PRP Records

Probable Primes Top 10000

(288515 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 ?
1001(42^127609+1)/43207140Paul Bourdelais07/2018
10022^687619+81563206994Enzo Doria08/2016
10032^686572-1845299206679Enzo Doria07/2015
1004(21^156217-1)/20206552Paul Bourdelais04/2010
1005(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
10062^685578+3206380Paul Bourdelais04/2012
10072^684836-49349206157Enzo Doria10/2015
1008(73^110603-1)/72206088Paul Bourdelais06/2018
10092^684163-2790967205954Enzo Doria12/2015
1010326^81943-325^81943205941Jean-Louis Charton07/2012
1011(2^684127-1)/23765203727205933Jens K. Andersen04/2009
10124^341233-3^341233205443Jean-Louis Charton01/2006
10132^681545+467205166Lelio R Paula11/2013
10142^681306+81049205094Enzo Doria07/2016
10152^680697+1877057204911Enzo Doria07/2016
10162^680415+71783204826Enzo Doria04/2016
10172^679860-459995204659Enzo Doria06/2015
10182^679593+1879547204578Enzo Doria09/2016
10192^678651+1875023204295Enzo Doria07/2016
10202^678561+678561204268Henri Lifchitz05/2006
10212^678101-114043204129Enzo Doria11/2014
10222^678028+1875631204107Enzo Doria06/2016
10232^676992-59783203795Enzo Doria10/2015
10242^676972+1866871203789Enzo Doria03/2016
10252^676761-9203726Robert Price01/2017
10262^676563-2792407203666Enzo Doria02/2016
10272^676306-114713203589Enzo Doria04/2015
1028(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
10292^674627-25161203083Enzo Doria09/2013
10302^674603-69337203076Enzo Doria12/2015
10312^674459+74213203033Enzo Doria04/2016
10322^674116-458879202930Enzo Doria04/2015
10332^674076-114755202918Enzo Doria04/2015
10345^289937-4^289937202658Jean-Louis Charton03/2013
1035(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
10362^672556-1835519202460Enzo Doria04/2015
10372^671446-351401202126Enzo Doria07/2015
10382^671373+77747202104Enzo Doria05/2016
10392^670726-114845201909Enzo Doria05/2015
10402^670539-25045201853Enzo Doria09/2013
104143284^43519-43519^43284201769Norbert Schneider08/2018
10422^670213+282317201755Enzo Doria09/2016
10432^670133+89201731Stefano Morozzi05/2021
10442^669854-113501201647Enzo Doria08/2014
10452^669718+81619201606Enzo Doria08/2016
1046(145*10^201504-1)/9201506Serge Batalov12/2014
10472^668938-1839821201371Enzo Doria06/2015
10482^668492+1879303201237Enzo Doria08/2016
10496^258413-5^258413201085Jean-Louis Charton03/2013
105010194^50161-50161^10194201063Norbert Schneider09/2020
10512^667894+1875589201057Enzo Doria06/2016
10522^667569-1836559200959Enzo Doria05/2015
1053(172*10^200746-1)/9200748Serge Batalov12/2014
10542^666430+782569200616Enzo Doria10/2016
1055(86^103471+1)/87200163Paul Bourdelais05/2018
1056103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
1057103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
1058numbpart(32235776596)200002Serge Batalov04/2017
1059(10^200001+149)/3200001Serge Batalov12/2014
106010^200000+571791200001Patrick De Geest08/2019
1061(3^419180-621444)/3200000Stefano Morozzi06/2019
1062(3^419180-1941384)/3200000Stefano Morozzi08/2019
106310^200000-45557200000Patrick De Geest08/2019
1064(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
1065(85*10^199951-139)/9199952Robert Price08/2021
1066(10^199926+7)/29/373/2339199919Alfred Reich08/2021
106723*10^199833-9199835Robert Price10/2021
1068(299*10^199801-17)/3199803Robert Price04/2020
10696*10^199788+77199789Robert Price06/2020
10702^663020-933075199589Paul Bourdelais06/2021
1071(14*10^199447+73)/3199448Robert Price12/2018
