PRP Records

Probable Primes Top 10000

(288949 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 ?
10012^699740+25210643Stefano Morozzi05/2021
10022^698929-2788423210399Enzo Doria11/2015
1003(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
10042^698316+1878601210215Enzo Doria08/2016
10052^697036+1878751209829Enzo Doria08/2016
10066^269407+5209640Paul Bourdelais02/2021
1007(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
10082^696254-115151209594Enzo Doria06/2015
1009(35^135623+1)/36209410Paul Bourdelais07/2018
10102^694633+1887257209106Enzo Doria05/2017
10112^693959+180923208903Enzo Doria07/2016
10122^693462-1847561208753Enzo Doria07/2015
10132^690890-59981207979Enzo Doria11/2015
1014(38^131591+1)/39207884Paul Bourdelais07/2018
10152^690163+1877063207760Enzo Doria07/2016
10167^245608-2207563Paul Bourdelais01/2021
10172^689286-29381207496Enzo Doria08/2015
10182^689122-114521207447Enzo Doria04/2015
10192^688373+6077207221Enzo Doria02/2016
10202^688201+1875527207170Enzo Doria07/2016
1021(42^127609+1)/43207140Paul Bourdelais07/2018
10222^687619+81563206994Enzo Doria08/2016
10232^686572-1845299206679Enzo Doria07/2015
1024(21^156217-1)/20206552Paul Bourdelais04/2010
1025(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
10262^685578+3206380Paul Bourdelais04/2012
10272^684836-49349206157Enzo Doria10/2015
1028(73^110603-1)/72206088Paul Bourdelais06/2018
10292^684163-2790967205954Enzo Doria12/2015
1030326^81943-325^81943205941Jean-Louis Charton07/2012
1031(2^684127-1)/23765203727205933Jens K. Andersen04/2009
10324^341233-3^341233205443Jean-Louis Charton01/2006
10332^681545+467205166Lelio R Paula11/2013
10342^681306+81049205094Enzo Doria07/2016
10352^680697+1877057204911Enzo Doria07/2016
10362^680415+71783204826Enzo Doria04/2016
10372^679860-459995204659Enzo Doria06/2015
10382^679593+1879547204578Enzo Doria09/2016
10392^678651+1875023204295Enzo Doria07/2016
10402^678561+678561204268Henri Lifchitz05/2006
10412^678101-114043204129Enzo Doria11/2014
10422^678028+1875631204107Enzo Doria06/2016
10432^676992-59783203795Enzo Doria10/2015
10442^676972+1866871203789Enzo Doria03/2016
10452^676761-9203726Robert Price01/2017
10462^676563-2792407203666Enzo Doria02/2016
10472^676306-114713203589Enzo Doria04/2015
1048(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
10492^674627-25161203083Enzo Doria09/2013
10502^674603-69337203076Enzo Doria12/2015
10512^674459+74213203033Enzo Doria04/2016
10522^674116-458879202930Enzo Doria04/2015
10532^674076-114755202918Enzo Doria04/2015
10545^289937-4^289937202658Jean-Louis Charton03/2013
1055(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
10562^672556-1835519202460Enzo Doria04/2015
10572^671446-351401202126Enzo Doria07/2015
10582^671373+77747202104Enzo Doria05/2016
10592^670726-114845201909Enzo Doria05/2015
10602^670539-25045201853Enzo Doria09/2013
106143284^43519-43519^43284201769Norbert Schneider08/2018
10622^670213+282317201755Enzo Doria09/2016
10632^670133+89201731Stefano Morozzi05/2021
10642^669854-113501201647Enzo Doria08/2014
10652^669718+81619201606Enzo Doria08/2016
1066(145*10^201504-1)/9201506Serge Batalov12/2014
10672^668938-1839821201371Enzo Doria06/2015
10682^668492+1879303201237Enzo Doria08/2016
10696^258413-5^258413201085Jean-Louis Charton03/2013
107010194^50161-50161^10194201063Norbert Schneider09/2020
10712^667894+1875589201057Enzo Doria06/2016
10722^667569-1836559200959Enzo Doria05/2015
1073(172*10^200746-1)/9200748Serge Batalov12/2014
10742^666430+782569200616Enzo Doria10/2016
1075(86^103471+1)/87200163Paul Bourdelais05/2018
1076103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
1077103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
1078numbpart(32235776596)200002Serge Batalov04/2017
1079(10^200001+149)/3200001Serge Batalov12/2014
108010^200000+571791200001Patrick De Geest08/2019
1081(3^419180-621444)/3200000Stefano Morozzi06/2019
1082(3^419180-1941384)/3200000Stefano Morozzi08/2019
