PRP Records

Probable Primes Top 10000

(295461 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 ?
20012^653601-69673196754Enzo Doria02/2016
2002(44*10^196684+1)/9196685Serge Batalov07/2010
20032^652786-1852571196509Enzo Doria08/2015
20042^652752-1325196498Yves Minet07/2015
20052^652470-1859141196414Enzo Doria10/2015
20062^652346+29329196376Enzo Doria02/2024
20072^652307+1877483196364Enzo Doria08/2016
20082^652293-115273196360Enzo Doria06/2015
2009(47*10^196281+403)/9196282Robert Price03/2019
20102^652025+218027196280Enzo Doria01/2024
20112^652004+23961196273Enzo Doria10/2023
2012(7*10^196125-31)/3196126Robert Price12/2021
201333^129128+129128^33196083Norbert Schneider06/2022
20146*10^196070+73196071Robert Price04/2019
20152^651218-1868201196037Enzo Doria04/2016
20162^651047-49687195985Enzo Doria10/2015
201710^195968-700001195968Robert Price08/2021
2018fibonacci(937485)+3195923Jon Grantham08/2023
2019(29*10^195875-197)/3195876Robert Price08/2021
2020(25*10^195808-97)/9195809Robert Price01/2022
20212^650285-2785333195756Enzo Doria10/2015
2022(10^195732+7)/18089/49605893195721Alfred Reich08/2021
2023(29*10^195648-41)/3195649Tyler Busby03/2024
2024(69^106397-1)/68195647Paul Bourdelais10/2017
20252^649811+1877573195613Enzo Doria08/2016
20262^649662-170531195568Hans Havermann10/2018
20272^649586+182839195545Enzo Doria11/2016
20282^649537-1867363195531Enzo Doria04/2016
20292^649536-1861499195530Enzo Doria12/2015
20302^649493+25907195517Enzo Doria11/2023
2031(103*10^195478-1)/3195480Serge Batalov12/2014
20322^649102-59351195400Enzo Doria10/2015
2033(2*10^195399+529)/9195399Robert Price01/2018
2034(202*10^195383-13)/9195385Robert Price01/2020
20352^648988+1178971195365Enzo Doria06/2016
20362^648975-114319195361Enzo Doria02/2015
2037(11*10^195350-137)/9195351Robert Price01/2018
20382^648619-24835195254Enzo Doria09/2013
20395*10^195250-21195251Robert Price12/2021
2040(14*10^195234-83)/3195235Robert Price12/2018
20415*10^195221+81195222Robert Price03/2019
204210^195143-5001195143Robert Price12/2021
20432^648190-24737195125Enzo Doria09/2013
2044(57^111119+1)/58195110Paul Bourdelais10/2017
2045(29*10^195098-197)/3195099Robert Price08/2021
204610^195060+89701195061Patrick De Geest02/2021
204810^195060-40000000001195060Robert Price09/2020
204710^195060-110337195060Patrick De Geest02/2021
204956*10^195032-3195034Robert Price03/2020
205011^187185-90194934Enzo Doria09/2012
20512^647468+220141194908Enzo Doria03/2024
2052(86*10^194818-437)/9194819Robert Price03/2021
20532^647068+77281194787Enzo Doria05/2016
20542*10^194716-93194717Robert Price12/2021
205515^165559-14^165559194713Jean-Louis Charton03/2011
2056F(931517)194676Henri Lifchitz09/2008
20574*10^194668+49194669Robert Price01/2019
20582^646589+1179407194643Enzo Doria06/2016
20592^646289-114621194553Enzo Doria05/2015
20602^646236-39659194537Enzo Doria09/2015
2061(16*10^194536+53)/3194537Robert Price03/2019
20622^646161-59833194514Enzo Doria11/2015
2063(17*10^194502+31)/3194503Robert Price01/2019
2064(19*10^194428+287)/9194429Robert Price10/2021
20652*10^194413+3194414Robert Price07/2015
20662^645360-1848599194273Enzo Doria08/2015
206722470^44641+44641^22470194260Norbert Schneider08/2023
2068(112*10^194150-1)/3194152Serge Batalov12/2014
2069Phi(293127,10)194041Makoto Kamada12/2023
20702*10^193981-43193982Robert Price04/2018
20712^644382+75169193979Enzo Doria04/2016
20722^644304-1861409193955Enzo Doria11/2015
2073(29*10^193950-23)/3193951Robert Price03/2022
20745*10^193907-9193908Robert Price05/2015
20752^644043+1876703193877Enzo Doria07/2016
20762*10^193841-63193842Robert Price01/2022
20772^643735+1879733193784Enzo Doria09/2016
2078(5^277183+1)/6193742Paul Bourdelais07/2010
20799*10^193712+71193713Robert Price08/2020
20802^643216-286565193628Enzo Doria07/2015
20812^643204+215011193624Enzo Doria11/2023
208210^193566+1126339193567Patrick De Geest09/2022
208410^193566-10000000001193566Robert Price04/2021
208310^193566-454041193566Patrick De Geest08/2021
