PRP Records

Probable Primes Top 10000

(296025 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 ?
2001numbpart(32235776596)200002Serge Batalov04/2017
2002(10^200001+149)/3200001Serge Batalov12/2014
200310^200000+571791200001Patrick De Geest08/2019
2004(3^419180-621444)/3200000Stefano Morozzi06/2019
2005(3^419180-1941384)/3200000Stefano Morozzi08/2019
200610^200000-45557200000Patrick De Geest08/2019
2007(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
20082593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
2009(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
2010(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
2011(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
2012(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
201392*10^199980-9199982Robert Price12/2021
2014(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
2015(85*10^199951-139)/9199952Robert Price08/2021
2016(10^199926+7)/29/373/2339199919Alfred Reich08/2021
20172^663838+25819199836Enzo Doria11/2023
201823*10^199833-9199835Robert Price10/2021
2019fibonacci(956176)-4199829Jon Grantham08/2023
2020(299*10^199801-17)/3199803Robert Price04/2020
20216*10^199788+77199789Robert Price06/2020
2022(2^663604+1)/270750449199757Anonymous10/2024
2023(23*10^199615+37)/3199616Robert Price02/2022
2024(17*10^199607-167)/3199608Robert Price05/2022
20252^663020-933075199589Paul Bourdelais06/2021
20262^663007+29963199585Enzo Doria03/2024
20273*2^662703-5199494Jon Grantham07/2023
2028(14*10^199447+73)/3199448Robert Price12/2018
2029(2^662424-15)/7199409Stefano Morozzi08/2022
20302^662194+22189199341Enzo Doria09/2023
20312^662103-29287199313Enzo Doria08/2015
2032(2*10^199283+457)/9199283Robert Price01/2018
2033(10^199248-19)/9199248Robert Price01/2018
2034(83*10^199213+529)/9199214Robert Price12/2021
2035(194*10^199146-17)/3199148Robert Price09/2020
2036(151*10^199003-1)/3199005Robert Price03/2020
20379*10^198946-73198947Robert Price01/2021
203845*10^198931-7198933Robert Price07/2020
20392^660482-2891198825Yves Minet05/2016
20402^659594+37729198558Enzo Doria10/2024
20412^659589-21198557Stefano Morozzi07/2022
20422^659583+1879223198555Enzo Doria08/2016
2043(53*10^198529+1)/9198530Serge Batalov07/2010
2044(49*10^198403+311)/9198404Robert Price06/2019
204596*10^198376-7198378Robert Price03/2021
2046(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
20472^658828-29819198327Enzo Doria08/2015
20482^658776-2791229198312Enzo Doria01/2016
2049(35*10^198294-377)/9198295Robert Price07/2018
2050(4*10^198268+137)/3198269Robert Price03/2018
20512^658544-1854029198242Enzo Doria09/2015
2052(62*10^198229-233)/9198230Robert Price02/2022
2053(26*10^198200-41)/3198201Robert Price02/2022
2054(157^90239-1)/156198154Alexander Zhirkov06/2016
20552^657815+26213198023Enzo Doria12/2023
20562*10^197959-37197960Robert Price11/2021
2057(29*10^197941-41)/3197942Tyler Busby03/2024
2058(232*10^197897+17)/3197899Robert Price04/2021
2059(4*10^197778+173)/3197779Robert Price02/2018
20602^656763+211373197706Enzo Doria08/2023
206178*10^197702-7197704Robert Price10/2020
2062(17*10^197640-23)/3197641Robert Price03/2021
2063(29*10^197629-77)/3197630Robert Price02/2020
20642^656462+1874419197615Enzo Doria06/2016
2065(89^101363+1)/90197595Paul Bourdelais11/2017
20662^655893-344563197444Enzo Doria07/2015
20672^655875+71333197439Enzo Doria04/2016
20682^655845-9197430Robert Price01/2017
2069(299*10^197426+1)/3197428Robert Price04/2020
20702^655682-1849121197380Enzo Doria08/2015
20714*10^197268-89197269Robert Price11/2018
2072(11*10^197198-89)/3197199Robert Price05/2021
20732^655045-49603197189Enzo Doria10/2015
20742^655000-2784089197175Enzo Doria10/2015
2075(18^157051-1)/17197141Paul Bourdelais03/2010
2076(4*10^197061+41)/9197061Serge Batalov11/2022
2077(154*10^197005+17)/9197007Robert Price06/2022
20782^654400-39719196995Enzo Doria09/2015
2079(5^281807-2^281807)/3196975Jon Grantham08/2023
2080(14*10^196965-221)/9196966Robert Price04/2018
20812^654216-459995196939Enzo Doria06/2015
