PRP Records

Probable Primes Top 10000

(301822 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 ?
20017*10^227178+39227179Robert Price01/2023
20029*10^227153-89227154Robert Price02/2023
20032^754473-2791513227120Enzo Doria01/2016
20042^754376+25227090Stefano Morozzi05/2021
20052^754138+213289227019Enzo Doria09/2023
20062^754038+25226989Stefano Morozzi05/2021
20072^753263+217133226755Enzo Doria12/2023
20087*10^226479-9226480Robert Price02/2023
2009(10^226381+1)/14973418875371226368Alfred Reich06/2025
20102^751655+33893226271Enzo Doria06/2024
20112^751426-764321226202Enzo Doria12/2013
2012(18^180181-1)/17226176Andy Steward04/2007
20132^750740-3225996Paul Bourdelais03/2012
20142^750725+60227225991Enzo Doria02/2016
20152^750525-113743225931Enzo Doria09/2014
2016(2^750151-1)/(429934042631*7590093831289*397764574647511*8361437834787151*17383638888678527263)225744Dario Alpern10/2014
20172^749444-1861889225606Enzo Doria12/2015
2018tau(311^16452)225560Nik Lygeros / Olivier Rozier / LR team10/2013
2019(3^472721+1)/9422189991086734893916225524Paul Vanderveen06/2025
20202^749096+1876861225501Enzo Doria07/2016
20212^748895+26213225440Enzo Doria12/2023
2022(519643#+43033)/(23*1871*2706283)225379Makoto Morimoto08/2019
20232^748657+79607225369Enzo Doria06/2016
2024(2^746920-11)/5224845Stefano Morozzi08/2022
20252^746653-291583224765Enzo Doria07/2015
20262^746461-114043224708Enzo Doria11/2014
20272^746302+25224660Stefano Morozzi05/2021
2028(202*10^224545-1)/3224547Robert Price06/2023
2029(19*10^224533-37)/9224534Alfred Reich12/2023
20302^745674+213949224471Enzo Doria10/2023
20312^745098-350471224297Enzo Doria06/2015
20322^745039-4897224280Yves Minet03/2021
203323*10^224232-7224234Robert Price10/2022
2034(154*10^224061-1)/9224063Serge Batalov12/2014
20352^744211-1845787224030Enzo Doria07/2015
20362^743773+37757223898Enzo Doria10/2024
20372^743592-134579223844Hans Havermann10/2018
20382^742452+3223501Paul Bourdelais06/2019
2039234178^9+9^234178223463Anatoly F. Selevich07/2011
204047747^47747-2512^2512223406Henri Lifchitz10/2024
20412^741651-461197223260Enzo Doria07/2015
204210^223236-1001223236Robert Price10/2022
20432^741362-1845251223173Enzo Doria07/2015
20443^467546-5*2^467546223077Jon Grantham08/2023
20452^740455-1863877222900Enzo Doria12/2015
20462^740274+217519222845Enzo Doria01/2024
2047(14*10^222718-41)/9222719Serge Batalov01/2023
20482^739636-2792219222653Enzo Doria02/2016
204911^213654-180222498Enzo Doria01/2013
20502^738957-1859743222449Enzo Doria11/2015
20514*10^222253-21222254Robert Price12/2022
20522^737825+57222108Stefano Morozzi05/2021
2053(54^128189+1)/55222073Paul Bourdelais11/2018
20543^232689+1^232689+4^232689+1^232689+5^232689+9^232689222042Henri Lifchitz03/2025
20552^737166+220099221910Enzo Doria03/2024
2056(10^221654+179)/9221654Serge Batalov12/2014
20572^736281+79817221643Enzo Doria06/2016
205810^221631+247617221632Patrick De Geest10/2013
205910^221631-9221631Alexander Gramolin02/2011
206010^221628+7221629Alfred Reich04/2021
20612^735970-1839821221550Enzo Doria06/2015
20622^735367+60293221368Enzo Doria03/2016
206377*10^221343+3221345Robert Price11/2023
2064299^299^299-582221328Henri Lifchitz03/2025
2065(241^92821-1)/240221099Anonymous04/2024
2066(202*10^221092-1)/3221094Robert Price06/2023
2067(5^316297-1)/220142716221074Paul Vanderveen05/2025
2068(29^151153+1)/30221045Paul Bourdelais09/2017
20692^734228+24751221025Enzo Doria10/2023
2070(28*10^220800+173)/3220801Robert Price07/2024
20712^733264-2784089220735Enzo Doria10/2015
20722^733114-24555220690Enzo Doria09/2013
20732^731891-636259220322Enzo Doria12/2013
207498*10^220185-9220187Robert Price05/2023
2075418319^39164+418318220161Alfred Reich11/2023
20762^4^182829+182829^4^2220149Henri Lifchitz03/2025
20772^731124-25539220091Enzo Doria09/2013
20782^730972-462029220045Enzo Doria07/2015
20792^730833+1868627220003Enzo Doria04/2016
20802^730645-2787133219947Enzo Doria11/2015
20812^730547-25581219917Enzo Doria09/2013
2082(113*13^197420-5)/12219916Anonymous11/2022
