PRP Records

Probable Primes Top 10000

(300940 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 ?
17512^775865+21489233559Enzo Doria05/2024
17522^775672+1866721233501Enzo Doria03/2016
17532^775238+57233370Stefano Morozzi05/2021
1754(11^223999+1)/12233270Paul Bourdelais02/2010
1755U(1302049)233238Serge Batalov07/2024
17562^774118+1885789233033Enzo Doria04/2017
175721^176191-20^176191232964Jean-Louis Charton01/2015
17582^773723+217523232914Enzo Doria01/2024
17592^773679-113425232901Enzo Doria08/2014
1760(7*10^232620+23)/3232621Robert Price05/2023
176110^232599+192489232600Patrick De Geest12/2013
176210^232599-3232599Markus Tervooren10/2010
17632^772552-458879232562Enzo Doria04/2015
17642^772214+1874899232460Enzo Doria06/2016
17652^771994-1862771232394Enzo Doria12/2015
17662^771889+1876037232362Enzo Doria07/2016
17672^771660+1866511232293Enzo Doria02/2016
17685^332150-18188232163Enzo Doria06/2014
17692^771227+61121232163Boyan Hu05/2024
17702^770623+212543231981Enzo Doria09/2023
17713^485977-2^485977231870Mike Oakes09/2009
17722^770082-114161231818Enzo Doria01/2015
17732^769791+25523231731Enzo Doria11/2023
17747^274120-2231659Paul Bourdelais08/2023
1775(20^177967+1)/21231540Paul Bourdelais05/2013
17762^769011+81231496Henri Lifchitz01/2025
1777(4*10^231254+23)/9231254Serge Batalov11/2022
17782^768205+22217231253Enzo Doria09/2023
177949262^49262-49247^49247231163Henri Lifchitz11/2024
17802^767622-9221231078Lelio R Paula01/2016
17812^767344+1880311230994Enzo Doria09/2016
17828*10^230921-13230922Robert Price08/2023
1783(3^483611-1)/2230741Paul Bourdelais02/2010
1784(10^230706+179)/9230706Serge Batalov12/2014
17852^766309+1875257230682Enzo Doria06/2016
1786(26131^52441-1)/(26131^229-1)230629Ryan Propper11/2023
17872^765635+1879883230480Enzo Doria09/2016
178843^141090+141090230467Kellen Shenton06/2023
1789(26*10^230394-119)/3230395Robert Price07/2023
17902^764348-113697230092Enzo Doria09/2014
17912^764131+78863230027Enzo Doria05/2016
17922^763701+60197229897Enzo Doria03/2016
17934*10^229836+21229837Robert Price12/2022
17942^763362+27799229795Enzo Doria01/2024
17952^762841-25905229639Enzo Doria10/2013
17962^762659+212633229584Enzo Doria09/2023
179777*10^229211+3229213Robert Price11/2023
17982^761117-113569229120Enzo Doria08/2014
1799(29022^51529-1)/(29022^227-1)228947Ryan Propper11/2023
1800(98^114859+1)/99228709Paul Bourdelais12/2018
18015*3^479067-2^479067228574Jon Grantham08/2023
18022^758645+216011228375Enzo Doria12/2023
1803(2^758231+1)/(3*27146942976539*73236839266867)228223Gord Palameta12/2018
180410^228208+111228209Boyan Hu10/2024
1805(298*10^228177-7)/3228179Robert Price02/2023
18062^757985-2790013228177Enzo Doria12/2015
180734*10^228129-9228131Robert Price05/2023
18082^757038-1862081227892Enzo Doria12/2015
18092^756839+95849227832Makoto Morimoto10/2013
1811(2^756839+6989)/756091227826Makoto Morimoto09/2016
1810(2^756839-50211)/(137*3203)227826Makoto Morimoto08/2019
18122^756773-112723227812Enzo Doria07/2014
1813(7*10^(2*113887+1)+9*10^113887-7)/9227775Robert Price08/2024
1814524309#+616367227431Makoto Morimoto02/2016
18152^755404+226575227400Enzo Doria09/2024
18162^755116+81227313Henri Lifchitz11/2024
18172^755097-114193227307Enzo Doria12/2014
18187*10^227178+39227179Robert Price01/2023
18199*10^227153-89227154Robert Price02/2023
18202^754473-2791513227120Enzo Doria01/2016
18212^754376+25227090Stefano Morozzi05/2021
18222^754138+213289227019Enzo Doria09/2023
18232^754038+25226989Stefano Morozzi05/2021
18242^753263+217133226755Enzo Doria12/2023
18257*10^226479-9226480Robert Price02/2023
18262^751655+33893226271Enzo Doria06/2024
18272^751426-764321226202Enzo Doria12/2013
1828(18^180181-1)/17226176Andy Steward04/2007
18292^750740-3225996Paul Bourdelais03/2012
18302^750725+60227225991Enzo Doria02/2016
18312^750525-113743225931Enzo Doria09/2014
1832(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
18332^749444-1861889225606Enzo Doria12/2015
