756139381Enzo Doria07/2014
5123(15*2^462951+1)/527139361Lelio R Paula08/2015
512431922^23205+23205^31922139359Hans Havermann05/2021
5125(19*10^139336+503)/9139337Alfred Reich11/2023
51272^462855-1865707139334Enzo Doria02/2016
512631237^28876+28876^31237139334Hans Havermann05/2021
5128(86*10^139315+121)/9139316Robert Price08/2019
51292^462786-292043139313Enzo Doria08/2015
513038915^3798+3798^38915139299Hans Havermann05/2021
5132(26*10^139289+1)/9139290Serge Batalov05/2010
5131(17*10^139289+7)/3139290Robert Price06/2023
513334065^12248+12248^34065139260Hans Havermann05/2021
513436425^6654+6654^36425139256Hans Havermann05/2021
513539252^3527+3527^39252139243Hans Havermann05/2021
5136(17*10^139239+67)/3139240Robert Price01/2019
513731887^23248+23248^31887139231Hans Havermann05/2021
5138(25*10^139210-97)/9139211Robert Price01/2022
51392^462238-935139148Yves Minet02/2014
5140(29*10^139134-119)/9139135Robert Price12/2021
5141U(687859)/4127153139105Serge Batalov07/2024
5142(109*10^139100-7)/3139102Robert Price03/2021
514338744^3885+3885^38744139068Hans Havermann05/2021
514431112^29499+29499^31112139065Hans Havermann05/2021
51452*10^139043-63139044Robert Price01/2022
514636390^6613+6613^36390139025Hans Havermann04/2021
514730554^30989-30989^30554138988Frank Doornink05/2024
51482*10^138975+33138976Robert Price11/2021
514942437^1882+1882^42437138966Hans Havermann05/2021
515032151^20990+20990^32151138958Hans Havermann05/2021
515132154^20933+20933^32154138933Hans Havermann04/2021
515231082^29499+29499^31082138931Hans Havermann04/2021
515330573^30962-30962^30573138876Frank Doornink05/2024
51542^461228+1870441138844Enzo Doria05/2016
51552^461204-113675138837Enzo Doria08/2014
5156(397227*29^94935-19)/28138837Eric Chen06/2025
5157(2^461139-7)/47138815Lelio R Paula08/2015
5158(17*10^138812-521)/9138813Robert Price04/2018
51593*10^138811-11138812Robert Price07/2018
516029109^31088-31088^29109138778Frank Doornink05/2024
5161(28*10^138768+173)/3138769Robert Price12/2019
5162(17*2^460963+1)/124051613138757Lelio R Paula08/2015
5163(379*10^138737-1)/9138739Robert Price02/2020
5164(43*10^138648+101)/9138649Robert Price11/2018
51652^460567-113541138645Enzo Doria08/2014
51662^460539+224789138637Enzo Doria07/2024
5167(10^138622+161)/9138622Robert Price09/2021
51687*10^138604+3138605Robert Price08/2015
5169(133*10^138600+17)/3138602Robert Price11/2021
517033912^12203+12203^33912138581Hans Havermann05/2021
51712^460330+69138574Lelio R Paula09/2017
5172(17*10^138569-77)/3138570Robert Price08/2019
517331186^27725+27725^31186138556Hans Havermann05/2021
5174(41^85909-3^85909)/38138552Robert Price09/2025
5175(16*10^138545+89)/3138546Robert Price03/2021
517639753^3056+3056^39753138546Hans Havermann05/2021
517731282^26847+26847^31282138545Hans Havermann05/2021
51786*10^138520-37138521Robert Price02/2021
51812^460078-69581138498Enzo Doria12/2015
517931830^22447+22447^31830138498Hans Havermann05/2021
5180Phi(237987,2^3)138498Henri Lifchitz12/2025
518237384^5065+5065^37384138492Hans Havermann05/2021
518328736^31055-31055^28736138457Frank Doornink05/2024
518434774^9585+9585^34774138456Hans Havermann05/2021
518510^138444-5001138444Robert Price12/2021
51862^459768+1531138404Lelio R Paula06/2012
5187(266*10^138328-17)/3138330Robert Price07/2020