10722^662103-29287199313Enzo Doria08/2015
1073(2*10^199283+457)/9199283Robert Price01/2018
1074(10^199248-19)/9199248Robert Price01/2018
1075(194*10^199146-17)/3199148Robert Price09/2020
1076(151*10^199003-1)/3199005Robert Price03/2020
10779*10^198946-73198947Robert Price01/2021
107845*10^198931-7198933Robert Price07/2020
10792^660482-2891198825Yves Minet05/2016
10802^659583+1879223198555Enzo Doria08/2016
1081(53*10^198529+1)/9198530Serge Batalov07/2010
1082(49*10^198403+311)/9198404Robert Price06/2019
108396*10^198376-7198378Robert Price03/2021
1084(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
10852^658828-29819198327Enzo Doria08/2015
10862^658776-2791229198312Enzo Doria01/2016
1087(35*10^198294-377)/9198295Robert Price07/2018
1088(4*10^198268+137)/3198269Robert Price03/2018
10892^658544-1854029198242Enzo Doria09/2015
1090(157^90239-1)/156198154Alexander Zhirkov06/2016
10912*10^197959-37197960Robert Price11/2021
1092(232*10^197897+17)/3197899Robert Price04/2021
1093(4*10^197778+173)/3197779Robert Price02/2018
109478*10^197702-7197704Robert Price10/2020
1095(17*10^197640-23)/3197641Robert Price03/2021
1096(29*10^197629-77)/3197630Robert Price02/2020
10972^656462+1874419197615Enzo Doria06/2016
1098(89^101363+1)/90197595Paul Bourdelais11/2017
10992^655893-344563197444Enzo Doria07/2015
11002^655875+71333197439Enzo Doria04/2016
11012^655845-9197430Robert Price01/2017
1102(299*10^197426+1)/3197428Robert Price04/2020
11032^655682-1849121197380Enzo Doria08/2015
11044*10^197268-89197269Robert Price11/2018
1105(11*10^197198-89)/3197199Robert Price05/2021
11062^655045-49603197189Enzo Doria10/2015
11072^655000-2784089197175Enzo Doria10/2015
1108(18^157051-1)/17197141Paul Bourdelais03/2010
11092^654400-39719196995Enzo Doria09/2015
1110(14*10^196965-221)/9196966Robert Price04/2018
11112^654216-459995196939Enzo Doria06/2015
1112(17*10^196921+31)/3196922Robert Price01/2019
1113(14*10^196885-89)/3196886Robert Price05/2020
11143*10^196881-59196882Robert Price09/2018
11152^653851+82295196829Enzo Doria09/2016
1116(38*10^196792+691)/9196793Robert Price10/2018
1117(65*10^196768+493)/9196769Robert Price08/2021
11182^653636-29429196765Enzo Doria08/2015
11192^653601-69673196754Enzo Doria02/2016
1120(44*10^196684+1)/9196685Serge Batalov07/2010
11212^652786-1852571196509Enzo Doria08/2015
11222^652752-1325196498Yves Minet07/2015
11232^652470-1859141196414Enzo Doria10/2015
11242^652307+1877483196364Enzo Doria08/2016
11252^652293-115273196360Enzo Doria06/2015
1126(47*10^196281+403)/9196282Robert Price03/2019
11276*10^196070+73196071Robert Price04/2019
11282^651218-1868201196037Enzo Doria04/2016
11292^651047-49687195985Enzo Doria10/2015
113010^195968-700001195968Robert Price08/2021
1131(29*10^195875-197)/3195876Robert Price08/2021
11322^650285-2785333195756Enzo Doria10/2015
1133(10^195732+7)/18089/49605893195721Alfred Reich08/2021
1134(69^106397-1)/68195647Paul Bourdelais10/2017
11352^649811+1877573195613Enzo Doria08/2016
11362^649662-170531195568Hans Havermann10/2018
11372^649586+182839195545Enzo Doria11/2016
11382^649537-1867363195531Enzo Doria04/2016
11392^649536-1861499195530Enzo Doria12/2015
1140(103*10^195478-1)/3195480Serge Batalov12/2014
11412^649102-59351195400Enzo Doria10/2015
1142(2*10^195399+529)/9195399Robert Price01/2018
1143(202*10^195383-13)/9195385Robert Price01/2020
11442^648988+1178971195365Enzo Doria06/2016
11452^648975-114319195361Enzo Doria02/2015
