PRP Records

Probable Primes Top 10000

(294613 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 ?
20012^636011-1860847191459Enzo Doria11/2015
20022^635926-1860611191433Enzo Doria11/2015
20033*2^635755+5191382Jon Grantham07/2023
20043*10^191152-7191153Robert Price08/2015
20052^634883-1865677191119Enzo Doria02/2016
20062^634801+1871957191095Enzo Doria05/2016
2007(77*10^191080+157)/9191081Robert Price05/2022
2008(35*10^191073+1)/9191074Serge Batalov07/2010
20099*10^191018-41191019Robert Price08/2020
20102^634470-59861190995Enzo Doria11/2015
20112^634368-29519190964Enzo Doria08/2015
2012(19*10^190935+11)/3190936Robert Price07/2023
20132^634188-350609190910Enzo Doria06/2015
2014(65*10^190899+493)/9190900Robert Price08/2021
2015(62*10^190795-413)/9190796Robert Price09/2021
2016(26*10^190789-131)/3190790Robert Price10/2019
2017(13*10^190732-61)/3190733Robert Price11/2018
20183*2^633524+5190711Jon Grantham07/2023
2019(7*10^190683+143)/3190684Robert Price03/2018
20202^633088-113879190579Enzo Doria10/2014
20212^633064+1874911190572Enzo Doria06/2016
20225*3^399402+2^399402190564Jon Grantham08/2023
2023(43*10^190547+83)/9190548Robert Price11/2018
202499*10^190543+7190545Robert Price05/2021
2025(299*10^190533+1)/3190535Robert Price04/2020
2026(1744*10^190519-1747)/3190522Robert Price12/2020
20272^632815-15190497Stefano Morozzi07/2022
20282^632795-351205190491Enzo Doria06/2015
202941171^41272+41272^41171190454Norbert Schneider05/2023
2030(16*10^190420-19)/3190421Robert Price02/2019
2031(43*10^190351+101)/9190352Robert Price11/2018
20322^632156+78391190298Enzo Doria06/2016
203397*10^190295-3190297Robert Price05/2020
20342^632082-1851971190276Enzo Doria08/2015
20352^632020+1880311190257Enzo Doria09/2016
2036(5*10^190242-77)/9190242Robert Price04/2021
20377*10^190210+13190211Robert Price03/2021
20382^631637-462373190142Enzo Doria08/2015
20392*10^190126-21190127Robert Price09/2020
2040(28*10^190105+191)/3190106Robert Price02/2020
20412*10^190093+33190094Robert Price11/2021
2042(68*10^190053-113)/9190054Robert Price03/2021
20432^631183+213413190006Enzo Doria09/2023
20442^631122-39251189987Enzo Doria08/2015
2045(26*10^189928-89)/9189929Robert Price06/2018
20462^630839-97189902Yves Minet07/2017
204799*10^189876-7189878Robert Price07/2020
20482^630359+1788953189757Enzo Doria05/2016
20492^630228+1871971189718Enzo Doria05/2016
20502^630108+781189682Lelio R Paula08/2013
20512^629870-1867811189610Enzo Doria04/2016
2052(359^74189-1)/358189558Alexander Zhirkov11/2017
20532^629326+2792929189447Enzo Doria02/2016
20544*10^189401+13189402Robert Price02/2021
2055(10^189385-61)/3189385Serge Batalov12/2014
20562^629036+1874011189359Enzo Doria06/2016
20572^628930+80779189327Enzo Doria07/2016
2058(134*10^189309-11)/3189311Robert Price01/2022
20599*10^189306-11189307Mischa Rodermond04/2023
20602^628582+1179439189223Enzo Doria06/2016
2061(44*10^188999-503)/9189000Robert Price12/2018
2062(16*10^188823+167)/3188824Robert Price06/2019
2063(10^188796+7)/4967/71933188788Alfred Reich08/2021
20642^627037-2785843188757Enzo Doria10/2015
2065(10^188566+7)/311640753181661188552Alfred Reich04/2022
2066(16*10^188457+161)/3188458Robert Price02/2019
2067L(901657)188436Renaud Lifchitz11/2008
2068(19*10^188375+137)/3188376Robert Price03/2022
20692^625651+74213188340Enzo Doria04/2016
20702^625584-460919188320Enzo Doria06/2015
2071(8*10^188308-71)/9188308Serge Batalov11/2022
20725^269399-3^269399-1188302Jon Grantham08/2023
2073(14*10^188218+139)/9188219Robert Price11/2021
2074(10^188164+359)/9188164Serge Batalov12/2014
20752^624481-113611187988Enzo Doria08/2014
2076(2^624389+125582)/2187960Stefano Morozzi09/2019
2077(2^624389+166982)/2187960Stefano Morozzi09/2019
2078(2^624389+179886)/2187960Stefano Morozzi09/2019
2079(2^624387+64466)/2187959Stefano Morozzi09/2019
2080(2^624378+112990)/2187957Stefano Morozzi09/2019
2081(2^624380+161986)/2187957Stefano Morozzi09/2019
2083(2^624376+55762)/2187956Stefano Morozzi09/2019
2082(2^624377+169506)/2187956Stefano Morozzi09/2019
