PRP Records

Probable Primes Top 10000

(301692 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 ?
45012^470183+72623141540Enzo Doria04/2016
45022^470173-16465141537Enzo Doria04/2013
450337297^6234+6234^37297141534Hans Havermann05/2021
45042^4^117533+117533^4^2141524Henri Lifchitz03/2025
4505(509*10^141479+13)/9141481Robert Price05/2022
450644*10^141476+9141478Robert Price10/2020
45072^469974-1841141477Enzo Doria05/2014
4508(23*2^469939+1)/25141466Lelio R Paula08/2015
4509312*33^93158+23141465Eric Chen12/2023
45102*10^141448+63141449Robert Price05/2018
45112^469824+43141432Lelio R Paula09/2017
45122*10^141407-27141408Robert Price05/2018
4513(214*10^141385-1)/3141387Robert Price01/2021
45142^469630-59711141373Enzo Doria10/2015
451535277^10172+10172^35277141370Hans Havermann04/2021
451633397^17100+17100^33397141370Hans Havermann04/2021
4517(25*10^141366-331)/9141367Robert Price08/2018
451836986^6639+6639^36986141365Hans Havermann06/2021
451934572^12271+12271^34572141361Hans Havermann06/2021
452037179^6338+6338^37179141353Hans Havermann05/2021
4521(2^469564-3)/611141351Lelio R Paula08/2015
4522197^61601+2141342Lelio R Paula08/2017
452333420^16951+16951^33420141340Hans Havermann05/2021
452431623^29458+29458^31623141330Hans Havermann05/2021
452548112^865+865^48112141306Hans Havermann05/2021
45262^469372-112949141296Enzo Doria07/2014
45275*10^141294-63141295Robert Price04/2021
45283^296115+4141283Tyler NeSmith01/2021
4529(64*10^141256+161)/9141257Robert Price08/2022
4531143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
4530143^65536+106^65536141253Serge Batalov03/2018
4532(11*10^141243-23)/3141244Robert Price09/2021
45342^469198+782569141243Enzo Doria10/2016
453338129^5062+5062^38129141243Hans Havermann05/2021
4535(41^87583-1)/192892799240141242Paul Vanderveen05/2025
45362^469076-2786939141206Enzo Doria11/2015
453738630^4521+4521^38630141202Hans Havermann05/2021
453831755^27836+27836^31755141139Hans Havermann05/2021
453935554^9325+9325^35554141137Hans Havermann05/2021
45402^468804+1874941141125Enzo Doria06/2016
45412^468787+81353141119Enzo Doria08/2016
454230204^31493-31493^30204141091Frank Doornink06/2024
45432^468595-350407141062Enzo Doria06/2015
45442^468564+87855141052Lelio R Paula01/2016
45452^468551-21987141048Enzo Doria07/2013
45462^468523-7141040Lelio R Paula08/2015
4547(25*10^141019-13)/3141020Robert Price09/2019
45482^468405+87855141004Lelio R Paula01/2016
454939338^3831+3831^39338140961Hans Havermann05/2021
455031458^30239+30239^31458140950Hans Havermann05/2021
45518*10^140932+29140933Robert Price11/2021
455233166^17691+17691^33166140881Hans Havermann06/2021
45532^467978-113051140876Enzo Doria07/2014
45542^467780-344429140816Enzo Doria07/2015
45559*10^140802-89140803Robert Price04/2020
45562^467605-1855603140764Enzo Doria09/2015
4557(9^147503-5^147503)/4140754Jon Grantham07/2023
45585*10^140744-7140745Robert Price09/2015
4559(5^201359-1)/4140744Paul Bourdelais12/2008
45602^467401-1850023140702Enzo Doria08/2015
4561(14*10^140693+13)/9140694Tyler Busby02/2023
4562(266*10^140681-17)/3140683Robert Price07/2020
4563(2^467270+78557)/23247140658Lelio R Paula07/2015
456432138^23781+23781^32138140644Hans Havermann05/2021
456531654^27735+27735^31654140640Hans Havermann05/2021
4566(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
45672^467166-1854941140631Enzo Doria09/2015
4568(203*10^140615-11)/3140617Robert Price12/2020
4569(85*10^140609+473)/9140610Robert Price01/2020
4570(3^672799)%L(672799)140607Henri Lifchitz06/2025
457139231^3836+3836^39231140600Hans Havermann06/2021
45725*3^294676+2^294676140597Jon Grantham08/2023
45732^466866-1840571140541Enzo Doria06/2015
45742^466829-459523140530Enzo Doria05/2015
45752^466692-113213140489Enzo Doria07/2014
457623*10^140464-3140466Robert Price10/2021
4577(2*10^140461-17)/3140461Serge Batalov11/2022
457829^96047-30140459Anonymous09/2024
457931335^30364+30364^31335140455Hans Havermann05/2021
458028511^31524-31524^28511140440Frank Doornink06/2024
458132795^19126+19126^32795140416Hans Havermann05/2021
4582(44*10^140410-503)/9140411Robert Price12/2018
458328332^31535-31535^28332140403Frank Doornink06/2024
4584153^64265-2140400Lelio R Paula11/2017
