PRP Records

Probable Primes Top 10000

(301668 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 ?
17515*3^514648+2^514648245551Jon Grantham08/2023
175288093#+(653879#)/(88093#)245374Makoto Morimoto11/2017
17532^815111-113857245373Enzo Doria10/2014
1754(34555^54289-1)/(34555^233-1)245334Ryan Propper11/2023
17552^814914-4001245314Yves Minet05/2017
1756846^83761-845^83761245200Jean-Louis Charton12/2012
17572^814356-2790449245146Enzo Doria12/2015
17582^814276-459029245122Enzo Doria04/2015
17592^814023+180923245046Enzo Doria07/2016
17602^813496+216751244887Enzo Doria12/2023
1761(3^513059-2^513059)/(1026119*5430216457)244776Mike Oakes03/2017
17623^513007+16244767Robert Price04/2020
1763(46^147197-31^147197)/15244752Aurel Gibier06/2024
17642^811882+27289244401Enzo Doria12/2023
17652^811842-113675244389Enzo Doria09/2014
17662^811132-2787929244176Enzo Doria11/2015
17672^809746-2790971243758Enzo Doria01/2016
1768(14*10^243724-197)/3243725Robert Price03/2023
17692^808767-3295243464Yves Minet12/2016
17702^808621-113809243420Enzo Doria09/2014
17712^808199+29693243293Enzo Doria03/2024
17722^807724+1879621243150Enzo Doria09/2016
17732^807417+217787243057Enzo Doria01/2024
1774(23*10^242909+91)/3242910Robert Price03/2023
17752^806708+20371242844Enzo Doria08/2023
17762*10^242822-91242823Robert Price02/2023
177720^186554-3242713Paul Bourdelais12/2020
17782^805843-113611242583Enzo Doria08/2014
17792^805745-459763242554Enzo Doria05/2015
17802^805353+782687242436Enzo Doria11/2016
1781(19*10^242362-7)/3242363Robert Price12/2023
17822^804895+29963242298Enzo Doria03/2024
17832^804725+28229242247Enzo Doria01/2024
17846^311257+5242206Paul Bourdelais02/2021
1785(21^242194)%(10^242194)242194Henri Lifchitz06/2025
17862^804277-417933242112Enzo Doria01/2014
17872^803468-269039241868Enzo Doria10/2013
17882^803172+80851241779Enzo Doria07/2016
17892^803011+220073241731Enzo Doria03/2024
17903^506233-2241535Robert Price11/2013
17912^802025-25999241434Enzo Doria10/2013
1792(3^505823+3^252912+1)/7241339Serge Batalov03/2014
17932^801575+25073241299Enzo Doria11/2023
17942^801303+1872923241217Enzo Doria05/2016
17952^801105+216977241157Enzo Doria12/2023
1796(23*10^241048-143)/3241049Robert Price12/2023
17972^800579-1862947240999Enzo Doria12/2015
17982^799999+16205240824Norman Luhn09/2023
17993^504206+2240568Luke W. Richards03/2018
18002^798973-26283240515Enzo Doria10/2013
18012^798671-69487240424Enzo Doria12/2015
18022^797220+79831239988Enzo Doria06/2016
18032^796910-26001239894Enzo Doria10/2013
1804(97^120721-1)/811245216239837Paul Vanderveen06/2025
18052^796598+653119239800Enzo Doria12/2016
18062^796432-1859729239750Enzo Doria11/2015
18072^796002-1852211239621Enzo Doria08/2015
18082^795884+214081239585Enzo Doria10/2023
18092^795709+75767239533Enzo Doria04/2016
18102^795708+81721239532Enzo Doria08/2016
18112^795468-2786249239460Enzo Doria10/2015
18122^795442+80779239452Enzo Doria07/2016
18132^795075-1852057239342Enzo Doria08/2015
1814(86^123677+1)/87239252Paul Bourdelais01/2019
18152^794043+1875023239031Enzo Doria06/2016
18162^793347-69577238822Enzo Doria01/2016
18175*2^793288+3238805Jon Grantham07/2023
18182^792988-344429238714Enzo Doria08/2015
18192^792700-2786369238627Enzo Doria11/2015
18202^792663-1844797238616Enzo Doria06/2015
18212^792605-291943238598Enzo Doria07/2015
18222^792366+218599238526Enzo Doria01/2024
1823(2^792061-2^396031+1)/5238434Thomas Ritschel03/2014
18242^791321+30077238212Enzo Doria03/2024
18254*10^238163+21238164Robert Price12/2022
1826(26*10^238157-77)/3238158Robert Price03/2023
182710^237670+9237671Robert Price08/2023
18282^789373+1869377237625Enzo Doria05/2016
1829((10^59387+1)^3*(10^59387+1+10^29694)-(10^118774+10^59387)*(10^29694-1)+10^178161)/27961237544Serge Batalov04/2015
1830Phi(1187740M,10)237544Anonymous03/2025
18312^789033+218537237523Enzo Doria01/2024
18322^788942+1866409237496Enzo Doria02/2016
18332^788844-114329237466Enzo Doria01/2015
18342^788705-1859713237424Enzo Doria11/2015
