PRP Records

Probable Primes Top 10000

(295149 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
37512^471464-111546435141925Paul Bourdelais10/2021
3752(904*19^110984-1)/3141924Curtis Bright05/2015
3753(14*10^141853+37)/3141854Robert Price12/2018
3754(41*10^141836-59)/9141837Robert Price10/2018
37554*5^202913-9141831Lelio R Paula04/2015
37562*7^167812-3141818Lelio R Paula12/2014
37572^471043+35141799Robert Price11/2015
3758(11*2^470956-1)/7945141770Lelio R Paula08/2015
375943636^1773+1773^43636141761Hans Havermann05/2021
3760(2*10^141751-17)/3141751Serge Batalov11/2022
3761(53*10^141722-611)/9141723Robert Price02/2022
3762(11*10^141718-131)/3141719Robert Price09/2018
3763(61*10^141716+47)/9141717Robert Price07/2022
376426057^32088-32088^26057141699Frank Doornink03/2024
37652^470692+76771141693Enzo Doria05/2016
376650160^667+667^50160141659Hans Havermann05/2021
376731522^31181+31181^31522141657Hans Havermann05/2021
376833076^19135+19135^33076141626Hans Havermann04/2021
3769(91*10^141610+71)/9141612Robert Price01/2022
3770(21*2^470391+1)/533141601Lelio R Paula09/2015
3771(5*10^141594-23)/9141594Serge Batalov11/2022
377231932^27155+27155^31932141582Hans Havermann05/2021
377336449^7660+7660^36449141577Hans Havermann05/2021
37742^470305-459373141576Enzo Doria05/2015
377532195^24936+24936^32195141556Hans Havermann05/2021
37762^470183+72623141540Enzo Doria04/2016
37772^470173-16465141537Enzo Doria04/2013
377837297^6234+6234^37297141534Hans Havermann05/2021
3779(509*10^141479+13)/9141481Robert Price05/2022
378044*10^141476+9141478Robert Price10/2020
37812^469974-1841141477Enzo Doria05/2014
3782(23*2^469939+1)/25141466Lelio R Paula08/2015
3783312*33^93158+23141465Eric Chen12/2023
37842*10^141448+63141449Robert Price05/2018
37852^469824+43141432Lelio R Paula09/2017
37862*10^141407-27141408Robert Price05/2018
3787(214*10^141385-1)/3141387Robert Price01/2021
37882^469630-59711141373Enzo Doria10/2015
378935277^10172+10172^35277141370Hans Havermann04/2021
379033397^17100+17100^33397141370Hans Havermann04/2021
3791(25*10^141366-331)/9141367Robert Price08/2018
379236986^6639+6639^36986141365Hans Havermann06/2021
379334572^12271+12271^34572141361Hans Havermann06/2021
379437179^6338+6338^37179141353Hans Havermann05/2021
3795(2^469564-3)/611141351Lelio R Paula08/2015
3796197^61601+2141342Lelio R Paula08/2017
379733420^16951+16951^33420141340Hans Havermann05/2021
379831623^29458+29458^31623141330Hans Havermann05/2021
379948112^865+865^48112141306Hans Havermann05/2021
38002^469372-112949141296Enzo Doria07/2014
38015*10^141294-63141295Robert Price04/2021
38023^296115+4141283Tyler NeSmith01/2021
3803(64*10^141256+161)/9141257Robert Price08/2022
3805143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
3804143^65536+106^65536141253Serge Batalov03/2018
3806(11*10^141243-23)/3141244Robert Price09/2021
38082^469198+782569141243Enzo Doria10/2016
380738129^5062+5062^38129141243Hans Havermann05/2021
38092^469076-2786939141206Enzo Doria11/2015
381038630^4521+4521^38630141202Hans Havermann05/2021
381131755^27836+27836^31755141139Hans Havermann05/2021
381235554^9325+9325^35554141137Hans Havermann05/2021