20862^642888-24965193529Enzo Doria09/2013
20852^642889+25367193529Enzo Doria11/2023
20872^642448-114825193397Enzo Doria05/2015
20882^642437-1856623193393Enzo Doria10/2015
20892^642039-59797193273Enzo Doria11/2015
20902^641987+39193258Jon Grantham08/2023
209110^193230+513861193231Patrick De Geest07/2018
209210^193230-8001193230Robert Price03/2018
2093(62*10^193225-233)/9193226Robert Price02/2022
20942^641692-286349193169Enzo Doria07/2015
20952^641690-24737193168Enzo Doria09/2013
209622268^44421+44421^22268193129Norbert Schneider06/2023
20972^641514+1876549193115Enzo Doria07/2016
20982^640888-2785619192927Enzo Doria10/2015
20992^640874-2783741192923Enzo Doria09/2015
210010^192922+192207192923Patrick De Geest08/2021
210110^192922-7001192922Robert Price04/2021
21022^640854+25192917Stefano Morozzi05/2021
210334*10^192868-9192870Robert Price06/2020
2104(46*10^192841+683)/9192842Robert Price03/2019
21052^640181+467192714Lelio R Paula08/2013
21062^640072+27541192681Enzo Doria01/2024
21072^639536-1850249192520Enzo Doria08/2015
210840714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
21095*10^192422-43192423Robert Price01/2019
21102^639110-2792441192392Enzo Doria02/2016
2111(241^80761-1)/240192372Anonymous04/2024
21122^638955-29827192345Enzo Doria08/2015
211315^163539+14192337Alfred Reich10/2023
21142^638713-2784223192272Enzo Doria10/2015
2115(10^192216+7)/149192214Alfred Reich07/2021
21162^638490-113507192205Enzo Doria08/2014
21172^638189-39943192115Enzo Doria09/2015
21182^638110+1877119192091Enzo Doria07/2016
2119MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440192083Sergey Batalov05/2024
2120MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)192083Sergey Batalov05/2024
21212^638066-2785211192078Enzo Doria10/2015
2122(35*10^191973-341)/9191974Robert Price08/2021
2123(112*10^191900+17)/3191902Robert Price03/2020
21242^637475-115309191900Enzo Doria07/2015
2125(68*10^191754-113)/9191755Robert Price03/2021
21262^636930-11191736Stefano Morozzi07/2022
2127(47*10^191732+259)/9191733Robert Price03/2022
21282^636661+1876577191655Enzo Doria07/2016
2129(9^200807-2^200807)/7191618Jon Grantham07/2023
2130(34^125101-1)/33191589Paul Bourdelais11/2017
2131fibonacci(916540)-2191546Jon Grantham08/2023
21322^636177-1855123191509Enzo Doria09/2015
21332^636158-113627191503Enzo Doria08/2014
2134(37*25^136966+63)/4191472Curtis Bright05/2015
21352^636035+79823191466Enzo Doria06/2016
21362^636011-1860847191459Enzo Doria11/2015
21372^635926-1860611191433Enzo Doria11/2015
21383*2^635755+5191382Jon Grantham07/2023
21393*10^191152-7191153Robert Price08/2015
21402^634883-1865677191119Enzo Doria02/2016
21412^634801+1871957191095Enzo Doria05/2016
2142(77*10^191080+157)/9191081Robert Price05/2022
2143(35*10^191073+1)/9191074Serge Batalov07/2010
21449*10^191018-41191019Robert Price08/2020
21452^634470-59861190995Enzo Doria11/2015
21462^634368-29519190964Enzo Doria08/2015
2147(19*10^190935+11)/3190936Robert Price07/2023
21482^634188-350609190910Enzo Doria06/2015
2149(65*10^190899+493)/9190900Robert Price08/2021
2150(62*10^190795-413)/9190796Robert Price09/2021
2151(26*10^190789-131)/3190790Robert Price10/2019
2152(13*10^190732-61)/3190733Robert Price11/2018
21533*2^633524+5190711Jon Grantham07/2023
2154(7*10^190683+143)/3190684Robert Price03/2018
21552^633088-113879190579Enzo Doria10/2014
21562^633064+1874911190572Enzo Doria06/2016
21575*3^399402+2^399402190564Jon Grantham08/2023
2158(43*10^190547+83)/9190548Robert Price11/2018
215999*10^190543+7190545Robert Price05/2021
2160(299*10^190533+1)/3190535Robert Price04/2020
2161(1744*10^190519-1747)/3190522Robert Price12/2020
21622^632815-15190497Stefano Morozzi07/2022
21632^632795-351205190491Enzo Doria06/2015
216441171^41272+41272^41171190454Norbert Schneider05/2023
2165(16*10^190420-19)/3190421Robert Price02/2019
2166(43*10^190351+101)/9190352Robert Price11/2018
21672^632156+78391190298Enzo Doria06/2016
216897*10^190295-3190297Robert Price05/2020
21692^632082-1851971190276Enzo Doria08/2015
