PRP Records

Probable Primes Top 10000

(301969 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 ?
4751(25*10^141019-13)/3141020Robert Price09/2019
47522^468405+87855141004Lelio R Paula01/2016
475339338^3831+3831^39338140961Hans Havermann05/2021
475431458^30239+30239^31458140950Hans Havermann05/2021
47558*10^140932+29140933Robert Price11/2021
475633166^17691+17691^33166140881Hans Havermann06/2021
47572^467978-113051140876Enzo Doria07/2014
47582^467780-344429140816Enzo Doria07/2015
47599*10^140802-89140803Robert Price04/2020
47602^467605-1855603140764Enzo Doria09/2015
4761(9^147503-5^147503)/4140754Jon Grantham07/2023
47625*10^140744-7140745Robert Price09/2015
4763(5^201359-1)/4140744Paul Bourdelais12/2008
47642^467401-1850023140702Enzo Doria08/2015
4765(14*10^140693+13)/9140694Tyler Busby02/2023
4766(266*10^140681-17)/3140683Robert Price07/2020
4767(2^467270+78557)/23247140658Lelio R Paula07/2015
476832138^23781+23781^32138140644Hans Havermann05/2021
476931654^27735+27735^31654140640Hans Havermann05/2021
4770(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
47712^467166-1854941140631Enzo Doria09/2015
4772(203*10^140615-11)/3140617Robert Price12/2020
4773(85*10^140609+473)/9140610Robert Price01/2020
4774(3^672799)%L(672799)140607Henri Lifchitz06/2025
477539231^3836+3836^39231140600Hans Havermann06/2021
47765*3^294676+2^294676140597Jon Grantham08/2023
4777(5^672618)%L(672618)140569Henri Lifchitz07/2025
47782^466866-1840571140541Enzo Doria06/2015
47792^466829-459523140530Enzo Doria05/2015
47802^466692-113213140489Enzo Doria07/2014
478123*10^140464-3140466Robert Price10/2021
4782(2*10^140461-17)/3140461Serge Batalov11/2022
478329^96047-30140459Anonymous09/2024
478431335^30364+30364^31335140455Hans Havermann05/2021
478528511^31524-31524^28511140440Frank Doornink06/2024
478632795^19126+19126^32795140416Hans Havermann05/2021
4787(44*10^140410-503)/9140411Robert Price12/2018
478828332^31535-31535^28332140403Frank Doornink06/2024
4789153^64265-2140400Lelio R Paula11/2017
479030323^31322-31322^30323140379Frank Doornink06/2024
4791(112*10^140357-1)/3140359Serge Batalov12/2014
4792(29*10^140337-17)/3140338Robert Price09/2019
47932^466181-112735140335Enzo Doria07/2014
4794(16*10^140290-37)/3140291Robert Price05/2021
4795(5*10^140281-119)/3140282Robert Price03/2018
479634568^11415+11415^34568140259Hans Havermann05/2021
4797(27*2^465872+1)/691140241Lelio R Paula08/2015
479833632^14781+14781^33632140236Hans Havermann05/2021
479931803^25670+25670^31803140233Hans Havermann05/2021
48002^465803-114817140221Enzo Doria05/2015
4801floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
48022^465503-112735140131Enzo Doria07/2014
4803(16*10^140091+167)/3140092Robert Price06/2019
4804(8*10^140087-137)/3140088Robert Price03/2022
48056^179964+179964^6-1140040Robert Price04/2014
4806(89*10^140008-179)/9140009Robert Price12/2019
4807(29*2^465077-1)/9140003Lelio R Paula08/2015
48082^465072-344789140001Enzo Doria07/2015
480934742^10683+10683^34742139965Hans Havermann05/2021
48105*10^139945+81139946Robert Price03/2019
481132648^19335+19335^32648139941Hans Havermann05/2021
48122^464864-17139939Lelio R Paula09/2017
