PRP Records

Probable Primes Top 10000

(295148 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 ?
200111^187185-90194934Enzo Doria09/2012
20022^647468+220141194908Enzo Doria03/2024
2003(86*10^194818-437)/9194819Robert Price03/2021
20042^647068+77281194787Enzo Doria05/2016
20052*10^194716-93194717Robert Price12/2021
200615^165559-14^165559194713Jean-Louis Charton03/2011
2007F(931517)194676Henri Lifchitz09/2008
20084*10^194668+49194669Robert Price01/2019
20092^646589+1179407194643Enzo Doria06/2016
20102^646289-114621194553Enzo Doria05/2015
20112^646236-39659194537Enzo Doria09/2015
2012(16*10^194536+53)/3194537Robert Price03/2019
20132^646161-59833194514Enzo Doria11/2015
2014(17*10^194502+31)/3194503Robert Price01/2019
2015(19*10^194428+287)/9194429Robert Price10/2021
20162*10^194413+3194414Robert Price07/2015
20172^645360-1848599194273Enzo Doria08/2015
201822470^44641+44641^22470194260Norbert Schneider08/2023
2019(112*10^194150-1)/3194152Serge Batalov12/2014
2020Phi(293127,10)194041Makoto Kamada12/2023
20212*10^193981-43193982Robert Price04/2018
20222^644382+75169193979Enzo Doria04/2016
20232^644304-1861409193955Enzo Doria11/2015
2024(29*10^193950-23)/3193951Robert Price03/2022
20255*10^193907-9193908Robert Price05/2015
20262^644043+1876703193877Enzo Doria07/2016
20272*10^193841-63193842Robert Price01/2022
20282^643735+1879733193784Enzo Doria09/2016
2029(5^277183+1)/6193742Paul Bourdelais07/2010
20309*10^193712+71193713Robert Price08/2020
20312^643216-286565193628Enzo Doria07/2015
20322^643204+215011193624Enzo Doria11/2023
203310^193566+1126339193567Patrick De Geest09/2022
203510^193566-10000000001193566Robert Price04/2021
203410^193566-454041193566Patrick De Geest08/2021
20372^642888-24965193529Enzo Doria09/2013
20362^642889+25367193529Enzo Doria11/2023
20382^642448-114825193397Enzo Doria05/2015
20392^642437-1856623193393Enzo Doria10/2015
20402^642039-59797193273Enzo Doria11/2015
20412^641987+39193258Jon Grantham08/2023
204210^193230+513861193231Patrick De Geest07/2018
204310^193230-8001193230Robert Price03/2018
2044(62*10^193225-233)/9193226Robert Price02/2022
20452^641692-286349193169Enzo Doria07/2015
20462^641690-24737193168Enzo Doria09/2013
204722268^44421+44421^22268193129Norbert Schneider06/2023
20482^641514+1876549193115Enzo Doria07/2016
20492^640888-2785619192927Enzo Doria10/2015
20502^640874-2783741192923Enzo Doria09/2015
205110^192922+192207192923Patrick De Geest08/2021
205210^192922-7001192922Robert Price04/2021
20532^640854+25192917Stefano Morozzi05/2021
205434*10^192868-9192870Robert Price06/2020
2055(46*10^192841+683)/9192842Robert Price03/2019
20562^640181+467192714Lelio R Paula08/2013
20572^640072+27541192681Enzo Doria01/2024
20582^639536-1850249192520Enzo Doria08/2015
205940714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
20605*10^192422-43192423Robert Price01/2019
20612^639110-2792441192392Enzo Doria02/2016
2062(241^80761-1)/240192372Anonymous04/2024
20632^638955-29827192345Enzo Doria08/2015
206415^163539+14192337Alfred Reich10/2023
20652^638713-2784223192272Enzo Doria10/2015
2066(10^192216+7)/149192214Alfred Reich07/2021
20672^638490-113507192205Enzo Doria08/2014
20682^638189-39943192115Enzo Doria09/2015
20692^638110+1877119192091Enzo Doria07/2016
20702^638066-2785211192078Enzo Doria10/2015
2071(35*10^191973-341)/9191974Robert Price08/2021
2072(112*10^191900+17)/3191902Robert Price03/2020
20732^637475-115309191900Enzo Doria07/2015
2074(68*10^191754-113)/9191755Robert Price03/2021
20752^636930-11191736Stefano Morozzi07/2022
2076(47*10^191732+259)/9191733Robert Price03/2022
20772^636661+1876577191655Enzo Doria07/2016
2078(9^200807-2^200807)/7191618Jon Grantham07/2023
2079(34^125101-1)/33191589Paul Bourdelais11/2017
2080fibonacci(916540)-2191546Jon Grantham08/2023
20812^636177-1855123191509Enzo Doria09/2015
20822^636158-113627191503Enzo Doria08/2014
2083(37*25^136966+63)/4191472Curtis Bright05/2015
20842^636035+79823191466Enzo Doria06/2016