2083(13^197420*113-5)/12219916Eric Chen10/2023
20842^730460+82291219891Enzo Doria09/2016
2085(5*10^219847-101)/3219848Robert Price08/2023
2086(2^730339+1)/(3*27839062003*7943469324347)219831Gord Palameta12/2018
2087L(1051849)219824Renaud Lifchitz03/2009
20883*2^730149+5219798Jon Grantham07/2023
20898*10^219740-3219741Serge Batalov01/2023
209011^210961-240219694Enzo Doria01/2013
2091(26*10^219639-77)/3219640Robert Price03/2023
20922^729611-113437219635Enzo Doria08/2014
20937^259710-2219481Paul Bourdelais01/2021
2094F(1049897)219416Henri Lifchitz10/2008
2095(1488^69151-1)/1487219386Alexander Zhirkov02/2023
20962^728604+1879321219332Enzo Doria10/2016
209733^144412+2219292Robert Price04/2015
20982^728277-183313219234Hans Havermann10/2018
20992^727998-1862711219150Enzo Doria12/2015
2100(29*10^219124+91)/3219125Robert Price12/2022
21012^727729-114073219069Enzo Doria12/2014
21022^727496-1851809218999Enzo Doria08/2015
21032^727025+25907218857Enzo Doria12/2023
21042^726591+2793143218726Enzo Doria02/2016
2105(7*10^218644+17)/3218645Robert Price06/2023
21062^725534-2791931218408Enzo Doria02/2016
2107Phi(220531,10)/2686456812680882641217774Makoto Kamada10/2020
21082^722184+1877821217400Enzo Doria08/2016
2109(109*10^217360-1)/9217362Serge Batalov12/2014
21102^721721-4453217260Yves Minet03/2021
211110^216950+49216951Robert Price02/2023
2112281*499979#/46410-2702372216849Robert Smith08/2016
2113281*499979#/46410+2400766216849Robert Smith08/2016
2114tau(311^15786)216429Nik Lygeros / Olivier Rozier / LR team10/2013
21152^718756-114107216368Enzo Doria12/2014
21162^717672+121216041Stefano Morozzi05/2021
21172^717305+80327215931Enzo Doria07/2016
21182^717069-59773215860Enzo Doria10/2015
211910^215802+33215803Robert Price08/2023
212030^146021-29^146021215691Jean-Louis Charton09/2018
2121277^88301-276^88301215674Jean-Louis Charton06/2012
21222^716428+215011215667Enzo Doria11/2023
2123(13*10^215592-43)/3215593Robert Price08/2023
2124p(41292)#+p(41292+1)215450Henri Lifchitz11/2024
2125(29^147319-1)/466757843690852215425Paul Vanderveen06/2025
2126227^91413-40215372Enzo Doria04/2015
2127(2^715008-21)/5215239Stefano Morozzi08/2022
21282^714717+782897215152Enzo Doria11/2016
2129(19^168013-1)/80910356454214837Paul Vanderveen05/2025
2130tau(373^15186)214796Nik Lygeros / Olivier Rozier / LR team10/2013
21312^713241+1879157214707Enzo Doria08/2016
2132(23*10^214633+91)/3214634Robert Price03/2023
213311^206081-10^206081214612Jean-Louis Charton10/2011
21342^712801-69553214575Enzo Doria01/2016
21352^712603-25357214515Enzo Doria09/2013
21362^711721-1846723214250Enzo Doria07/2015
21372^710730-396765213952Enzo Doria09/2013
2138(19*10^213934-37)/9213935Alfred Reich12/2023
2139(19*10^213730-37)/9213731Alfred Reich12/2023
2140(713^74897-1)/712213685Jinyuan Wang08/2023
21412^709773+25907213663Enzo Doria12/2023
21422^708468-114329213271Enzo Doria02/2015
21432^708293+27557213218Enzo Doria01/2024
2144379*10^213199+9213202Jason Yuen01/2025
21452^707277+28997212912Enzo Doria02/2024
2146(163*10^212779-1)/9212781Serge Batalov12/2014
21472^706838-69041212780Enzo Doria11/2015
21482^705653+25907212423Enzo Doria12/2023
214922*10^212339+7212341Robert Price10/2022
21502^704577-113871212099Enzo Doria10/2014
2151(2^704548-19)/3212090Stefano Morozzi08/2022
21522^704110-2792441211959Enzo Doria02/2016
21532^704084+28531211951Enzo Doria02/2024
21542^703943-1862947211908Enzo Doria12/2015
2155(60^119083+1)/61211746Paul Bourdelais10/2018
2156(184*10^211682-1)/3211684Robert Price12/2022
2157(10^211610-91)/9211610Serge Batalov12/2014
2158227^89797+2211565Lelio R Paula08/2012
21592^702194-3211382Paul Bourdelais03/2012
21602^702064+1874911211343Enzo Doria07/2016
21612^701968-113873211314Enzo Doria10/2014
2162(14*10^211262-41)/9211263Serge Batalov01/2023
21632^701713-113779211237Enzo Doria09/2014
21642^701616-216803211208Enzo Doria01/2024
21652^701449-25201211158Enzo Doria09/2013
21662^701403-2786977211144Enzo Doria11/2015
21672^701189-25423211079Enzo Doria09/2013