2082(17*10^196921+31)/3196922Robert Price01/2019
2083(14*10^196885-89)/3196886Robert Price05/2020
20843*10^196881-59196882Robert Price09/2018
20852^653851+82295196829Enzo Doria09/2016
2086(38*10^196792+691)/9196793Robert Price10/2018
2087(65*10^196768+493)/9196769Robert Price08/2021
20892^653636-29429196765Enzo Doria08/2015
20882^653638-11196765Stefano Morozzi07/2022
20902^653601-69673196754Enzo Doria02/2016
2091(44*10^196684+1)/9196685Serge Batalov07/2010
20922^652786-1852571196509Enzo Doria08/2015
20932^652752-1325196498Yves Minet07/2015
20942^652470-1859141196414Enzo Doria10/2015
20952^652346+29329196376Enzo Doria02/2024
20962^652307+1877483196364Enzo Doria08/2016
20972^652293-115273196360Enzo Doria06/2015
2098(47*10^196281+403)/9196282Robert Price03/2019
20992^652025+218027196280Enzo Doria01/2024
21002^652004+23961196273Enzo Doria10/2023
2101(7*10^196125-31)/3196126Robert Price12/2021
210233^129128+129128^33196083Norbert Schneider06/2022
21036*10^196070+73196071Robert Price04/2019
21042^651218-1868201196037Enzo Doria04/2016
21052^651047-49687195985Enzo Doria10/2015
210610^195968-700001195968Robert Price08/2021
2107fibonacci(937485)+3195923Jon Grantham08/2023
2108(29*10^195875-197)/3195876Robert Price08/2021
2109(25*10^195808-97)/9195809Robert Price01/2022
21102^650285-2785333195756Enzo Doria10/2015
2111(10^195732+7)/18089/49605893195721Alfred Reich08/2021
2112(29*10^195648-41)/3195649Tyler Busby03/2024
2113(69^106397-1)/68195647Paul Bourdelais10/2017
21142^649811+1877573195613Enzo Doria08/2016
21152^649662-170531195568Hans Havermann10/2018
21162^649586+182839195545Enzo Doria11/2016
21172^649537-1867363195531Enzo Doria04/2016
21182^649536-1861499195530Enzo Doria12/2015
21192^649493+25907195517Enzo Doria11/2023
2120(103*10^195478-1)/3195480Serge Batalov12/2014
21212^649102-59351195400Enzo Doria10/2015
2122(2*10^195399+529)/9195399Robert Price01/2018
2123(202*10^195383-13)/9195385Robert Price01/2020
21242^648988+1178971195365Enzo Doria06/2016
21252^648975-114319195361Enzo Doria02/2015
2126(11*10^195350-137)/9195351Robert Price01/2018
21272^648619-24835195254Enzo Doria09/2013
21285*10^195250-21195251Robert Price12/2021
2129(14*10^195234-83)/3195235Robert Price12/2018
21305*10^195221+81195222Robert Price03/2019
213110^195143-5001195143Robert Price12/2021
21322^648190-24737195125Enzo Doria09/2013
2133(57^111119+1)/58195110Paul Bourdelais10/2017
2134(29*10^195098-197)/3195099Robert Price08/2021
213510^195060+89701195061Patrick De Geest02/2021
213710^195060-40000000001195060Robert Price09/2020
213610^195060-110337195060Patrick De Geest02/2021
213856*10^195032-3195034Robert Price03/2020
213911^187185-90194934Enzo Doria09/2012
21402^647468+220141194908Enzo Doria03/2024
2141(86*10^194818-437)/9194819Robert Price03/2021
21427^230492-230492^7194789Henri Lifchitz07/2024
21432^647068+77281194787Enzo Doria05/2016
21442*10^194716-93194717Robert Price12/2021
214515^165559-14^165559194713Jean-Louis Charton03/2011
2146F(931517)194676Henri Lifchitz09/2008
21474*10^194668+49194669Robert Price01/2019
21482^646589+1179407194643Enzo Doria06/2016
21492^646289-114621194553Enzo Doria05/2015
21502^646236-39659194537Enzo Doria09/2015
2151(16*10^194536+53)/3194537Robert Price03/2019
21522^646161-59833194514Enzo Doria11/2015
2153(17*10^194502+31)/3194503Robert Price01/2019
2154(19*10^194428+287)/9194429Robert Price10/2021
21552*10^194413+3194414Robert Price07/2015
21562^645360-1848599194273Enzo Doria08/2015
215722470^44641+44641^22470194260Norbert Schneider08/2023
2158(112*10^194150-1)/3194152Serge Batalov12/2014
2159Phi(293127,10)194041Makoto Kamada12/2023
21602*10^193981-43193982Robert Price04/2018
21612^644382+75169193979Enzo Doria04/2016
21622^644304-1861409193955Enzo Doria11/2015
2163(29*10^193950-23)/3193951Robert Price03/2022
21645*10^193907-9193908Robert Price05/2015
21652^644043+1876703193877Enzo Doria07/2016
21662*10^193841-63193842Robert Price01/2022
21672^643735+1879733193784Enzo Doria09/2016
2168(5^277183+1)/6193742Paul Bourdelais07/2010