20852^636011-1860847191459Enzo Doria11/2015
20862^635926-1860611191433Enzo Doria11/2015
20873*2^635755+5191382Jon Grantham07/2023
20883*10^191152-7191153Robert Price08/2015
20892^634883-1865677191119Enzo Doria02/2016
20902^634801+1871957191095Enzo Doria05/2016
2091(77*10^191080+157)/9191081Robert Price05/2022
2092(35*10^191073+1)/9191074Serge Batalov07/2010
20939*10^191018-41191019Robert Price08/2020
20942^634470-59861190995Enzo Doria11/2015
20952^634368-29519190964Enzo Doria08/2015
2096(19*10^190935+11)/3190936Robert Price07/2023
20972^634188-350609190910Enzo Doria06/2015
2098(65*10^190899+493)/9190900Robert Price08/2021
2099(62*10^190795-413)/9190796Robert Price09/2021
2100(26*10^190789-131)/3190790Robert Price10/2019
2101(13*10^190732-61)/3190733Robert Price11/2018
21023*2^633524+5190711Jon Grantham07/2023
2103(7*10^190683+143)/3190684Robert Price03/2018
21042^633088-113879190579Enzo Doria10/2014
21052^633064+1874911190572Enzo Doria06/2016
21065*3^399402+2^399402190564Jon Grantham08/2023
2107(43*10^190547+83)/9190548Robert Price11/2018
210899*10^190543+7190545Robert Price05/2021
2109(299*10^190533+1)/3190535Robert Price04/2020
2110(1744*10^190519-1747)/3190522Robert Price12/2020
21112^632815-15190497Stefano Morozzi07/2022
21122^632795-351205190491Enzo Doria06/2015
211341171^41272+41272^41171190454Norbert Schneider05/2023
2114(16*10^190420-19)/3190421Robert Price02/2019
2115(43*10^190351+101)/9190352Robert Price11/2018
21162^632156+78391190298Enzo Doria06/2016
211797*10^190295-3190297Robert Price05/2020
21182^632082-1851971190276Enzo Doria08/2015
21192^632020+1880311190257Enzo Doria09/2016
2120(5*10^190242-77)/9190242Robert Price04/2021
21217*10^190210+13190211Robert Price03/2021
21222^631637-462373190142Enzo Doria08/2015
21232*10^190126-21190127Robert Price09/2020
2124(28*10^190105+191)/3190106Robert Price02/2020
21252*10^190093+33190094Robert Price11/2021
2126(68*10^190053-113)/9190054Robert Price03/2021
21272^631183+213413190006Enzo Doria09/2023
21282^631122-39251189987Enzo Doria08/2015
2129(26*10^189928-89)/9189929Robert Price06/2018
21302^630839-97189902Yves Minet07/2017
213199*10^189876-7189878Robert Price07/2020
21322^630359+1788953189757Enzo Doria05/2016
21332^630228+1871971189718Enzo Doria05/2016
21342^630108+781189682Lelio R Paula08/2013
21352^629870-1867811189610Enzo Doria04/2016
2136(359^74189-1)/358189558Alexander Zhirkov11/2017
21372^629326+2792929189447Enzo Doria02/2016
21384*10^189401+13189402Robert Price02/2021
2139(10^189385-61)/3189385Serge Batalov12/2014
21402^629036+1874011189359Enzo Doria06/2016
21412^628930+80779189327Enzo Doria07/2016
2142(134*10^189309-11)/3189311Robert Price01/2022
21439*10^189306-11189307Mischa Rodermond04/2023
21442^628582+1179439189223Enzo Doria06/2016
2145(44*10^188999-503)/9189000Robert Price12/2018
2146(16*10^188823+167)/3188824Robert Price06/2019
2147(10^188796+7)/4967/71933188788Alfred Reich08/2021
21482^627037-2785843188757Enzo Doria10/2015
2149(10^188566+7)/311640753181661188552Alfred Reich04/2022
2150(16*10^188457+161)/3188458Robert Price02/2019
2151L(901657)188436Renaud Lifchitz11/2008
2152(19*10^188375+137)/3188376Robert Price03/2022
21532^625651+74213188340Enzo Doria04/2016
21542^625584-460919188320Enzo Doria06/2015
2155(8*10^188308-71)/9188308Serge Batalov11/2022
21565^269399-3^269399-1188302Jon Grantham08/2023
2157(14*10^188218+139)/9188219Robert Price11/2021
2158(10^188164+359)/9188164Serge Batalov12/2014
21592^624481-113611187988Enzo Doria08/2014
2160(2^624389+125582)/2187960Stefano Morozzi09/2019
2161(2^624389+166982)/2187960Stefano Morozzi09/2019
2162(2^624389+179886)/2187960Stefano Morozzi09/2019
2163(2^624387+64466)/2187959Stefano Morozzi09/2019
2164(2^624378+112990)/2187957Stefano Morozzi09/2019
2165(2^624380+161986)/2187957Stefano Morozzi09/2019
2167(2^624376+55762)/2187956Stefano Morozzi09/2019
2166(2^624377+169506)/2187956Stefano Morozzi09/2019
2168(2^624355+80178)/2187950Stefano Morozzi09/2019