21702^632020+1880311190257Enzo Doria09/2016
2171(5*10^190242-77)/9190242Robert Price04/2021
21727*10^190210+13190211Robert Price03/2021
21732^631637-462373190142Enzo Doria08/2015
21742*10^190126-21190127Robert Price09/2020
2175(28*10^190105+191)/3190106Robert Price02/2020
21762*10^190093+33190094Robert Price11/2021
2177(68*10^190053-113)/9190054Robert Price03/2021
21782^631183+213413190006Enzo Doria09/2023
21792^631122-39251189987Enzo Doria08/2015
2180(26*10^189928-89)/9189929Robert Price06/2018
21812^630839-97189902Yves Minet07/2017
218299*10^189876-7189878Robert Price07/2020
21832^630359+1788953189757Enzo Doria05/2016
21842^630228+1871971189718Enzo Doria05/2016
21852^630108+781189682Lelio R Paula08/2013
21862^629870-1867811189610Enzo Doria04/2016
2187(359^74189-1)/358189558Alexander Zhirkov11/2017
21882^629326+2792929189447Enzo Doria02/2016
21894*10^189401+13189402Robert Price02/2021
2190(10^189385-61)/3189385Serge Batalov12/2014
21912^629036+1874011189359Enzo Doria06/2016
21922^628930+80779189327Enzo Doria07/2016
2193(134*10^189309-11)/3189311Robert Price01/2022
21949*10^189306-11189307Mischa Rodermond04/2023
21953^396740-396740^3189294Henri Lifchitz07/2024
21962^628582+1179439189223Enzo Doria06/2016
2197(44*10^188999-503)/9189000Robert Price12/2018
2198(16*10^188823+167)/3188824Robert Price06/2019
2199(10^188796+7)/4967/71933188788Alfred Reich08/2021
22002^627037-2785843188757Enzo Doria10/2015
2201(10^188566+7)/311640753181661188552Alfred Reich04/2022
2202(16*10^188457+161)/3188458Robert Price02/2019
2203L(901657)188436Renaud Lifchitz11/2008
2204(19*10^188375+137)/3188376Robert Price03/2022
22052^625651+74213188340Enzo Doria04/2016
22062^625584-460919188320Enzo Doria06/2015
2207(8*10^188308-71)/9188308Serge Batalov11/2022
22085^269399-3^269399-1188302Jon Grantham08/2023
2209(14*10^188218+139)/9188219Robert Price11/2021
2210(10^188164+359)/9188164Serge Batalov12/2014
22112^624481-113611187988Enzo Doria08/2014
2212(2^624389+125582)/2187960Stefano Morozzi09/2019
2213(2^624389+166982)/2187960Stefano Morozzi09/2019
2214(2^624389+179886)/2187960Stefano Morozzi09/2019
2215(2^624387+64466)/2187959Stefano Morozzi09/2019
2216(2^624378+112990)/2187957Stefano Morozzi09/2019
2217(2^624380+161986)/2187957Stefano Morozzi09/2019
2219(2^624376+55762)/2187956Stefano Morozzi09/2019
2218(2^624377+169506)/2187956Stefano Morozzi09/2019
2220(2^624355+80178)/2187950Stefano Morozzi09/2019
2221(2^624351+61350)/2187949Stefano Morozzi09/2019
2222(2^624341+63462)/2187946Stefano Morozzi09/2019
2223(2^624344+135990)/2187946Stefano Morozzi09/2019
2224(2^624344+183898)/2187946Stefano Morozzi09/2019
2226(2^624340+126982)/2187945Stefano Morozzi09/2019
2225(2^624338+196110)/2187945Stefano Morozzi09/2019
2227(2^624337+105162)/2187944Stefano Morozzi09/2019
2228(2^624333+44594)/2187943Stefano Morozzi09/2019
2229(2^624321+88742)/2187940Stefano Morozzi09/2019
2230(2^624324+135178)/2187940Stefano Morozzi09/2019
2231(2^624317+14186)/2187938Stefano Morozzi09/2019
2232(2^624313+24450)/2187937Stefano Morozzi09/2019
2233(2^624309+184590)/2187936Stefano Morozzi09/2019
2235(2^624307+152658)/2187935Stefano Morozzi09/2019
2234(2^624307+185978)/2187935Stefano Morozzi09/2019
2236(2^624303+40814)/2187934Stefano Morozzi09/2019
2237(2^624304+99238)/2187934Stefano Morozzi09/2019
22382^624077-112723187866Enzo Doria07/2014
22392^624008+1874941187846Enzo Doria06/2016
22402^623870+78679187804Enzo Doria05/2016
22412^623714-114035187757Enzo Doria11/2014
22422^623651-1834251187738Enzo Doria07/2015
2243(7*10^187645+53)/3187646Robert Price05/2018
224421650^43269+43269^21650187591Norbert Schneider02/2023
22452^623146+1879609187586Enzo Doria09/2016
2246(401*10^187512+13)/9187514Robert Price09/2021
2247(5*10^187471+91)/3187472Robert Price04/2018
22482^622500+81931187392Enzo Doria08/2016
2249(13*10^187382-157)/9187383Robert Price05/2021
22502^622300-1861739187331Enzo Doria12/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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