38132^468804+1874941141125Enzo Doria06/2016
38142^468787+81353141119Enzo Doria08/2016
38152^468595-350407141062Enzo Doria06/2015
38162^468564+87855141052Lelio R Paula01/2016
38172^468551-21987141048Enzo Doria07/2013
38182^468523-7141040Lelio R Paula08/2015
3819(25*10^141019-13)/3141020Robert Price09/2019
38202^468405+87855141004Lelio R Paula01/2016
382139338^3831+3831^39338140961Hans Havermann05/2021
382231458^30239+30239^31458140950Hans Havermann05/2021
38238*10^140932+29140933Robert Price11/2021
382433166^17691+17691^33166140881Hans Havermann06/2021
38252^467978-113051140876Enzo Doria07/2014
38262^467780-344429140816Enzo Doria07/2015
38279*10^140802-89140803Robert Price04/2020
38282^467605-1855603140764Enzo Doria09/2015
3829(9^147503-5^147503)/4140754Jon Grantham07/2023
38305*10^140744-7140745Robert Price09/2015
3831(5^201359-1)/4140744Paul Bourdelais12/2008
38322^467401-1850023140702Enzo Doria08/2015
3833(14*10^140693+13)/9140694Tyler Busby02/2023
3834(266*10^140681-17)/3140683Robert Price07/2020
3835(2^467270+78557)/23247140658Lelio R Paula07/2015
383632138^23781+23781^32138140644Hans Havermann05/2021
383731654^27735+27735^31654140640Hans Havermann05/2021
3838(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
38392^467166-1854941140631Enzo Doria09/2015
3840(203*10^140615-11)/3140617Robert Price12/2020
3841(85*10^140609+473)/9140610Robert Price01/2020
384239231^3836+3836^39231140600Hans Havermann06/2021
38435*3^294676+2^294676140597Jon Grantham08/2023
38442^466866-1840571140541Enzo Doria06/2015
38452^466829-459523140530Enzo Doria05/2015
38462^466692-113213140489Enzo Doria07/2014
384723*10^140464-3140466Robert Price10/2021
3848(2*10^140461-17)/3140461Serge Batalov11/2022
384931335^30364+30364^31335140455Hans Havermann05/2021
385032795^19126+19126^32795140416Hans Havermann05/2021
3851(44*10^140410-503)/9140411Robert Price12/2018
3852153^64265-2140400Lelio R Paula11/2017
3853(112*10^140357-1)/3140359Serge Batalov12/2014
3854(29*10^140337-17)/3140338Robert Price09/2019
38552^466181-112735140335Enzo Doria07/2014
3856(16*10^140290-37)/3140291Robert Price05/2021
3857(5*10^140281-119)/3140282Robert Price03/2018
385834568^11415+11415^34568140259Hans Havermann05/2021
3859(27*2^465872+1)/691140241Lelio R Paula08/2015
386033632^14781+14781^33632140236Hans Havermann05/2021
386131803^25670+25670^31803140233Hans Havermann05/2021
38622^465803-114817140221Enzo Doria05/2015
3863floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
38642^465503-112735140131Enzo Doria07/2014
3865(16*10^140091+167)/3140092Robert Price06/2019
3866(8*10^140087-137)/3140088Robert Price03/2022
38676^179964+179964^6-1140040Robert Price04/2014
3868(89*10^140008-179)/9140009Robert Price12/2019
3869(29*2^465077-1)/9140003Lelio R Paula08/2015
38702^465072-344789140001Enzo Doria07/2015
387134742^10683+10683^34742139965Hans Havermann05/2021
38725*10^139945+81139946Robert Price03/2019
387332648^19335+19335^32648139941Hans Havermann05/2021
38742^464864-17139939Lelio R Paula09/2017
38758*10^139920+51139921Robert Price08/2019
3876(85*10^139913-1)/3139915Robert Price02/2020