21682^701162-459161211071Enzo Doria05/2015
21692^700793+219407210960Enzo Doria03/2024
2170(24^152783-1)/23210872Paul Bourdelais04/2018
21712^700400+9385210842Lelio R Paula01/2014
21722^700304-17210813Stefano Morozzi07/2022
21732^700131+1874693210761Enzo Doria06/2016
2174(2^700095+225414)/2210750Stefano Morozzi04/2020
2175(2^700090+278254)/2210748Stefano Morozzi04/2020
2176(2^700075+303666)/2210744Stefano Morozzi04/2020
2177(2^700073+75882)/2210743Stefano Morozzi04/2020
2178(2^700074+328890)/2210743Stefano Morozzi04/2020
2179(2^700052+79162)/2210737Stefano Morozzi04/2020
2180(2^700052+304458)/2210737Stefano Morozzi04/2020
2181(2^700048+376578)/2210736Stefano Morozzi04/2020
218211^202357-1140210734Enzo Doria12/2012
2183(2^700021+25874)/2210728Stefano Morozzi04/2020
2184(2^700018+377518)/2210727Stefano Morozzi04/2020
21852^699999+300729210721Norman Luhn09/2023
2186(238*10^210712-1)/3210714Robert Price09/2023
21872^699740+25210643Stefano Morozzi05/2021
2188(23*10^210525-143)/3210526Robert Price12/2023
21892^698929-2788423210399Enzo Doria11/2015
2190(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
21912^698316+1878601210215Enzo Doria08/2016
219234*10^210097-9210099Robert Price05/2023
2193(19*10^210011-49)/3210012Robert Price06/2023
21946*10^209846-91209847Robert Price05/2023
21952^697036+1878751209829Enzo Doria08/2016
21962^696813+28607209762Enzo Doria02/2024
2197(238*10^209715-1)/3209717Robert Price09/2023
21986^269407+5209640Paul Bourdelais02/2021
2199(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
22002^696254-115151209594Enzo Doria06/2015
22012^695841+225209470Henri Lifchitz01/2025
2202(35^135623+1)/36209410Paul Bourdelais07/2018
22037*10^209161+39209162Robert Price01/2023
22042^694633+1887257209106Enzo Doria05/2017
2205fibonacci(999790)-4208944Jon Grantham08/2023
22062^693959+180923208903Enzo Doria07/2016
2207(2^693747-11)/3208839Stefano Morozzi08/2022
22082^693462-1847561208753Enzo Doria07/2015
22092^690890-59981207979Enzo Doria11/2015
2210(38^131591+1)/39207884Paul Bourdelais07/2018
22113*2^690484+5207857Jon Grantham07/2023
22122^690163+1877063207760Enzo Doria07/2016
2213Phi(64773,-64773)207680Henri Lifchitz06/2025
22147^245608-2207563Paul Bourdelais01/2021
2215(67*10^207556+23)/9207557Serge Batalov01/2023
22162^689286-29381207496Enzo Doria08/2015
22172^689122-114521207447Enzo Doria04/2015
22189*10^207254-89207255Robert Price02/2023
22192^688373+6077207221Enzo Doria02/2016
22202^688201+1875527207170Enzo Doria07/2016
2221(42^127609+1)/43207140Paul Bourdelais07/2018
22222^687938+213589207090Enzo Doria10/2023
22232^687619+81563206994Enzo Doria08/2016
22243*10^206927+37206928Robert Price08/2023
22252^687383+21803206923Enzo Doria09/2023
2226(11*10^206688+19)/3206689Robert Price07/2024
22272^686572-1845299206679Enzo Doria07/2015
2228(21^156217-1)/20206552Paul Bourdelais04/2010
22292^685970+39415206498Enzo Doria11/2024
2230(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
22312^685578+3206380Paul Bourdelais04/2012
22322^685078+218599206230Enzo Doria01/2024
22332^684836-49349206157Enzo Doria10/2015
2234(73^110603-1)/72206088Paul Bourdelais06/2018
22352^684163-2790967205954Enzo Doria12/2015
2236326^81943-325^81943205941Jean-Louis Charton07/2012
2237(2^684127-1)/23765203727205933Jens K. Andersen04/2009
2238(68*10^205510+13)/9205511Serge Batalov01/2023
22394^341233-3^341233205443Jean-Louis Charton01/2006
22402^682414+215029205428Enzo Doria11/2023
2241(963^68821-1)/962205334Jinyuan Wang01/2024
2242(43*10^205183-421)/9205184Robert Price10/2023
22432^681545+467205166Lelio R Paula11/2013
22442^681306+81049205094Enzo Doria07/2016
22452^680697+1877057204911Enzo Doria07/2016
22462^680415+71783204826Enzo Doria04/2016
224710^204764-8001204764Robert Price03/2023
2248(26*10^204730-77)/3204731Robert Price03/2023
22492^679860-459995204659Enzo Doria06/2015
22502^679593+1879547204578Enzo Doria09/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 23 2025 10:09 (Time in France)

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