458530323^31322-31322^30323140379Frank Doornink06/2024
4586(112*10^140357-1)/3140359Serge Batalov12/2014
4587(29*10^140337-17)/3140338Robert Price09/2019
45882^466181-112735140335Enzo Doria07/2014
4589(16*10^140290-37)/3140291Robert Price05/2021
4590(5*10^140281-119)/3140282Robert Price03/2018
459134568^11415+11415^34568140259Hans Havermann05/2021
4592(27*2^465872+1)/691140241Lelio R Paula08/2015
459333632^14781+14781^33632140236Hans Havermann05/2021
459431803^25670+25670^31803140233Hans Havermann05/2021
45952^465803-114817140221Enzo Doria05/2015
4596floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
45972^465503-112735140131Enzo Doria07/2014
4598(16*10^140091+167)/3140092Robert Price06/2019
4599(8*10^140087-137)/3140088Robert Price03/2022
46006^179964+179964^6-1140040Robert Price04/2014
4601(89*10^140008-179)/9140009Robert Price12/2019
4602(29*2^465077-1)/9140003Lelio R Paula08/2015
46032^465072-344789140001Enzo Doria07/2015
460434742^10683+10683^34742139965Hans Havermann05/2021
46055*10^139945+81139946Robert Price03/2019
460632648^19335+19335^32648139941Hans Havermann05/2021
46072^464864-17139939Lelio R Paula09/2017
46088*10^139920+51139921Robert Price08/2019
4609(85*10^139913-1)/3139915Robert Price02/2020
461031203^30436+30436^31203139896Hans Havermann04/2021
46112^464642+22189139872Enzo Doria09/2023
461226138^31663-31663^26138139865Frank Doornink03/2024
4613(16^116139+619)/5139845Anonymous08/2022
4614(2^464556+619)/5139845Eric Chen10/2023
46154*10^139839-27139840Robert Price08/2021
461633582^14573+14573^33582139821Hans Havermann05/2021
4617(17^113621+1)/18139804Paul Bourdelais09/2011
46192*10^139800-21139801Robert Price09/2020
461832628^19261+19261^32628139801Hans Havermann04/2021
4620(13*10^139782+191)/3139783Robert Price11/2018
4621(64*10^139776+791)/9139777Robert Price01/2022
4622(695*10^139772+7)/9139774Robert Price12/2021
4623(19*2^464312-1)/3139773Lelio R Paula08/2015
4624(74*10^139723+133)/9139724Robert Price06/2019
46253*10^139722+13139723Robert Price07/2018
462631577^26592+26592^31577139721Hans Havermann05/2021
462777*10^139692+3139694Robert Price06/2020
4628(31*2^463970+1)/5139670Lelio R Paula08/2015
4629(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
463039640^3321+3321^39640139584Hans Havermann05/2021
463136663^6410+6410^36663139571Hans Havermann05/2021
46322^463633-2788423139568Enzo Doria11/2015
463333659^13978+13978^33659139532Hans Havermann05/2021
463431811^24318+24318^31811139521Hans Havermann04/2021
463534149^12172+12172^34149139512Hans Havermann04/2021
4636(29*10^139476+313)/9139477Robert Price04/2021
463731721^24940+24940^31721139474Hans Havermann05/2021
463832833^17698+17698^32833139473Hans Havermann05/2021
46392^463271-109501139459Enzo Doria04/2014
4640(5*10^139457+79)/3139458Robert Price03/2018
46412^463237-99139449Lelio R Paula09/2017
4642(49*10^139442+383)/9139443Robert Price04/2019
464331155^29902+29902^31155139441Hans Havermann05/2021
4644(7*10^139417-547)/9139417Robert Price01/2018
464529636^31175-31175^29636139409Frank Doornink05/2024
4646(10^139398+191)/3139398Robert Price02/2018
464723*10^139386-3139388Robert Price10/2021
46482^463019+79463139383Enzo Doria06/2016
46493^292129-112756139381Enzo Doria07/2014
4650(15*2^462951+1)/527139361Lelio R Paula08/2015
465131922^23205+23205^31922139359Hans Havermann05/2021
4652(19*10^139336+503)/9139337Alfred Reich11/2023
46542^462855-1865707139334Enzo Doria02/2016
465331237^28876+28876^31237139334Hans Havermann05/2021
4655(86*10^139315+121)/9139316Robert Price08/2019
46562^462786-292043139313Enzo Doria08/2015
465738915^3798+3798^38915139299Hans Havermann05/2021
4659(26*10^139289+1)/9139290Serge Batalov05/2010
4658(17*10^139289+7)/3139290Robert Price06/2023
466034065^12248+12248^34065139260Hans Havermann05/2021
466136425^6654+6654^36425139256Hans Havermann05/2021
466239252^3527+3527^39252139243Hans Havermann05/2021
4663(17*10^139239+67)/3139240Robert Price01/2019
466431887^23248+23248^31887139231Hans Havermann05/2021
4665(25*10^139210-97)/9139211Robert Price01/2022
46662^462238-935139148Yves Minet02/2014
4667(29*10^139134-119)/9139135Robert Price12/2021
4668U(687859)/4127153139105Serge Batalov07/2024