48138*10^139920+51139921Robert Price08/2019
4814(85*10^139913-1)/3139915Robert Price02/2020
481531203^30436+30436^31203139896Hans Havermann04/2021
48162^464642+22189139872Enzo Doria09/2023
481726138^31663-31663^26138139865Frank Doornink03/2024
4818(16^116139+619)/5139845Anonymous08/2022
4819(2^464556+619)/5139845Eric Chen10/2023
48204*10^139839-27139840Robert Price08/2021
482133582^14573+14573^33582139821Hans Havermann05/2021
4822(17^113621+1)/18139804Paul Bourdelais09/2011
48242*10^139800-21139801Robert Price09/2020
482332628^19261+19261^32628139801Hans Havermann04/2021
4825(13*10^139782+191)/3139783Robert Price11/2018
4826(64*10^139776+791)/9139777Robert Price01/2022
4827(695*10^139772+7)/9139774Robert Price12/2021
4828(19*2^464312-1)/3139773Lelio R Paula08/2015
4829(74*10^139723+133)/9139724Robert Price06/2019
48303*10^139722+13139723Robert Price07/2018
483131577^26592+26592^31577139721Hans Havermann05/2021
483277*10^139692+3139694Robert Price06/2020
4833(31*2^463970+1)/5139670Lelio R Paula08/2015
4834(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
483539640^3321+3321^39640139584Hans Havermann05/2021
483636663^6410+6410^36663139571Hans Havermann05/2021
48372^463633-2788423139568Enzo Doria11/2015
483833659^13978+13978^33659139532Hans Havermann05/2021
483931811^24318+24318^31811139521Hans Havermann04/2021
484034149^12172+12172^34149139512Hans Havermann04/2021
4841(29*10^139476+313)/9139477Robert Price04/2021
484231721^24940+24940^31721139474Hans Havermann05/2021
484332833^17698+17698^32833139473Hans Havermann05/2021
48442^463271-109501139459Enzo Doria04/2014
4845(5*10^139457+79)/3139458Robert Price03/2018
48462^463237-99139449Lelio R Paula09/2017
4847(49*10^139442+383)/9139443Robert Price04/2019
484831155^29902+29902^31155139441Hans Havermann05/2021
4849(7*10^139417-547)/9139417Robert Price01/2018
485029636^31175-31175^29636139409Frank Doornink05/2024
4851(10^139398+191)/3139398Robert Price02/2018
485223*10^139386-3139388Robert Price10/2021
48532^463019+79463139383Enzo Doria06/2016
48543^292129-112756139381Enzo Doria07/2014
4855(15*2^462951+1)/527139361Lelio R Paula08/2015
485631922^23205+23205^31922139359Hans Havermann05/2021
4857(19*10^139336+503)/9139337Alfred Reich11/2023
48592^462855-1865707139334Enzo Doria02/2016
485831237^28876+28876^31237139334Hans Havermann05/2021
4860(86*10^139315+121)/9139316Robert Price08/2019
48612^462786-292043139313Enzo Doria08/2015
486238915^3798+3798^38915139299Hans Havermann05/2021
4864(26*10^139289+1)/9139290Serge Batalov05/2010
4863(17*10^139289+7)/3139290Robert Price06/2023
486534065^12248+12248^34065139260Hans Havermann05/2021
486636425^6654+6654^36425139256Hans Havermann05/2021
486739252^3527+3527^39252139243Hans Havermann05/2021
4868(17*10^139239+67)/3139240Robert Price01/2019
486931887^23248+23248^31887139231Hans Havermann05/2021
4870(25*10^139210-97)/9139211Robert Price01/2022
48712^462238-935139148Yves Minet02/2014
4872(29*10^139134-119)/9139135Robert Price12/2021
4873U(687859)/4127153139105Serge Batalov07/2024
4874(109*10^139100-7)/3139102Robert Price03/2021
487538744^3885+3885^38744139068Hans Havermann05/2021
487631112^29499+29499^31112139065Hans Havermann05/2021