518827200^31193-31193^27200138328Frank Doornink01/2024
51892024^41836+2025138319Henri Lifchitz01/2025
519028782^31019-31019^28782138318Frank Doornink05/2024
519132963^15696+15696^32963138306Hans Havermann05/2021
51922^459343-113611138277Enzo Doria08/2014
5193(28*10^138240+113)/3138241Robert Price03/2020
51942^459199+1874393138233Enzo Doria06/2016
519533339^14002+14002^33339138230Hans Havermann05/2021
519630137^30860-30860^30137138226Frank Doornink05/2024
51972^459063-345307138192Enzo Doria06/2015
51982*10^138162-43138163Robert Price04/2018
51992^458927-112747138151Enzo Doria06/2014
52002^458927-69217138151Enzo Doria11/2015
520130907^29458+29458^30907138130Hans Havermann05/2021
520232882^15837+15837^32882138094Hans Havermann05/2021
520339252^3295+3295^39252138083Hans Havermann05/2021
520433789^12190+12190^33789138062Hans Havermann06/2021
5205555555*2^458524+1513138036Darren Bedwell08/2009
520628095^31028-31028^28095138033Frank Doornink05/2024
520730931^29002+29002^30931138028Hans Havermann05/2021
52082^458465+2^32+1138012T. D. Noe06/2007
520932206^19275+19275^32206138003Hans Havermann05/2021
52102^458321-113053137969Enzo Doria07/2014
52116^177298+323137965Riley Fisher03/2023
52122^458298+79459137962Enzo Doria06/2016
521330254^30789-30789^30254137959Frank Doornink05/2024
52142^458248-21815137947Enzo Doria07/2013
52152^458194+1876549137931Enzo Doria07/2016
5216(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
5217(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
5218(793*10^137887+53)/9137889Robert Price01/2022
52192^457937+57137853Lelio R Paula09/2017
522028714^30921-30921^28714137849Frank Doornink05/2024
5221(8*10^137845+13)/3137846Robert Price06/2018
52222^457822+105137819Donovan Johnson06/2006
52232^457754-113711137798Enzo Doria09/2014
522411^132315-360137792Enzo Doria09/2012
5225(2^659318)%L(659318)137787Henri Lifchitz05/2025
522632072^19689+19689^32072137725Hans Havermann06/2021
522726529^31132-31132^26529137720Frank Doornink03/2024
522844592^1225+1225^44592137707Hans Havermann05/2021
522928986^30857-30857^28986137690Frank Doornink05/2024
52302^457347-37137676Lelio R Paula09/2017
52312^457322-2786393137668Enzo Doria10/2015
5232gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
5233Phi(699340M,10)137664Anonymous03/2025
523434015^11134+11134^34015137647Hans Havermann06/2021
52352^457240-59939137643Enzo Doria10/2015
5236(856*10^137633-1)/9137635Robert Price03/2020
523736232^6289+6289^36232137631Hans Havermann05/2021
52382^457120-21575137607Enzo Doria07/2013
5239(11*2^456978+1)/15137564Lelio R Paula07/2015
524030963^27722+27722^30963137564Hans Havermann04/2021
524133722^12003+12003^33722137562Hans Havermann06/2021
5242(7*25^98399+10613)/12137556Curtis Bright05/2015
524341901^1918+1918^41901137555Hans Havermann06/2021
5244(7*10^137551-1)/3137552Robert Price08/2022
524532930^15021+15021^32930137539Hans Havermann05/2021
524631178^25785+25785^31178137538Hans Havermann05/2021
5247419^52446+52446^419137525Norbert Schneider11/2020
52482^456813+214175137515Enzo Doria10/2023
52492^456796-113513137510Enzo Doria08/2014
525031788^21137+21137^31788137485Hans Havermann04/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 21 2026 15:15 (Time in France)

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