108310^200000-45557200000Patrick De Geest08/2019
1084(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
108592*10^199980-9199982Robert Price12/2021
1086(85*10^199951-139)/9199952Robert Price08/2021
1087(10^199926+7)/29/373/2339199919Alfred Reich08/2021
108823*10^199833-9199835Robert Price10/2021
1089(299*10^199801-17)/3199803Robert Price04/2020
10906*10^199788+77199789Robert Price06/2020
10912^663020-933075199589Paul Bourdelais06/2021
1092(14*10^199447+73)/3199448Robert Price12/2018
10932^662103-29287199313Enzo Doria08/2015
1094(2*10^199283+457)/9199283Robert Price01/2018
1095(10^199248-19)/9199248Robert Price01/2018
1096(83*10^199213+529)/9199214Robert Price12/2021
1097(194*10^199146-17)/3199148Robert Price09/2020
1098(151*10^199003-1)/3199005Robert Price03/2020
10999*10^198946-73198947Robert Price01/2021
110045*10^198931-7198933Robert Price07/2020
11012^660482-2891198825Yves Minet05/2016
11022^659583+1879223198555Enzo Doria08/2016
1103(53*10^198529+1)/9198530Serge Batalov07/2010
1104(49*10^198403+311)/9198404Robert Price06/2019
110596*10^198376-7198378Robert Price03/2021
1106(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
11072^658828-29819198327Enzo Doria08/2015
11082^658776-2791229198312Enzo Doria01/2016
1109(35*10^198294-377)/9198295Robert Price07/2018
1110(4*10^198268+137)/3198269Robert Price03/2018
11112^658544-1854029198242Enzo Doria09/2015
1112(157^90239-1)/156198154Alexander Zhirkov06/2016
11132*10^197959-37197960Robert Price11/2021
1114(232*10^197897+17)/3197899Robert Price04/2021
1115(4*10^197778+173)/3197779Robert Price02/2018
111678*10^197702-7197704Robert Price10/2020
1117(17*10^197640-23)/3197641Robert Price03/2021
1118(29*10^197629-77)/3197630Robert Price02/2020
11192^656462+1874419197615Enzo Doria06/2016
1120(89^101363+1)/90197595Paul Bourdelais11/2017
11212^655893-344563197444Enzo Doria07/2015
11222^655875+71333197439Enzo Doria04/2016
11232^655845-9197430Robert Price01/2017
1124(299*10^197426+1)/3197428Robert Price04/2020
11252^655682-1849121197380Enzo Doria08/2015
11264*10^197268-89197269Robert Price11/2018
1127(11*10^197198-89)/3197199Robert Price05/2021
11282^655045-49603197189Enzo Doria10/2015
11292^655000-2784089197175Enzo Doria10/2015
1130(18^157051-1)/17197141Paul Bourdelais03/2010
11312^654400-39719196995Enzo Doria09/2015
1132(14*10^196965-221)/9196966Robert Price04/2018
11332^654216-459995196939Enzo Doria06/2015
1134(17*10^196921+31)/3196922Robert Price01/2019
1135(14*10^196885-89)/3196886Robert Price05/2020
11363*10^196881-59196882Robert Price09/2018
11372^653851+82295196829Enzo Doria09/2016
1138(38*10^196792+691)/9196793Robert Price10/2018
1139(65*10^196768+493)/9196769Robert Price08/2021
11402^653636-29429196765Enzo Doria08/2015
11412^653601-69673196754Enzo Doria02/2016
1142(44*10^196684+1)/9196685Serge Batalov07/2010
11432^652786-1852571196509Enzo Doria08/2015
11442^652752-1325196498Yves Minet07/2015
11452^652470-1859141196414Enzo Doria10/2015
11462^652307+1877483196364Enzo Doria08/2016
11472^652293-115273196360Enzo Doria06/2015
1148(47*10^196281+403)/9196282Robert Price03/2019
1149(7*10^196125-31)/3196126Robert Price12/2021
11506*10^196070+73196071Robert Price04/2019
11512^651218-1868201196037Enzo Doria04/2016
11522^651047-49687195985Enzo Doria10/2015
115310^195968-700001195968Robert Price08/2021
1154(29*10^195875-197)/3195876Robert Price08/2021
1155(25*10^195808-97)/9195809Robert Price01/2022
11562^650285-2785333195756Enzo Doria10/2015
1157(10^195732+7)/18089/49605893195721Alfred Reich08/2021
1158(69^106397-1)/68195647Paul Bourdelais10/2017
11592^649811+1877573195613Enzo Doria08/2016
11602^649662-170531195568Hans Havermann10/2018
11612^649586+182839195545Enzo Doria11/2016
11622^649537-1867363195531Enzo Doria04/2016
11632^649536-1861499195530Enzo Doria12/2015
1164(103*10^195478-1)/3195480Serge Batalov12/2014
11652^649102-59351195400Enzo Doria10/2015
1166(2*10^195399+529)/9195399Robert Price01/2018