2169(2^624351+61350)/2187949Stefano Morozzi09/2019
2170(2^624341+63462)/2187946Stefano Morozzi09/2019
2171(2^624344+135990)/2187946Stefano Morozzi09/2019
2172(2^624344+183898)/2187946Stefano Morozzi09/2019
2174(2^624340+126982)/2187945Stefano Morozzi09/2019
2173(2^624338+196110)/2187945Stefano Morozzi09/2019
2175(2^624337+105162)/2187944Stefano Morozzi09/2019
2176(2^624333+44594)/2187943Stefano Morozzi09/2019
2177(2^624321+88742)/2187940Stefano Morozzi09/2019
2178(2^624324+135178)/2187940Stefano Morozzi09/2019
2179(2^624317+14186)/2187938Stefano Morozzi09/2019
2180(2^624313+24450)/2187937Stefano Morozzi09/2019
2181(2^624309+184590)/2187936Stefano Morozzi09/2019
2183(2^624307+152658)/2187935Stefano Morozzi09/2019
2182(2^624307+185978)/2187935Stefano Morozzi09/2019
2184(2^624303+40814)/2187934Stefano Morozzi09/2019
2185(2^624304+99238)/2187934Stefano Morozzi09/2019
21862^624077-112723187866Enzo Doria07/2014
21872^624008+1874941187846Enzo Doria06/2016
21882^623870+78679187804Enzo Doria05/2016
21892^623714-114035187757Enzo Doria11/2014
21902^623651-1834251187738Enzo Doria07/2015
2191(7*10^187645+53)/3187646Robert Price05/2018
219221650^43269+43269^21650187591Norbert Schneider02/2023
21932^623146+1879609187586Enzo Doria09/2016
2194(401*10^187512+13)/9187514Robert Price09/2021
2195(5*10^187471+91)/3187472Robert Price04/2018
21962^622500+81931187392Enzo Doria08/2016
2197(13*10^187382-157)/9187383Robert Price05/2021
21982^622300-1861739187331Enzo Doria12/2015
2199(22*10^187317-91)/3187318Robert Price02/2022
2200(38*10^187281+349)/9187282Robert Price10/2018
22012^622052+76771187257Enzo Doria05/2016
22022^622005-24091187243Enzo Doria08/2013
22037*10^187205-57187206Robert Price06/2020
22042^621879-351787187205Enzo Doria07/2015
2205(5*10^187168-53)/3187169Robert Price09/2020
2206(23*10^187164-143)/3187165Robert Price12/2019
22072^621700+79411187151Enzo Doria06/2016
22082^621597+39187120Jon Grantham08/2023
2209(7*10^187101+131)/3187102Robert Price06/2020
2210(2*10^187062-71)/3187062Robert Price12/2017
22112^620929-113203186919Enzo Doria07/2014
221210^186842+168223186843Patrick De Geest07/2018
221310^186842-8001186842Robert Price03/2018
22142^620347-1777186744Lelio R Paula07/2013
2215(11*10^186659+133)/9186660Robert Price04/2022
221611^179143-4170186559Enzo Doria12/2012
2217(5^266863+1)/6186529Paul Bourdelais07/2010
22182*10^186517+33186518Robert Price11/2021
22192^619297-2792353186427Enzo Doria02/2016
2220(49*10^186409+383)/9186410Robert Price04/2019
22212^618940-460139186320Enzo Doria06/2015
22222^618046+74179186051Enzo Doria04/2016
22233*10^186019+11186020Robert Price07/2018
2224(16*10^185978-19)/3185979Robert Price02/2019
2225(22*10^185950-7)/3185951Robert Price12/2022
22262*10^185930-3185931Robert Price07/2015
2227(82^97151+1)/83185928Paul Bourdelais10/2017
22284*10^185905+91185906Robert Price08/2018
2229(34*10^185902-601)/9185903Robert Price07/2022
2230(19*10^185873+131)/3185874Robert Price06/2020
2231(37*10^185811+377)/9185812Robert Price11/2018
22322^617250+9385185811Lelio R Paula07/2013
22332^617130+9185775Stefano Morozzi05/2021
223439^116749+2185756Robert Price04/2015
22352^616924-39719185713Enzo Doria09/2015
22362^616712+1867621185649Enzo Doria04/2016
2237(3^388897+2^388897)/5185551Jean-Louis Charton09/2011
22388*10^185529-67185530Robert Price08/2019
2239(5*10^185520-11)/3185521Tyler Busby02/2023
22405*2^616124+3185473Jon Grantham07/2023
22412^615916+26791185410Enzo Doria12/2023
22424*10^185355+9185356Robert Price05/2015
2243(16*10^185347+89)/3185348Robert Price03/2021
22442^615622+76639185321Enzo Doria05/2016
22452^615591+1879223185312Enzo Doria08/2016
22462^615587+217013185311Enzo Doria12/2023
22472^615503+1876643185285Enzo Doria07/2016
22485^265007-4^265007185232Jean-Louis Charton02/2013
2250(4*10^185221-91)/3185222Robert Price03/2018
2249(7*10^185221+131)/3185222Robert Price06/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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