1834tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
18352^749096+1876861225501Enzo Doria07/2016
18362^748895+26213225440Enzo Doria12/2023
1837(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
18382^748657+79607225369Enzo Doria06/2016
1839(2^746920-11)/5224845Stefano Morozzi08/2022
18402^746653-291583224765Enzo Doria07/2015
18412^746461-114043224708Enzo Doria11/2014
18422^746302+25224660Stefano Morozzi05/2021
1843(202*10^224545-1)/3224547Robert Price06/2023
1844(19*10^224533-37)/9224534Alfred Reich12/2023
18452^745674+213949224471Enzo Doria10/2023
18462^745098-350471224297Enzo Doria06/2015
18472^745039-4897224280Yves Minet03/2021
184823*10^224232-7224234Robert Price10/2022
1849(154*10^224061-1)/9224063Serge Batalov12/2014
18502^744211-1845787224030Enzo Doria07/2015
18512^743773+37757223898Enzo Doria10/2024
18522^743592-134579223844Hans Havermann10/2018
18532^742452+3223501Paul Bourdelais06/2019
1854234178^9+9^234178223463Anatoly F. Selevich07/2011
185547747^47747-2512^2512223406Henri Lifchitz10/2024
18562^741651-461197223260Enzo Doria07/2015
185710^223236-1001223236Robert Price10/2022
18582^741362-1845251223173Enzo Doria07/2015
18593^467546-5*2^467546223077Jon Grantham08/2023
18602^740455-1863877222900Enzo Doria12/2015
18612^740274+217519222845Enzo Doria01/2024
1862(14*10^222718-41)/9222719Serge Batalov01/2023
18632^739636-2792219222653Enzo Doria02/2016
186411^213654-180222498Enzo Doria01/2013
18652^738957-1859743222449Enzo Doria11/2015
18664*10^222253-21222254Robert Price12/2022
18672^737825+57222108Stefano Morozzi05/2021
1868(54^128189+1)/55222073Paul Bourdelais11/2018
18692^737166+220099221910Enzo Doria03/2024
1870(10^221654+179)/9221654Serge Batalov12/2014
18712^736281+79817221643Enzo Doria06/2016
187210^221631+247617221632Patrick De Geest10/2013
187310^221631-9221631Alexander Gramolin02/2011
187410^221628+7221629Alfred Reich04/2021
18752^735970-1839821221550Enzo Doria06/2015
18762^735367+60293221368Enzo Doria03/2016
187777*10^221343+3221345Robert Price11/2023
1878(241^92821-1)/240221099Anonymous04/2024
1879(202*10^221092-1)/3221094Robert Price06/2023
1880(29^151153+1)/30221045Paul Bourdelais09/2017
18812^734228+24751221025Enzo Doria10/2023
1882(28*10^220800+173)/3220801Robert Price07/2024
18832^733264-2784089220735Enzo Doria10/2015
18842^733114-24555220690Enzo Doria09/2013
18852^731891-636259220322Enzo Doria12/2013
188698*10^220185-9220187Robert Price05/2023
1887418319^39164+418318220161Alfred Reich11/2023
18882^731124-25539220091Enzo Doria09/2013
18892^730972-462029220045Enzo Doria07/2015
18902^730833+1868627220003Enzo Doria04/2016
18912^730645-2787133219947Enzo Doria11/2015
18922^730547-25581219917Enzo Doria09/2013
1893(113*13^197420-5)/12219916Anonymous11/2022
1894(13^197420*113-5)/12219916Eric Chen10/2023
18952^730460+82291219891Enzo Doria09/2016
1896(5*10^219847-101)/3219848Robert Price08/2023
1897(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
1898L(1051849)219824Renaud Lifchitz03/2009
18993*2^730149+5219798Jon Grantham07/2023
19008*10^219740-3219741Serge Batalov01/2023
190111^210961-240219694Enzo Doria01/2013
1902(26*10^219639-77)/3219640Robert Price03/2023
19032^729611-113437219635Enzo Doria08/2014
19047^259710-2219481Paul Bourdelais01/2021
1905F(1049897)219416Henri Lifchitz10/2008
1906(1488^69151-1)/1487219386Alexander Zhirkov02/2023
19072^728604+1879321219332Enzo Doria10/2016
190833^144412+2219292Robert Price04/2015
19092^728277-183313219234Hans Havermann10/2018
19102^727998-1862711219150Enzo Doria12/2015
1911(29*10^219124+91)/3219125Robert Price12/2022
19122^727729-114073219069Enzo Doria12/2014
19132^727496-1851809218999Enzo Doria08/2015
19142^727025+25907218857Enzo Doria12/2023
19152^726591+2793143218726Enzo Doria02/2016
1916(7*10^218644+17)/3218645Robert Price06/2023
19172^725534-2791931218408Enzo Doria02/2016
1918Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
19192^722184+1877821217400Enzo Doria08/2016