48772*10^139043-63139044Robert Price01/2022
487836390^6613+6613^36390139025Hans Havermann04/2021
487930554^30989-30989^30554138988Frank Doornink05/2024
48802*10^138975+33138976Robert Price11/2021
488142437^1882+1882^42437138966Hans Havermann05/2021
488232151^20990+20990^32151138958Hans Havermann05/2021
488332154^20933+20933^32154138933Hans Havermann04/2021
488431082^29499+29499^31082138931Hans Havermann04/2021
488530573^30962-30962^30573138876Frank Doornink05/2024
48862^461228+1870441138844Enzo Doria05/2016
48872^461204-113675138837Enzo Doria08/2014
4888(397227*29^94935-19)/28138837Eric Chen06/2025
4889(2^461139-7)/47138815Lelio R Paula08/2015
4890(17*10^138812-521)/9138813Robert Price04/2018
48913*10^138811-11138812Robert Price07/2018
489229109^31088-31088^29109138778Frank Doornink05/2024
4893(28*10^138768+173)/3138769Robert Price12/2019
4894(17*2^460963+1)/124051613138757Lelio R Paula08/2015
4895(379*10^138737-1)/9138739Robert Price02/2020
4896(43*10^138648+101)/9138649Robert Price11/2018
48972^460567-113541138645Enzo Doria08/2014
48982^460539+224789138637Enzo Doria07/2024
4899(10^138622+161)/9138622Robert Price09/2021
49007*10^138604+3138605Robert Price08/2015
4901(133*10^138600+17)/3138602Robert Price11/2021
490233912^12203+12203^33912138581Hans Havermann05/2021
49032^460330+69138574Lelio R Paula09/2017
4904(17*10^138569-77)/3138570Robert Price08/2019
490531186^27725+27725^31186138556Hans Havermann05/2021
4906(41^85909-3^85909)/38138552Robert Price09/2025
4907(16*10^138545+89)/3138546Robert Price03/2021
490839753^3056+3056^39753138546Hans Havermann05/2021
490931282^26847+26847^31282138545Hans Havermann05/2021
49106*10^138520-37138521Robert Price02/2021
49122^460078-69581138498Enzo Doria12/2015
491131830^22447+22447^31830138498Hans Havermann05/2021
491337384^5065+5065^37384138492Hans Havermann05/2021
491428736^31055-31055^28736138457Frank Doornink05/2024
491534774^9585+9585^34774138456Hans Havermann05/2021
491610^138444-5001138444Robert Price12/2021
49172^459768+1531138404Lelio R Paula06/2012
4918(266*10^138328-17)/3138330Robert Price07/2020
491927200^31193-31193^27200138328Frank Doornink01/2024
49202024^41836+2025138319Henri Lifchitz01/2025
492128782^31019-31019^28782138318Frank Doornink05/2024
492232963^15696+15696^32963138306Hans Havermann05/2021
49232^459343-113611138277Enzo Doria08/2014
4924(28*10^138240+113)/3138241Robert Price03/2020
49252^459199+1874393138233Enzo Doria06/2016
492633339^14002+14002^33339138230Hans Havermann05/2021
492730137^30860-30860^30137138226Frank Doornink05/2024
49282^459063-345307138192Enzo Doria06/2015
49292*10^138162-43138163Robert Price04/2018
49302^458927-112747138151Enzo Doria06/2014
49312^458927-69217138151Enzo Doria11/2015
493230907^29458+29458^30907138130Hans Havermann05/2021
493332882^15837+15837^32882138094Hans Havermann05/2021
493439252^3295+3295^39252138083Hans Havermann05/2021
493533789^12190+12190^33789138062Hans Havermann06/2021
4936555555*2^458524+1513138036Darren Bedwell08/2009
493728095^31028-31028^28095138033Frank Doornink05/2024
493830931^29002+29002^30931138028Hans Havermann05/2021
49392^458465+2^32+1138012T. D. Noe06/2007