4669(109*10^139100-7)/3139102Robert Price03/2021
467038744^3885+3885^38744139068Hans Havermann05/2021
467131112^29499+29499^31112139065Hans Havermann05/2021
46722*10^139043-63139044Robert Price01/2022
467336390^6613+6613^36390139025Hans Havermann04/2021
467430554^30989-30989^30554138988Frank Doornink05/2024
46752*10^138975+33138976Robert Price11/2021
467642437^1882+1882^42437138966Hans Havermann05/2021
467732151^20990+20990^32151138958Hans Havermann05/2021
467832154^20933+20933^32154138933Hans Havermann04/2021
467931082^29499+29499^31082138931Hans Havermann04/2021
468030573^30962-30962^30573138876Frank Doornink05/2024
46812^461228+1870441138844Enzo Doria05/2016
46822^461204-113675138837Enzo Doria08/2014
4683(397227*29^94935-19)/28138837Eric Chen06/2025
4684(2^461139-7)/47138815Lelio R Paula08/2015
4685(17*10^138812-521)/9138813Robert Price04/2018
46863*10^138811-11138812Robert Price07/2018
468729109^31088-31088^29109138778Frank Doornink05/2024
4688(28*10^138768+173)/3138769Robert Price12/2019
4689(17*2^460963+1)/124051613138757Lelio R Paula08/2015
4690(379*10^138737-1)/9138739Robert Price02/2020
4691(43*10^138648+101)/9138649Robert Price11/2018
46922^460567-113541138645Enzo Doria08/2014
46932^460539+224789138637Enzo Doria07/2024
4694(10^138622+161)/9138622Robert Price09/2021
46957*10^138604+3138605Robert Price08/2015
4696(133*10^138600+17)/3138602Robert Price11/2021
469733912^12203+12203^33912138581Hans Havermann05/2021
46982^460330+69138574Lelio R Paula09/2017
4699(17*10^138569-77)/3138570Robert Price08/2019
470031186^27725+27725^31186138556Hans Havermann05/2021
4701(16*10^138545+89)/3138546Robert Price03/2021
470239753^3056+3056^39753138546Hans Havermann05/2021
470331282^26847+26847^31282138545Hans Havermann05/2021
47046*10^138520-37138521Robert Price02/2021
47062^460078-69581138498Enzo Doria12/2015
470531830^22447+22447^31830138498Hans Havermann05/2021
470737384^5065+5065^37384138492Hans Havermann05/2021
470828736^31055-31055^28736138457Frank Doornink05/2024
470934774^9585+9585^34774138456Hans Havermann05/2021
471010^138444-5001138444Robert Price12/2021
47112^459768+1531138404Lelio R Paula06/2012
4712(266*10^138328-17)/3138330Robert Price07/2020
471327200^31193-31193^27200138328Frank Doornink01/2024
47142024^41836+2025138319Henri Lifchitz01/2025
471528782^31019-31019^28782138318Frank Doornink05/2024
471632963^15696+15696^32963138306Hans Havermann05/2021
47172^459343-113611138277Enzo Doria08/2014
4718(28*10^138240+113)/3138241Robert Price03/2020
47192^459199+1874393138233Enzo Doria06/2016
472033339^14002+14002^33339138230Hans Havermann05/2021
472130137^30860-30860^30137138226Frank Doornink05/2024
47222^459063-345307138192Enzo Doria06/2015
47232*10^138162-43138163Robert Price04/2018
47242^458927-112747138151Enzo Doria06/2014
47252^458927-69217138151Enzo Doria11/2015
472630907^29458+29458^30907138130Hans Havermann05/2021
472732882^15837+15837^32882138094Hans Havermann05/2021
472839252^3295+3295^39252138083Hans Havermann05/2021
472933789^12190+12190^33789138062Hans Havermann06/2021
4730555555*2^458524+1513138036Darren Bedwell08/2009
473128095^31028-31028^28095138033Frank Doornink05/2024
473230931^29002+29002^30931138028Hans Havermann05/2021
47332^458465+2^32+1138012T. D. Noe06/2007
473432206^19275+19275^32206138003Hans Havermann05/2021
47352^458321-113053137969Enzo Doria07/2014
47366^177298+323137965Riley Fisher03/2023
47372^458298+79459137962Enzo Doria06/2016
473830254^30789-30789^30254137959Frank Doornink05/2024
47392^458248-21815137947Enzo Doria07/2013
47402^458194+1876549137931Enzo Doria07/2016
4741(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
4742(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
4743(793*10^137887+53)/9137889Robert Price01/2022
47442^457937+57137853Lelio R Paula09/2017
474528714^30921-30921^28714137849Frank Doornink05/2024
4746(8*10^137845+13)/3137846Robert Price06/2018
47472^457822+105137819Donovan Johnson06/2006
47482^457754-113711137798Enzo Doria09/2014
474911^132315-360137792Enzo Doria09/2012
4750(2^659318)%L(659318)137787Henri Lifchitz05/2025


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

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