PRP Records

Probable Primes Top 10000

(301723 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 ?
17512^822296+76501247536Enzo Doria05/2016
17522^821590-114167247324Enzo Doria12/2014
17532^821512-2790659247300Enzo Doria12/2015
1754(21996^57121-1)/(21996^239-1)247002Ryan Propper11/2023
17552^820356+7246952Jon Grantham08/2023
17562^820077+382847246868Enzo Doria11/2016
17572^820008+81246848Henri Lifchitz01/2025
17582^820001+81269246845Enzo Doria07/2016
17592^819463-59197246683Enzo Doria10/2015
17602^819296+80581246633Enzo Doria07/2016
17612^818764+21573246473Enzo Doria11/2023
17622^817852+215491246198Enzo Doria11/2023
17632^817160-350369245990Enzo Doria06/2015
17642^816039-19245653Stefano Morozzi07/2022
17652^816029+219407245650Enzo Doria02/2024
1766(71*10^245558-17)/9245559Serge Batalov01/2023
17675*3^514648+2^514648245551Jon Grantham08/2023
176888093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
17692^815111-113857245373Enzo Doria10/2014
1770(34555^54289-1)/(34555^233-1)245334Ryan Propper11/2023
17712^814914-4001245314Yves Minet05/2017
1772846^83761-845^83761245200Jean-Louis Charton12/2012
17732^814356-2790449245146Enzo Doria12/2015
17742^814276-459029245122Enzo Doria04/2015
17752^814023+180923245046Enzo Doria07/2016
17762^813496+216751244887Enzo Doria12/2023
1777(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
17783^513007+16244767Robert Price04/2020
1779(46^147197-31^147197)/15244752Aurel Gibier06/2024
17802^811882+27289244401Enzo Doria12/2023
17812^811842-113675244389Enzo Doria09/2014
17822^811132-2787929244176Enzo Doria11/2015
17832^809746-2790971243758Enzo Doria01/2016
1784(14*10^243724-197)/3243725Robert Price03/2023
17852^808767-3295243464Yves Minet12/2016
17862^808621-113809243420Enzo Doria09/2014
17872^808199+29693243293Enzo Doria03/2024
17882^807724+1879621243150Enzo Doria09/2016
17892^807417+217787243057Enzo Doria01/2024
1790(23*10^242909+91)/3242910Robert Price03/2023
17912^806708+20371242844Enzo Doria08/2023
17922*10^242822-91242823Robert Price02/2023
179320^186554-3242713Paul Bourdelais12/2020
17942^805843-113611242583Enzo Doria08/2014
17952^805745-459763242554Enzo Doria05/2015
17962^805353+782687242436Enzo Doria11/2016
1797(19*10^242362-7)/3242363Robert Price12/2023
17982^804895+29963242298Enzo Doria03/2024
17992^804725+28229242247Enzo Doria01/2024
18006^311257+5242206Paul Bourdelais02/2021
1801(21^242194)%(10^242194)242194Henri Lifchitz06/2025
18022^804277-417933242112Enzo Doria01/2014
18032^803468-269039241868Enzo Doria10/2013
18042^803172+80851241779Enzo Doria07/2016
18052^803011+220073241731Enzo Doria03/2024
18063^506233-2241535Robert Price11/2013
18072^802025-25999241434Enzo Doria10/2013
1808(3^505823+3^252912+1)/7241339Serge Batalov03/2014
18092^801575+25073241299Enzo Doria11/2023
18102^801303+1872923241217Enzo Doria05/2016
18112^801105+216977241157Enzo Doria12/2023
1812(23*10^241048-143)/3241049Robert Price12/2023
18132^800579-1862947240999Enzo Doria12/2015
18142^799999+16205240824Norman Luhn09/2023
18153^504206+2240568Luke W. Richards03/2018
18162^798973-26283240515Enzo Doria10/2013
18172^798671-69487240424Enzo Doria12/2015
18182^797220+79831239988Enzo Doria06/2016
18192^796910-26001239894Enzo Doria10/2013
1820(97^120721-1)/811245216239837Paul Vanderveen06/2025
18212^796598+653119239800Enzo Doria12/2016
18222^796432-1859729239750Enzo Doria11/2015
18232^796002-1852211239621Enzo Doria08/2015
18242^795884+214081239585Enzo Doria10/2023
18252^795709+75767239533Enzo Doria04/2016
18262^795708+81721239532Enzo Doria08/2016
18272^795468-2786249239460Enzo Doria10/2015
18282^795442+80779239452Enzo Doria07/2016
18292^795075-1852057239342Enzo Doria08/2015
1830(86^123677+1)/87239252Paul Bourdelais01/2019
18312^794043+1875023239031Enzo Doria06/2016
18322^793347-69577238822Enzo Doria01/2016
18335*2^793288+3238805Jon Grantham07/2023
18342^792988-344429238714Enzo Doria08/2015