18352^788325+224789237310Enzo Doria07/2024
183615^201475+14236953Alfred Reich10/2023
18372^786663+219173236810Enzo Doria02/2024
18382^786180+1871971236664Enzo Doria05/2016
183911^227092-90236492Enzo Doria11/2012
18402^785260+1866361236387Enzo Doria02/2016
18412^785220+1880611236375Enzo Doria10/2016
1842(2^784689-15)/7236215Stefano Morozzi08/2022
184319^184650-2236122Robert Price10/2014
184410^236059+216513236060Patrick De Geest04/2016
184510^236059-20909236059Robert Price09/2015
18462^783988+38011236004Enzo Doria10/2024
18472^783893-21235976Stefano Morozzi07/2022
1848(47^140983-1)/2792206142311142462235719Paul Vanderveen06/2025
18492^782821+37577235653Enzo Doria10/2024
1850(87^121487-1)/86235625Paul Bourdelais12/2018
18512^782634-113981235597Enzo Doria11/2014
18522^782423+1879733235533Enzo Doria09/2016
1853(10^(2*117707+1)+12*10^117707-1)/3235415Robert Price10/2023
1854(2^781970)/(781970^2)235385Henri Lifchitz06/2025
18552^781682-2789543235310Enzo Doria12/2015
18562^780481+21489234949Enzo Doria05/2024
18572^780408-113453234927Enzo Doria08/2014
18587*10^234915+9234916Robert Price04/2023
18592^780368-1864829234915Enzo Doria01/2016
18602^780284+7234889Jon Grantham08/2023
18612^779593-1836559234681Enzo Doria05/2015
1862(8713#+(549391#)/(8713#))/360295171234487Makoto Morimoto11/2017
1863(5^335429+1)/6234455Paul Bourdelais08/2010
18642^778788+22201234439Enzo Doria09/2023
18652^778395-113617234321Enzo Doria08/2014
18665*2^778090+3234230Jon Grantham07/2023
1867(21430^54289-1)/(21430^233-1)234118Ryan Propper11/2023
1868(5*10^234054-101)/3234055Robert Price08/2023
186923*10^234025-7234027Robert Price10/2022
18702^777170+21489233952Enzo Doria05/2024
1871Phi(78125,5517)233857Anonymous09/2022
18725^334359-3^334359-1233707Jon Grantham08/2023
18732^776245-2792353233674Enzo Doria02/2016
187449748^49748+49735^49735233656Henri Lifchitz11/2024
18752^776060-114029233618Enzo Doria11/2014
18762^775987-2789557233596Enzo Doria12/2015
18772*10^233564-91233565Robert Price02/2023
18782^775865+21489233559Enzo Doria05/2024
18792^775672+1866721233501Enzo Doria03/2016
18802^775238+57233370Stefano Morozzi05/2021
1881(11^223999+1)/12233270Paul Bourdelais02/2010
1882U(1302049)233238Serge Batalov07/2024
18832^774118+1885789233033Enzo Doria04/2017
188421^176191-20^176191232964Jean-Louis Charton01/2015
18852^773723+217523232914Enzo Doria01/2024
18862^773679-113425232901Enzo Doria08/2014
1887(7*10^232620+23)/3232621Robert Price05/2023
188810^232599+192489232600Patrick De Geest12/2013
188910^232599-3232599Markus Tervooren10/2010
18902^772552-458879232562Enzo Doria04/2015
18912^772214+1874899232460Enzo Doria06/2016
18922^771994-1862771232394Enzo Doria12/2015
18932^771889+1876037232362Enzo Doria07/2016
18942^771660+1866511232293Enzo Doria02/2016
18955^332150-18188232163Enzo Doria06/2014
18962^771227+61121232163Boyan Hu05/2024
18972^770623+212543231981Enzo Doria09/2023
18983^485977-2^485977231870Mike Oakes09/2009
18992^770082-114161231818Enzo Doria01/2015
19002^769791+25523231731Enzo Doria11/2023
19017^274120-2231659Paul Bourdelais08/2023
1902(20^177967+1)/21231540Paul Bourdelais05/2013
19032^769011+81231496Henri Lifchitz01/2025
1904(71^125029-1)/105024430231453Paul Vanderveen06/2025
1905(4*10^231254+23)/9231254Serge Batalov11/2022
19062^768205+22217231253Enzo Doria09/2023
190749262^49262-49247^49247231163Henri Lifchitz11/2024
19082^767622-9221231078Lelio R Paula01/2016
19092^767344+1880311230994Enzo Doria09/2016
19108*10^230921-13230922Robert Price08/2023
1911(3^483611-1)/2230741Paul Bourdelais02/2010
1912(10^230706+179)/9230706Serge Batalov12/2014
19132^766309+1875257230682Enzo Doria06/2016
1914(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
19152^765635+1879883230480Enzo Doria09/2016
191643^141090+141090230467Kellen Shenton06/2023
1917(26*10^230394-119)/3230395Robert Price07/2023
19182^764348-113697230092Enzo Doria09/2014
19192^764131+78863230027Enzo Doria05/2016