1920(109*10^217360-1)/9217362Serge Batalov12/2014
19212^721721-4453217260Yves Minet03/2021
192210^216950+49216951Robert Price02/2023
1923281*499979#/46410-2702372216849Robert Smith08/2016
1924281*499979#/46410+2400766216849Robert Smith08/2016
1925tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
19262^718756-114107216368Enzo Doria12/2014
19272^717672+121216041Stefano Morozzi05/2021
19282^717305+80327215931Enzo Doria07/2016
19292^717069-59773215860Enzo Doria10/2015
193010^215802+33215803Robert Price08/2023
193130^146021-29^146021215691Jean-Louis Charton09/2018
1932277^88301-276^88301215674Jean-Louis Charton06/2012
19332^716428+215011215667Enzo Doria11/2023
1934(13*10^215592-43)/3215593Robert Price08/2023
1935p(41292)#+p(41292+1)215450Henri Lifchitz11/2024
1936227^91413-40215372Enzo Doria04/2015
1937(2^715008-21)/5215239Stefano Morozzi08/2022
19382^714717+782897215152Enzo Doria11/2016
1939tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
19402^713241+1879157214707Enzo Doria08/2016
1941(23*10^214633+91)/3214634Robert Price03/2023
194211^206081-10^206081214612Jean-Louis Charton10/2011
19432^712801-69553214575Enzo Doria01/2016
19442^712603-25357214515Enzo Doria09/2013
19452^711721-1846723214250Enzo Doria07/2015
19462^710730-396765213952Enzo Doria09/2013
1947(19*10^213934-37)/9213935Alfred Reich12/2023
1948(19*10^213730-37)/9213731Alfred Reich12/2023
1949(713^74897-1)/712213685Jinyuan Wang08/2023
19502^709773+25907213663Enzo Doria12/2023
19512^708468-114329213271Enzo Doria02/2015
19522^708293+27557213218Enzo Doria01/2024
1953379*10^213199+9213202Jason Yuen01/2025
19542^707277+28997212912Enzo Doria02/2024
1955(163*10^212779-1)/9212781Serge Batalov12/2014
19562^706838-69041212780Enzo Doria11/2015
19572^705653+25907212423Enzo Doria12/2023
195822*10^212339+7212341Robert Price10/2022
19592^704577-113871212099Enzo Doria10/2014
1960(2^704548-19)/3212090Stefano Morozzi08/2022
19612^704110-2792441211959Enzo Doria02/2016
19622^704084+28531211951Enzo Doria02/2024
19632^703943-1862947211908Enzo Doria12/2015
1964(60^119083+1)/61211746Paul Bourdelais10/2018
1965(184*10^211682-1)/3211684Robert Price12/2022
1966(10^211610-91)/9211610Serge Batalov12/2014
1967227^89797+2211565Lelio R Paula08/2012
19682^702194-3211382Paul Bourdelais03/2012
19692^702064+1874911211343Enzo Doria07/2016
19702^701968-113873211314Enzo Doria10/2014
1971(14*10^211262-41)/9211263Serge Batalov01/2023
19722^701713-113779211237Enzo Doria09/2014
19732^701616-216803211208Enzo Doria01/2024
19742^701449-25201211158Enzo Doria09/2013
19752^701403-2786977211144Enzo Doria11/2015
19762^701189-25423211079Enzo Doria09/2013
19772^701162-459161211071Enzo Doria05/2015
19782^700793+219407210960Enzo Doria03/2024
1979(24^152783-1)/23210872Paul Bourdelais04/2018
19802^700400+9385210842Lelio R Paula01/2014
19812^700304-17210813Stefano Morozzi07/2022
19822^700131+1874693210761Enzo Doria06/2016
1983(2^700095+225414)/2210750Stefano Morozzi04/2020
1984(2^700090+278254)/2210748Stefano Morozzi04/2020
1985(2^700075+303666)/2210744Stefano Morozzi04/2020
1986(2^700073+75882)/2210743Stefano Morozzi04/2020
1987(2^700074+328890)/2210743Stefano Morozzi04/2020
1988(2^700052+79162)/2210737Stefano Morozzi04/2020
1989(2^700052+304458)/2210737Stefano Morozzi04/2020
1990(2^700048+376578)/2210736Stefano Morozzi04/2020
199111^202357-1140210734Enzo Doria12/2012
1992(2^700021+25874)/2210728Stefano Morozzi04/2020
1993(2^700018+377518)/2210727Stefano Morozzi04/2020
19942^699999+300729210721Norman Luhn09/2023
1995(238*10^210712-1)/3210714Robert Price09/2023
19962^699740+25210643Stefano Morozzi05/2021
1997(23*10^210525-143)/3210526Robert Price12/2023
19982^698929-2788423210399Enzo Doria11/2015
1999(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
20002^698316+1878601210215Enzo Doria08/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 10 2025 11:16 (Time in France)

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