18352^792700-2786369238627Enzo Doria11/2015
18362^792663-1844797238616Enzo Doria06/2015
18372^792605-291943238598Enzo Doria07/2015
18382^792366+218599238526Enzo Doria01/2024
1839(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
18402^791321+30077238212Enzo Doria03/2024
18414*10^238163+21238164Robert Price12/2022
1842(26*10^238157-77)/3238158Robert Price03/2023
184310^237670+9237671Robert Price08/2023
18442^789373+1869377237625Enzo Doria05/2016
1845((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
1846Phi(1187740M,10)237544Anonymous03/2025
18472^789033+218537237523Enzo Doria01/2024
18482^788942+1866409237496Enzo Doria02/2016
18492^788844-114329237466Enzo Doria01/2015
18502^788705-1859713237424Enzo Doria11/2015
18512^788325+224789237310Enzo Doria07/2024
185215^201475+14236953Alfred Reich10/2023
18532^786663+219173236810Enzo Doria02/2024
18542^786180+1871971236664Enzo Doria05/2016
185511^227092-90236492Enzo Doria11/2012
18562^785260+1866361236387Enzo Doria02/2016
18572^785220+1880611236375Enzo Doria10/2016
1858(2^784689-15)/7236215Stefano Morozzi08/2022
185919^184650-2236122Robert Price10/2014
186010^236059+216513236060Patrick De Geest04/2016
186110^236059-20909236059Robert Price09/2015
18622^783988+38011236004Enzo Doria10/2024
18632^783893-21235976Stefano Morozzi07/2022
1864(47^140983-1)/2792206142311142462235719Paul Vanderveen06/2025
18652^782821+37577235653Enzo Doria10/2024
1866(87^121487-1)/86235625Paul Bourdelais12/2018
18672^782634-113981235597Enzo Doria11/2014
18682^782423+1879733235533Enzo Doria09/2016
1869(10^(2*117707+1)+12*10^117707-1)/3235415Robert Price10/2023
1870(2^781970)/(781970^2)235385Henri Lifchitz06/2025
18712^781682-2789543235310Enzo Doria12/2015
18722^780481+21489234949Enzo Doria05/2024
18732^780408-113453234927Enzo Doria08/2014
18747*10^234915+9234916Robert Price04/2023
18752^780368-1864829234915Enzo Doria01/2016
18762^780284+7234889Jon Grantham08/2023
18772^779593-1836559234681Enzo Doria05/2015
1878(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1879(5^335429+1)/6234455Paul Bourdelais08/2010
18802^778788+22201234439Enzo Doria09/2023
18812^778395-113617234321Enzo Doria08/2014
18825*2^778090+3234230Jon Grantham07/2023
1883(21430^54289-1)/(21430^233-1)234118Ryan Propper11/2023
1884(5*10^234054-101)/3234055Robert Price08/2023
188523*10^234025-7234027Robert Price10/2022
18862^777170+21489233952Enzo Doria05/2024
1887Phi(78125,5517)233857Anonymous09/2022
18885^334359-3^334359-1233707Jon Grantham08/2023
18892^776245-2792353233674Enzo Doria02/2016
189049748^49748+49735^49735233656Henri Lifchitz11/2024
18912^776060-114029233618Enzo Doria11/2014
18922^775987-2789557233596Enzo Doria12/2015
18932*10^233564-91233565Robert Price02/2023
18942^775865+21489233559Enzo Doria05/2024
18952^775672+1866721233501Enzo Doria03/2016
18962^775238+57233370Stefano Morozzi05/2021
1897(11^223999+1)/12233270Paul Bourdelais02/2010
1898U(1302049)233238Serge Batalov07/2024
18992^774118+1885789233033Enzo Doria04/2017
190021^176191-20^176191232964Jean-Louis Charton01/2015
19012^773723+217523232914Enzo Doria01/2024
19022^773679-113425232901Enzo Doria08/2014
1903(7*10^232620+23)/3232621Robert Price05/2023
190410^232599+192489232600Patrick De Geest12/2013
190510^232599-3232599Markus Tervooren10/2010
19062^772552-458879232562Enzo Doria04/2015
19072^772214+1874899232460Enzo Doria06/2016
19082^771994-1862771232394Enzo Doria12/2015
19092^771889+1876037232362Enzo Doria07/2016
19102^771660+1866511232293Enzo Doria02/2016
19115^332150-18188232163Enzo Doria06/2014
19122^771227+61121232163Boyan Hu05/2024
19132^770623+212543231981Enzo Doria09/2023
19143^485977-2^485977231870Mike Oakes09/2009
19152^770082-114161231818Enzo Doria01/2015
19162^769791+25523231731Enzo Doria11/2023
19177^274120-2231659Paul Bourdelais08/2023
1918(20^177967+1)/21231540Paul Bourdelais05/2013
19192^769011+81231496Henri Lifchitz01/2025
1920(71^125029-1)/105024430231453Paul Vanderveen06/2025