2084(2^624355+80178)/2187950Stefano Morozzi09/2019
2085(2^624351+61350)/2187949Stefano Morozzi09/2019
2086(2^624341+63462)/2187946Stefano Morozzi09/2019
2087(2^624344+135990)/2187946Stefano Morozzi09/2019
2088(2^624344+183898)/2187946Stefano Morozzi09/2019
2090(2^624340+126982)/2187945Stefano Morozzi09/2019
2089(2^624338+196110)/2187945Stefano Morozzi09/2019
2091(2^624337+105162)/2187944Stefano Morozzi09/2019
2092(2^624333+44594)/2187943Stefano Morozzi09/2019
2093(2^624321+88742)/2187940Stefano Morozzi09/2019
2094(2^624324+135178)/2187940Stefano Morozzi09/2019
2095(2^624317+14186)/2187938Stefano Morozzi09/2019
2096(2^624313+24450)/2187937Stefano Morozzi09/2019
2097(2^624309+184590)/2187936Stefano Morozzi09/2019
2099(2^624307+152658)/2187935Stefano Morozzi09/2019
2098(2^624307+185978)/2187935Stefano Morozzi09/2019
2100(2^624303+40814)/2187934Stefano Morozzi09/2019
2101(2^624304+99238)/2187934Stefano Morozzi09/2019
21022^624077-112723187866Enzo Doria07/2014
21032^624008+1874941187846Enzo Doria06/2016
21042^623870+78679187804Enzo Doria05/2016
21052^623714-114035187757Enzo Doria11/2014
21062^623651-1834251187738Enzo Doria07/2015
2107(7*10^187645+53)/3187646Robert Price05/2018
210821650^43269+43269^21650187591Norbert Schneider02/2023
21092^623146+1879609187586Enzo Doria09/2016
2110(401*10^187512+13)/9187514Robert Price09/2021
2111(5*10^187471+91)/3187472Robert Price04/2018
21122^622500+81931187392Enzo Doria08/2016
2113(13*10^187382-157)/9187383Robert Price05/2021
21142^622300-1861739187331Enzo Doria12/2015
2115(22*10^187317-91)/3187318Robert Price02/2022
2116(38*10^187281+349)/9187282Robert Price10/2018
21172^622052+76771187257Enzo Doria05/2016
21182^622005-24091187243Enzo Doria08/2013
21197*10^187205-57187206Robert Price06/2020
21202^621879-351787187205Enzo Doria07/2015
2121(5*10^187168-53)/3187169Robert Price09/2020
2122(23*10^187164-143)/3187165Robert Price12/2019
21232^621700+79411187151Enzo Doria06/2016
21242^621597+39187120Jon Grantham08/2023
2125(7*10^187101+131)/3187102Robert Price06/2020
2126(2*10^187062-71)/3187062Robert Price12/2017
21272^620929-113203186919Enzo Doria07/2014
212810^186842+168223186843Patrick De Geest07/2018
212910^186842-8001186842Robert Price03/2018
21302^620347-1777186744Lelio R Paula07/2013
2131(11*10^186659+133)/9186660Robert Price04/2022
213211^179143-4170186559Enzo Doria12/2012
2133(5^266863+1)/6186529Paul Bourdelais07/2010
21342*10^186517+33186518Robert Price11/2021
21352^619297-2792353186427Enzo Doria02/2016
2136(49*10^186409+383)/9186410Robert Price04/2019
21372^618940-460139186320Enzo Doria06/2015
21382^618046+74179186051Enzo Doria04/2016
21393*10^186019+11186020Robert Price07/2018
2140(16*10^185978-19)/3185979Robert Price02/2019
2141(22*10^185950-7)/3185951Robert Price12/2022
21422*10^185930-3185931Robert Price07/2015
2143(82^97151+1)/83185928Paul Bourdelais10/2017
21444*10^185905+91185906Robert Price08/2018
2145(34*10^185902-601)/9185903Robert Price07/2022
2146(19*10^185873+131)/3185874Robert Price06/2020
2147(37*10^185811+377)/9185812Robert Price11/2018
21482^617250+9385185811Lelio R Paula07/2013
21492^617130+9185775Stefano Morozzi05/2021
215039^116749+2185756Robert Price04/2015
21512^616924-39719185713Enzo Doria09/2015
21522^616712+1867621185649Enzo Doria04/2016
2153(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
21548*10^185529-67185530Robert Price08/2019
2155(5*10^185520-11)/3185521Tyler Busby02/2023
21565*2^616124+3185473Jon Grantham07/2023
21572^615916+26791185410Enzo Doria12/2023
21584*10^185355+9185356Robert Price05/2015
2159(16*10^185347+89)/3185348Robert Price03/2021
21602^615622+76639185321Enzo Doria05/2016
21612^615591+1879223185312Enzo Doria08/2016
21622^615587+217013185311Enzo Doria12/2023
21632^615503+1876643185285Enzo Doria07/2016
21645^265007-4^265007185232Jean-Louis Charton02/2013
2166(4*10^185221-91)/3185222Robert Price03/2018
2165(7*10^185221+131)/3185222Robert Price06/2020
2167(62*10^185216-413)/9185217Robert Price09/2021
2168(232*10^185180+17)/3185182Robert Price04/2021