494032206^19275+19275^32206138003Hans Havermann05/2021
49412^458321-113053137969Enzo Doria07/2014
49426^177298+323137965Riley Fisher03/2023
49432^458298+79459137962Enzo Doria06/2016
494430254^30789-30789^30254137959Frank Doornink05/2024
49452^458248-21815137947Enzo Doria07/2013
49462^458194+1876549137931Enzo Doria07/2016
4947(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
4948(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
4949(793*10^137887+53)/9137889Robert Price01/2022
49502^457937+57137853Lelio R Paula09/2017
495128714^30921-30921^28714137849Frank Doornink05/2024
4952(8*10^137845+13)/3137846Robert Price06/2018
49532^457822+105137819Donovan Johnson06/2006
49542^457754-113711137798Enzo Doria09/2014
495511^132315-360137792Enzo Doria09/2012
4956(2^659318)%L(659318)137787Henri Lifchitz05/2025
495732072^19689+19689^32072137725Hans Havermann06/2021
495826529^31132-31132^26529137720Frank Doornink03/2024
495944592^1225+1225^44592137707Hans Havermann05/2021
496028986^30857-30857^28986137690Frank Doornink05/2024
49612^457347-37137676Lelio R Paula09/2017
49622^457322-2786393137668Enzo Doria10/2015
4963gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
4964Phi(699340M,10)137664Anonymous03/2025
496534015^11134+11134^34015137647Hans Havermann06/2021
49662^457240-59939137643Enzo Doria10/2015
4967(856*10^137633-1)/9137635Robert Price03/2020
496836232^6289+6289^36232137631Hans Havermann05/2021
49692^457120-21575137607Enzo Doria07/2013
4971(11*2^456978+1)/15137564Lelio R Paula07/2015
497030963^27722+27722^30963137564Hans Havermann04/2021
497233722^12003+12003^33722137562Hans Havermann06/2021
4973(7*25^98399+10613)/12137556Curtis Bright05/2015
497441901^1918+1918^41901137555Hans Havermann06/2021
4975(7*10^137551-1)/3137552Robert Price08/2022
497632930^15021+15021^32930137539Hans Havermann05/2021
497731178^25785+25785^31178137538Hans Havermann05/2021
4978419^52446+52446^419137525Norbert Schneider11/2020
49792^456813+214175137515Enzo Doria10/2023
49802^456796-113513137510Enzo Doria08/2014
498131788^21137+21137^31788137485Hans Havermann04/2021
4982(7*2^456655+1)/39137467Lelio R Paula07/2015
498327151^31004-31004^27151137466Frank Doornink01/2024
49842^456503-114361137422Enzo Doria01/2015
4985(11*2^456387+1)/19137386Lelio R Paula07/2015
498630618^30618-5^5137352Serge Batalov04/2024
498736248^6147+6147^36248137332Hans Havermann05/2021
498831986^19651+19651^31986137329Hans Havermann05/2021
49892^456167+22313137320Enzo Doria09/2023
499031817^20656+20656^31817137292Hans Havermann05/2021
4991(37^87559-1)/3966428818030710150468137289Paul Vanderveen06/2025
4992(71*10^137250+1)/9137251Serge Batalov05/2010
49932^455922+76249137247Enzo Doria05/2016
499431310^24171+24171^31310137241Hans Havermann05/2021
499514^119741-119741^14137239Serge Batalov04/2016
499635014^8297+8297^35014137218Hans Havermann05/2021
4997(19*2^455760+1)/3455137196Lelio R Paula07/2015
4999124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
4998124^65536+57^65536137195Serge Batalov03/2018
50002^455689+72677137177Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 02 2025 16:06 (Time in France)

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