387731203^30436+30436^31203139896Hans Havermann04/2021
38782^464642+22189139872Enzo Doria09/2023
387926138^31663-31663^26138139865Frank Doornink03/2024
3880(16^116139+619)/5139845Anonymous08/2022
3881(2^464556+619)/5139845Eric Chen10/2023
38824*10^139839-27139840Robert Price08/2021
388333582^14573+14573^33582139821Hans Havermann05/2021
3884(17^113621+1)/18139804Paul Bourdelais09/2011
38862*10^139800-21139801Robert Price09/2020
388532628^19261+19261^32628139801Hans Havermann04/2021
3887(13*10^139782+191)/3139783Robert Price11/2018
3888(64*10^139776+791)/9139777Robert Price01/2022
3889(695*10^139772+7)/9139774Robert Price12/2021
3890(19*2^464312-1)/3139773Lelio R Paula08/2015
3891(74*10^139723+133)/9139724Robert Price06/2019
38923*10^139722+13139723Robert Price07/2018
389331577^26592+26592^31577139721Hans Havermann05/2021
389477*10^139692+3139694Robert Price06/2020
3895(31*2^463970+1)/5139670Lelio R Paula08/2015
3896(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
389739640^3321+3321^39640139584Hans Havermann05/2021
389836663^6410+6410^36663139571Hans Havermann05/2021
38992^463633-2788423139568Enzo Doria11/2015
390033659^13978+13978^33659139532Hans Havermann05/2021
390131811^24318+24318^31811139521Hans Havermann04/2021
390234149^12172+12172^34149139512Hans Havermann04/2021
3903(29*10^139476+313)/9139477Robert Price04/2021
390431721^24940+24940^31721139474Hans Havermann05/2021
390532833^17698+17698^32833139473Hans Havermann05/2021
39062^463271-109501139459Enzo Doria04/2014
3907(5*10^139457+79)/3139458Robert Price03/2018
39082^463237-99139449Lelio R Paula09/2017
3909(49*10^139442+383)/9139443Robert Price04/2019
391031155^29902+29902^31155139441Hans Havermann05/2021
3911(7*10^139417-547)/9139417Robert Price01/2018
391229636^31175-31175^29636139409Frank Doornink05/2024
3913(10^139398+191)/3139398Robert Price02/2018
391423*10^139386-3139388Robert Price10/2021
39152^463019+79463139383Enzo Doria06/2016
39163^292129-112756139381Enzo Doria07/2014
3917(15*2^462951+1)/527139361Lelio R Paula08/2015
391831922^23205+23205^31922139359Hans Havermann05/2021
3919(19*10^139336+503)/9139337Alfred Reich11/2023
39212^462855-1865707139334Enzo Doria02/2016
392031237^28876+28876^31237139334Hans Havermann05/2021
3922(86*10^139315+121)/9139316Robert Price08/2019
39232^462786-292043139313Enzo Doria08/2015
392438915^3798+3798^38915139299Hans Havermann05/2021
3926(26*10^139289+1)/9139290Serge Batalov05/2010
3925(17*10^139289+7)/3139290Robert Price06/2023
392734065^12248+12248^34065139260Hans Havermann05/2021
392836425^6654+6654^36425139256Hans Havermann05/2021
392939252^3527+3527^39252139243Hans Havermann05/2021
3930(17*10^139239+67)/3139240Robert Price01/2019
393131887^23248+23248^31887139231Hans Havermann05/2021
3932(25*10^139210-97)/9139211Robert Price01/2022
39332^462238-935139148Yves Minet02/2014
3934(29*10^139134-119)/9139135Robert Price12/2021
3935(109*10^139100-7)/3139102Robert Price03/2021
393638744^3885+3885^38744139068Hans Havermann05/2021
393731112^29499+29499^31112139065Hans Havermann05/2021
39382*10^139043-63139044Robert Price01/2022
393936390^6613+6613^36390139025Hans Havermann04/2021