216956*10^185139-3185141Robert Price03/2020
2170(28*10^185105+47)/3185106Robert Price02/2021
21712^614783-2790097185069Enzo Doria12/2015
21722^614745-29323185057Enzo Doria07/2015
2173(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840185052Serge Batalov07/2013
2174(49*10^184993-67)/9184994Robert Price03/2019
2175(5*10^184954-191)/3184955Robert Price05/2021
2176(14*10^184950+211)/9184951Robert Price04/2018
21772^614360+215221184941Enzo Doria11/2023
21782^614315+81353184928Enzo Doria08/2016
21792^614294-1849961184921Enzo Doria08/2015
21802^614266+1877809184913Enzo Doria08/2016
2181(185*10^184878-11)/3184880Robert Price10/2020
218291*10^184867-9184869Robert Price06/2021
2183(14789^44521-1)/(14789^211-1)184770Ryan Propper11/2023
2184(85*10^184768+77)/9184769Robert Price07/2022
21852^613715-1860727184747Enzo Doria11/2015
2186(4*10^184730+89)/3184731Robert Price08/2021
21872*10^184723+41184724Robert Price05/2018
2188(49*10^184703+293)/9184704Robert Price03/2021
21892^613487-349987184678Enzo Doria07/2015
2190(95^93377+1)/96184672Paul Bourdelais11/2017
219114^161089-161089^14184629Serge Batalov05/2016
21922^613033-114621184542Enzo Doria05/2015
21933*2^612759+5184460Jon Grantham07/2023
21942^612587+213413184408Enzo Doria09/2023
2195(9^193247+1)/10184404Paul Bourdelais02/2010
21962^612424+212341184358Enzo Doria08/2023
21972^612341-1604809184334Enzo Doria05/2015
2198(11*10^184308-161)/3184309Robert Price11/2021
2199(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
2200(14*10^184150+37)/3184151Robert Price12/2018
22012^611731-4837184150Yves Minet08/2018
22023*10^184124-7184125Robert Price08/2015
22032^611644+29371184124Enzo Doria02/2024
22049*10^184122-11184123Mischa Rodermond04/2023
22052^611628-24537184119Enzo Doria08/2013
22063*10^184110+13184111Robert Price07/2018
2207(14280^44521-1)/(14280^211-1)184097Ryan Propper11/2023
2208(194*10^184093+1)/3184095Robert Price01/2022
22092^611460+71881184068Enzo Doria04/2016
22104*10^184004-63184005Robert Price10/2018
22112^610982-1867301183924Enzo Doria03/2016
2212(10^183917+1)/11/9952852373183906Alfred Reich02/2024
22133*10^183872-49183873Robert Price07/2018
22142^610597+1178897183809Enzo Doria05/2016
2215(8*10^183773-269)/9183773Robert Price09/2021
2216(65*10^183768-29)/9183769Robert Price01/2021
2217(17*10^183764+31)/3183765Robert Price01/2019
2218(28*10^183760-1)/9183761Serge Batalov10/2014
22192^610401+1277183750Lelio R Paula07/2013
22202^610356-1849019183736Enzo Doria08/2015
2221(63^102103+1)/64183717Paul Bourdelais10/2017
222223*10^183710-7183712Robert Price02/2020
2223(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
2224(4*10^183659+149)/9183659Robert Price04/2018
2225(4*10^183657+41)/9183657Serge Batalov11/2022
22267*10^183596+39183597Robert Price01/2023
22272^609846-1834251183582Enzo Doria07/2015
222810^183546+1547323183547Patrick De Geest02/2021
223010^183546-800000001183546Robert Price09/2020
222910^183546-584297183546Patrick De Geest02/2021
22317*10^183511+39183512Robert Price01/2023
2232(23*10^183477-71)/3183478Robert Price07/2020
223311^176176-240183469Enzo Doria11/2012
2234(41^113749+1)/42183451Paul Bourdelais11/2017
22356*10^183429+53183430Robert Price05/2020
2236(28*10^183403+191)/3183404Robert Price02/2020
2237(101^91463+1)/102183320Paul Bourdelais11/2017
22382^608965-113989183317Enzo Doria10/2014
2239A005165(43592)183312Serge Batalov07/2017
2240(61*10^183294+119)/9183295Robert Price05/2019
22412^608814-461261183272Enzo Doria06/2015
2242(163*10^183227-1)/9183229Serge Batalov12/2014
22432^608541-608541^2183190Henri Lifchitz02/2018
22442^608293+143807183115Enzo Doria10/2016
22452^608164-462419183076Enzo Doria08/2015
22462^607950-1862303183012Enzo Doria12/2015
22475*3^383376+2^383376182918Jon Grantham08/2023
2248(46*10^182896+683)/9182897Robert Price03/2019
2249(2*10^182787+73)/3182787Robert Price09/2020
22502^607101+1871987182756Enzo Doria05/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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