21699*10^193712+71193713Robert Price08/2020
21702^643216-286565193628Enzo Doria07/2015
21712^643204+215011193624Enzo Doria11/2023
217210^193566+1126339193567Patrick De Geest09/2022
217410^193566-10000000001193566Robert Price04/2021
217310^193566-454041193566Patrick De Geest08/2021
21762^642888-24965193529Enzo Doria09/2013
21752^642889+25367193529Enzo Doria11/2023
21772^642448-114825193397Enzo Doria05/2015
21782^642437-1856623193393Enzo Doria10/2015
21792^642039-59797193273Enzo Doria11/2015
21802^641987+39193258Jon Grantham08/2023
218110^193230+513861193231Patrick De Geest07/2018
218210^193230-8001193230Robert Price03/2018
2183(62*10^193225-233)/9193226Robert Price02/2022
21842^641692-286349193169Enzo Doria07/2015
21852^641690-24737193168Enzo Doria09/2013
218622268^44421+44421^22268193129Norbert Schneider06/2023
21872^641514+1876549193115Enzo Doria07/2016
21882^640888-2785619192927Enzo Doria10/2015
21892^640874-2783741192923Enzo Doria09/2015
219010^192922+192207192923Patrick De Geest08/2021
219110^192922-7001192922Robert Price04/2021
21922^640854+25192917Stefano Morozzi05/2021
219334*10^192868-9192870Robert Price06/2020
2194(46*10^192841+683)/9192842Robert Price03/2019
21952^640181+467192714Lelio R Paula08/2013
21962^640072+27541192681Enzo Doria01/2024
21972^639536-1850249192520Enzo Doria08/2015
219840714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
21995*10^192422-43192423Robert Price01/2019
22002^639110-2792441192392Enzo Doria02/2016
2201(241^80761-1)/240192372Anonymous04/2024
22022^638955-29827192345Enzo Doria08/2015
220315^163539+14192337Alfred Reich10/2023
22042^638713-2784223192272Enzo Doria10/2015
2205(10^192216+7)/149192214Alfred Reich07/2021
22062^638490-113507192205Enzo Doria08/2014
22072^638189-39943192115Enzo Doria09/2015
22082^638110+1877119192091Enzo Doria07/2016
2209MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)+82440192083Sergey Batalov05/2024
2210MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832)192083Sergey Batalov05/2024
22112^638066-2785211192078Enzo Doria10/2015
2212(35*10^191973-341)/9191974Robert Price08/2021
2213(112*10^191900+17)/3191902Robert Price03/2020
22142^637475-115309191900Enzo Doria07/2015
2215(68*10^191754-113)/9191755Robert Price03/2021
22162^636930-11191736Stefano Morozzi07/2022
2217(47*10^191732+259)/9191733Robert Price03/2022
22182^636661+1876577191655Enzo Doria07/2016
2219(9^200807-2^200807)/7191618Jon Grantham07/2023
2220(34^125101-1)/33191589Paul Bourdelais11/2017
2221fibonacci(916540)-2191546Jon Grantham08/2023
22222^636177-1855123191509Enzo Doria09/2015
22232^636158-113627191503Enzo Doria08/2014
2224(37*25^136966+63)/4191472Curtis Bright05/2015
22252^636035+79823191466Enzo Doria06/2016
22262^636011-1860847191459Enzo Doria11/2015
22272^635926-1860611191433Enzo Doria11/2015
22283*2^635755+5191382Jon Grantham07/2023
22293*10^191152-7191153Robert Price08/2015
22302^634883-1865677191119Enzo Doria02/2016
22312^634801+1871957191095Enzo Doria05/2016
2232(77*10^191080+157)/9191081Robert Price05/2022
2233(35*10^191073+1)/9191074Serge Batalov07/2010
22349*10^191018-41191019Robert Price08/2020
22352^634470-59861190995Enzo Doria11/2015
22362^634368-29519190964Enzo Doria08/2015
2237(19*10^190935+11)/3190936Robert Price07/2023
22382^634188-350609190910Enzo Doria06/2015
2239(65*10^190899+493)/9190900Robert Price08/2021
2240(62*10^190795-413)/9190796Robert Price09/2021
2241(26*10^190789-131)/3190790Robert Price10/2019
2242(13*10^190732-61)/3190733Robert Price11/2018
22433*2^633524+5190711Jon Grantham07/2023
2244(7*10^190683+143)/3190684Robert Price03/2018
22452^633088-113879190579Enzo Doria10/2014
22462^633064+1874911190572Enzo Doria06/2016
22475*3^399402+2^399402190564Jon Grantham08/2023
2248(43*10^190547+83)/9190548Robert Price11/2018
224999*10^190543+7190545Robert Price05/2021
2250(299*10^190533+1)/3190535Robert Price04/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 22 2024 15:56 (Time in France)

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