394030554^30989-30989^30554138988Frank Doornink05/2024
39412*10^138975+33138976Robert Price11/2021
394242437^1882+1882^42437138966Hans Havermann05/2021
394332151^20990+20990^32151138958Hans Havermann05/2021
394432154^20933+20933^32154138933Hans Havermann04/2021
394531082^29499+29499^31082138931Hans Havermann04/2021
394630573^30962-30962^30573138876Frank Doornink05/2024
39472^461228+1870441138844Enzo Doria05/2016
39482^461204-113675138837Enzo Doria08/2014
3949(2^461139-7)/47138815Lelio R Paula08/2015
3950(17*10^138812-521)/9138813Robert Price04/2018
39513*10^138811-11138812Robert Price07/2018
395229109^31088-31088^29109138778Frank Doornink05/2024
3953(28*10^138768+173)/3138769Robert Price12/2019
3954(17*2^460963+1)/124051613138757Lelio R Paula08/2015
3955(379*10^138737-1)/9138739Robert Price02/2020
3956(43*10^138648+101)/9138649Robert Price11/2018
39572^460567-113541138645Enzo Doria08/2014
3958(10^138622+161)/9138622Robert Price09/2021
39597*10^138604+3138605Robert Price08/2015
3960(133*10^138600+17)/3138602Robert Price11/2021
396133912^12203+12203^33912138581Hans Havermann05/2021
39622^460330+69138574Lelio R Paula09/2017
3963(17*10^138569-77)/3138570Robert Price08/2019
396431186^27725+27725^31186138556Hans Havermann05/2021
3965(16*10^138545+89)/3138546Robert Price03/2021
396639753^3056+3056^39753138546Hans Havermann05/2021
396731282^26847+26847^31282138545Hans Havermann05/2021
39686*10^138520-37138521Robert Price02/2021
39702^460078-69581138498Enzo Doria12/2015
396931830^22447+22447^31830138498Hans Havermann05/2021
397137384^5065+5065^37384138492Hans Havermann05/2021
397228736^31055-31055^28736138457Frank Doornink05/2024
397334774^9585+9585^34774138456Hans Havermann05/2021
397410^138444-5001138444Robert Price12/2021
39752^459768+1531138404Lelio R Paula06/2012
3976(266*10^138328-17)/3138330Robert Price07/2020
397727200^31193-31193^27200138328Frank Doornink01/2024
397828782^31019-31019^28782138318Frank Doornink05/2024
397932963^15696+15696^32963138306Hans Havermann05/2021
39802^459343-113611138277Enzo Doria08/2014
3981(28*10^138240+113)/3138241Robert Price03/2020
39822^459199+1874393138233Enzo Doria06/2016
398333339^14002+14002^33339138230Hans Havermann05/2021
398430137^30860-30860^30137138226Frank Doornink05/2024
39852^459063-345307138192Enzo Doria06/2015
39862*10^138162-43138163Robert Price04/2018
39872^458927-112747138151Enzo Doria06/2014
39882^458927-69217138151Enzo Doria11/2015
398930907^29458+29458^30907138130Hans Havermann05/2021
399032882^15837+15837^32882138094Hans Havermann05/2021
399139252^3295+3295^39252138083Hans Havermann05/2021
399233789^12190+12190^33789138062Hans Havermann06/2021
3993555555*2^458524+1513138036Darren Bedwell08/2009
399428095^31028-31028^28095138033Frank Doornink05/2024
399530931^29002+29002^30931138028Hans Havermann05/2021
39962^458465+2^32+1138012T. D. Noe06/2007
399732206^19275+19275^32206138003Hans Havermann05/2021
39982^458321-113053137969Enzo Doria07/2014
39996^177298+323137965Riley Fisher03/2023
40002^458298+79459137962Enzo Doria06/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 22 2024 21:19 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!