19202^763701+60197229897Enzo Doria03/2016
19214*10^229836+21229837Robert Price12/2022
19222^763362+27799229795Enzo Doria01/2024
19232^762841-25905229639Enzo Doria10/2013
19242^762659+212633229584Enzo Doria09/2023
192577*10^229211+3229213Robert Price11/2023
19262^761117-113569229120Enzo Doria08/2014
1927(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1928(98^114859+1)/99228709Paul Bourdelais12/2018
19295*3^479067-2^479067228574Jon Grantham08/2023
19302^758645+216011228375Enzo Doria12/2023
1931(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
193210^228208+111228209Boyan Hu10/2024
1933(298*10^228177-7)/3228179Robert Price02/2023
19342^757985-2790013228177Enzo Doria12/2015
193534*10^228129-9228131Robert Price05/2023
19362^757038-1862081227892Enzo Doria12/2015
19372^756839+95849227832Makoto Morimoto10/2013
1939(2^756839+6989)/756091227826Makoto Morimoto09/2016
1938(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
19402^756773-112723227812Enzo Doria07/2014
1941(7*10^(2*113887+1)+9*10^113887-7)/9227775Robert Price08/2024
1942(10^227542)/(227542^10)227489Henri Lifchitz05/2025
1943524309#+616367227431Makoto Morimoto02/2016
19442^755404+226575227400Enzo Doria09/2024
19452^755116+81227313Henri Lifchitz11/2024
19462^755097-114193227307Enzo Doria12/2014
19477*10^227178+39227179Robert Price01/2023
19489*10^227153-89227154Robert Price02/2023
19492^754473-2791513227120Enzo Doria01/2016
19502^754376+25227090Stefano Morozzi05/2021
19512^754138+213289227019Enzo Doria09/2023
19522^754038+25226989Stefano Morozzi05/2021
19532^753263+217133226755Enzo Doria12/2023
19547*10^226479-9226480Robert Price02/2023
1955(10^226381+1)/14973418875371226368Alfred Reich06/2025
19562^751655+33893226271Enzo Doria06/2024
19572^751426-764321226202Enzo Doria12/2013
1958(18^180181-1)/17226176Andy Steward04/2007
19592^750740-3225996Paul Bourdelais03/2012
19602^750725+60227225991Enzo Doria02/2016
19612^750525-113743225931Enzo Doria09/2014
1962(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
19632^749444-1861889225606Enzo Doria12/2015
1964tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
1965(3^472721+1)/9422189991086734893916225524Paul Vanderveen06/2025
19662^749096+1876861225501Enzo Doria07/2016
19672^748895+26213225440Enzo Doria12/2023
1968(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
19692^748657+79607225369Enzo Doria06/2016
1970(2^746920-11)/5224845Stefano Morozzi08/2022
19712^746653-291583224765Enzo Doria07/2015
19722^746461-114043224708Enzo Doria11/2014
19732^746302+25224660Stefano Morozzi05/2021
1974(202*10^224545-1)/3224547Robert Price06/2023
1975(19*10^224533-37)/9224534Alfred Reich12/2023
19762^745674+213949224471Enzo Doria10/2023
19772^745098-350471224297Enzo Doria06/2015
19782^745039-4897224280Yves Minet03/2021
197923*10^224232-7224234Robert Price10/2022
1980(154*10^224061-1)/9224063Serge Batalov12/2014
19812^744211-1845787224030Enzo Doria07/2015
19822^743773+37757223898Enzo Doria10/2024
19832^743592-134579223844Hans Havermann10/2018
19842^742452+3223501Paul Bourdelais06/2019
1985234178^9+9^234178223463Anatoly F. Selevich07/2011
198647747^47747-2512^2512223406Henri Lifchitz10/2024
19872^741651-461197223260Enzo Doria07/2015
198810^223236-1001223236Robert Price10/2022
19892^741362-1845251223173Enzo Doria07/2015
19903^467546-5*2^467546223077Jon Grantham08/2023
19912^740455-1863877222900Enzo Doria12/2015
19922^740274+217519222845Enzo Doria01/2024
1993(14*10^222718-41)/9222719Serge Batalov01/2023
19942^739636-2792219222653Enzo Doria02/2016
199511^213654-180222498Enzo Doria01/2013
19962^738957-1859743222449Enzo Doria11/2015
19974*10^222253-21222254Robert Price12/2022
19982^737825+57222108Stefano Morozzi05/2021
1999(54^128189+1)/55222073Paul Bourdelais11/2018
20003^232689+1^232689+4^232689+1^232689+5^232689+9^232689222042Henri Lifchitz03/2025


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2025 15:18 (Time in France)

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