1167(202*10^195383-13)/9195385Robert Price01/2020
11682^648988+1178971195365Enzo Doria06/2016
11692^648975-114319195361Enzo Doria02/2015
1170(11*10^195350-137)/9195351Robert Price01/2018
11712^648619-24835195254Enzo Doria09/2013
11725*10^195250-21195251Robert Price12/2021
1173(14*10^195234-83)/3195235Robert Price12/2018
11745*10^195221+81195222Robert Price03/2019
117510^195143-5001195143Robert Price12/2021
11762^648190-24737195125Enzo Doria09/2013
1177(57^111119+1)/58195110Paul Bourdelais10/2017
1178(29*10^195098-197)/3195099Robert Price08/2021
117910^195060+89701195061Patrick De Geest02/2021
118110^195060-40000000001195060Robert Price09/2020
118010^195060-110337195060Patrick De Geest02/2021
118256*10^195032-3195034Robert Price03/2020
118311^187185-90194934Enzo Doria09/2012
1184(86*10^194818-437)/9194819Robert Price03/2021
11852^647068+77281194787Enzo Doria05/2016
11862*10^194716-93194717Robert Price12/2021
118715^165559-14^165559194713Jean-Louis Charton03/2011
1188F(931517)194676Henri Lifchitz09/2008
11894*10^194668+49194669Robert Price01/2019
11902^646589+1179407194643Enzo Doria06/2016
11912^646289-114621194553Enzo Doria05/2015
11922^646236-39659194537Enzo Doria09/2015
1193(16*10^194536+53)/3194537Robert Price03/2019
11942^646161-59833194514Enzo Doria11/2015
1195(17*10^194502+31)/3194503Robert Price01/2019
1196(19*10^194428+287)/9194429Robert Price10/2021
11972*10^194413+3194414Robert Price07/2015
11982^645360-1848599194273Enzo Doria08/2015
1199(112*10^194150-1)/3194152Serge Batalov12/2014
12002*10^193981-43193982Robert Price04/2018
12012^644382+75169193979Enzo Doria04/2016
12022^644304-1861409193955Enzo Doria11/2015
12035*10^193907-9193908Robert Price05/2015
12042^644043+1876703193877Enzo Doria07/2016
12052*10^193841-63193842Robert Price01/2022
12062^643735+1879733193784Enzo Doria09/2016
1207(5^277183+1)/6193742Paul Bourdelais07/2010
12089*10^193712+71193713Robert Price08/2020
12092^643216-286565193628Enzo Doria07/2015
121010^193566-10000000001193566Robert Price04/2021
121110^193566-454041193566Patrick De Geest08/2021
12122^642888-24965193529Enzo Doria09/2013
12132^642448-114825193397Enzo Doria05/2015
12142^642437-1856623193393Enzo Doria10/2015
12152^642039-59797193273Enzo Doria11/2015
121610^193230+513861193231Patrick De Geest07/2018
121710^193230-8001193230Robert Price03/2018
12182^641692-286349193169Enzo Doria07/2015
12192^641690-24737193168Enzo Doria09/2013
12202^641514+1876549193115Enzo Doria07/2016
12212^640888-2785619192927Enzo Doria10/2015
12222^640874-2783741192923Enzo Doria09/2015
122310^192922+192207192923Patrick De Geest08/2021
122410^192922-7001192922Robert Price04/2021
12252^640854+25192917Stefano Morozzi05/2021
122634*10^192868-9192870Robert Price06/2020
1227(46*10^192841+683)/9192842Robert Price03/2019
12282^640181+467192714Lelio R Paula08/2013
12292^639536-1850249192520Enzo Doria08/2015
123040714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
12315*10^192422-43192423Robert Price01/2019
12322^639110-2792441192392Enzo Doria02/2016
12332^638955-29827192345Enzo Doria08/2015
12342^638713-2784223192272Enzo Doria10/2015
1235(10^192216+7)/149192214Alfred Reich07/2021
12362^638490-113507192205Enzo Doria08/2014
12372^638189-39943192115Enzo Doria09/2015
12382^638110+1877119192091Enzo Doria07/2016
12392^638066-2785211192078Enzo Doria10/2015
1240(35*10^191973-341)/9191974Robert Price08/2021
1241(112*10^191900+17)/3191902Robert Price03/2020
12422^637475-115309191900Enzo Doria07/2015
1243(68*10^191754-113)/9191755Robert Price03/2021
12442^636661+1876577191655Enzo Doria07/2016
1245(34^125101-1)/33191589Paul Bourdelais11/2017
12462^636177-1855123191509Enzo Doria09/2015
12472^636158-113627191503Enzo Doria08/2014
1248(37*25^136966+63)/4191472Curtis Bright05/2015
12492^636035+79823191466Enzo Doria06/2016
12502^636011-1860847191459Enzo Doria11/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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