1921(4*10^231254+23)/9231254Serge Batalov11/2022
19222^768205+22217231253Enzo Doria09/2023
192349262^49262-49247^49247231163Henri Lifchitz11/2024
19242^767622-9221231078Lelio R Paula01/2016
19252^767344+1880311230994Enzo Doria09/2016
19268*10^230921-13230922Robert Price08/2023
1927(3^483611-1)/2230741Paul Bourdelais02/2010
1928(10^230706+179)/9230706Serge Batalov12/2014
19292^766309+1875257230682Enzo Doria06/2016
1930(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
19312^765635+1879883230480Enzo Doria09/2016
193243^141090+141090230467Kellen Shenton06/2023
1933(26*10^230394-119)/3230395Robert Price07/2023
19342^764348-113697230092Enzo Doria09/2014
19352^764131+78863230027Enzo Doria05/2016
19362^763701+60197229897Enzo Doria03/2016
19374*10^229836+21229837Robert Price12/2022
19382^763362+27799229795Enzo Doria01/2024
19392^762841-25905229639Enzo Doria10/2013
19402^762659+212633229584Enzo Doria09/2023
194177*10^229211+3229213Robert Price11/2023
19422^761117-113569229120Enzo Doria08/2014
1943(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1944(98^114859+1)/99228709Paul Bourdelais12/2018
19455*3^479067-2^479067228574Jon Grantham08/2023
19462^758645+216011228375Enzo Doria12/2023
1947(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
194810^228208+111228209Boyan Hu10/2024
1949(298*10^228177-7)/3228179Robert Price02/2023
19502^757985-2790013228177Enzo Doria12/2015
195134*10^228129-9228131Robert Price05/2023
19522^757038-1862081227892Enzo Doria12/2015
19532^756839+95849227832Makoto Morimoto10/2013
1954(2^756839+6989)/756091227826Makoto Morimoto09/2016
1955(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
19562^756773-112723227812Enzo Doria07/2014
1957(7*10^(2*113887+1)+9*10^113887-7)/9227775Robert Price08/2024
1958(10^227542)/(227542^10)227489Henri Lifchitz05/2025
1959524309#+616367227431Makoto Morimoto02/2016
19602^755404+226575227400Enzo Doria09/2024
19612^755116+81227313Henri Lifchitz11/2024
19622^755097-114193227307Enzo Doria12/2014
19637*10^227178+39227179Robert Price01/2023
19649*10^227153-89227154Robert Price02/2023
19652^754473-2791513227120Enzo Doria01/2016
19662^754376+25227090Stefano Morozzi05/2021
19672^754138+213289227019Enzo Doria09/2023
19682^754038+25226989Stefano Morozzi05/2021
19692^753263+217133226755Enzo Doria12/2023
19707*10^226479-9226480Robert Price02/2023
1971(10^226381+1)/14973418875371226368Alfred Reich06/2025
19722^751655+33893226271Enzo Doria06/2024
19732^751426-764321226202Enzo Doria12/2013
1974(18^180181-1)/17226176Andy Steward04/2007
19752^750740-3225996Paul Bourdelais03/2012
19762^750725+60227225991Enzo Doria02/2016
19772^750525-113743225931Enzo Doria09/2014
1978(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
19792^749444-1861889225606Enzo Doria12/2015
1980tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
1981(3^472721+1)/9422189991086734893916225524Paul Vanderveen06/2025
19822^749096+1876861225501Enzo Doria07/2016
19832^748895+26213225440Enzo Doria12/2023
1984(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
19852^748657+79607225369Enzo Doria06/2016
1986(2^746920-11)/5224845Stefano Morozzi08/2022
19872^746653-291583224765Enzo Doria07/2015
19882^746461-114043224708Enzo Doria11/2014
19892^746302+25224660Stefano Morozzi05/2021
1990(202*10^224545-1)/3224547Robert Price06/2023
1991(19*10^224533-37)/9224534Alfred Reich12/2023
19922^745674+213949224471Enzo Doria10/2023
19932^745098-350471224297Enzo Doria06/2015
19942^745039-4897224280Yves Minet03/2021
199523*10^224232-7224234Robert Price10/2022
1996(154*10^224061-1)/9224063Serge Batalov12/2014
19972^744211-1845787224030Enzo Doria07/2015
19982^743773+37757223898Enzo Doria10/2024
19992^743592-134579223844Hans Havermann10/2018
20002^742452+3223501Paul Bourdelais06/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 10 2025 14:11 (Time in France)

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