1146(11*10^195350-137)/9195351Robert Price01/2018
11472^648619-24835195254Enzo Doria09/2013
1148(14*10^195234-83)/3195235Robert Price12/2018
11495*10^195221+81195222Robert Price03/2019
11502^648190-24737195125Enzo Doria09/2013
1151(57^111119+1)/58195110Paul Bourdelais10/2017
1152(29*10^195098-197)/3195099Robert Price08/2021
115310^195060+89701195061Patrick De Geest02/2021
115510^195060-40000000001195060Robert Price09/2020
115410^195060-110337195060Patrick De Geest02/2021
115656*10^195032-3195034Robert Price03/2020
115711^187185-90194934Enzo Doria09/2012
1158(86*10^194818-437)/9194819Robert Price03/2021
11592^647068+77281194787Enzo Doria05/2016
116015^165559-14^165559194713Jean-Louis Charton03/2011
1161F(931517)194676Henri Lifchitz09/2008
11624*10^194668+49194669Robert Price01/2019
11632^646589+1179407194643Enzo Doria06/2016
11642^646289-114621194553Enzo Doria05/2015
11652^646236-39659194537Enzo Doria09/2015
1166(16*10^194536+53)/3194537Robert Price03/2019
11672^646161-59833194514Enzo Doria11/2015
1168(17*10^194502+31)/3194503Robert Price01/2019
1169(19*10^194428+287)/9194429Robert Price10/2021
11702*10^194413+3194414Robert Price07/2015
11712^645360-1848599194273Enzo Doria08/2015
1172(112*10^194150-1)/3194152Serge Batalov12/2014
11732*10^193981-43193982Robert Price04/2018
11742^644382+75169193979Enzo Doria04/2016
11752^644304-1861409193955Enzo Doria11/2015
11765*10^193907-9193908Robert Price05/2015
11772^644043+1876703193877Enzo Doria07/2016
11782^643735+1879733193784Enzo Doria09/2016
1179(5^277183+1)/6193742Paul Bourdelais07/2010
11809*10^193712+71193713Robert Price08/2020
11812^643216-286565193628Enzo Doria07/2015
118310^193566-10000000001193566Robert Price04/2021
118210^193566-454041193566Patrick De Geest08/2021
11842^642888-24965193529Enzo Doria09/2013
11852^642448-114825193397Enzo Doria05/2015
11862^642437-1856623193393Enzo Doria10/2015
11872^642039-59797193273Enzo Doria11/2015
118810^193230+513861193231Patrick De Geest07/2018
118910^193230-8001193230Robert Price03/2018
11902^641692-286349193169Enzo Doria07/2015
11912^641690-24737193168Enzo Doria09/2013
11922^641514+1876549193115Enzo Doria07/2016
11932^640888-2785619192927Enzo Doria10/2015
11942^640874-2783741192923Enzo Doria09/2015
119510^192922+192207192923Patrick De Geest08/2021
119610^192922-7001192922Robert Price04/2021
11972^640854+25192917Stefano Morozzi05/2021
119834*10^192868-9192870Robert Price06/2020
1199(46*10^192841+683)/9192842Robert Price03/2019
12002^640181+467192714Lelio R Paula08/2013
12012^639536-1850249192520Enzo Doria08/2015
120240714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
12035*10^192422-43192423Robert Price01/2019
12042^639110-2792441192392Enzo Doria02/2016
12052^638955-29827192345Enzo Doria08/2015
12062^638713-2784223192272Enzo Doria10/2015
1207(10^192216+7)/149192214Alfred Reich07/2021
12082^638490-113507192205Enzo Doria08/2014
12092^638189-39943192115Enzo Doria09/2015
12102^638110+1877119192091Enzo Doria07/2016
12112^638066-2785211192078Enzo Doria10/2015
1212(35*10^191973-341)/9191974Robert Price08/2021
1213(112*10^191900+17)/3191902Robert Price03/2020
12142^637475-115309191900Enzo Doria07/2015
1215(68*10^191754-113)/9191755Robert Price03/2021
12162^636661+1876577191655Enzo Doria07/2016
1217(34^125101-1)/33191589Paul Bourdelais11/2017
12182^636177-1855123191509Enzo Doria09/2015
12192^636158-113627191503Enzo Doria08/2014
1220(37*25^136966+63)/4191472Curtis Bright05/2015
12212^636035+79823191466Enzo Doria06/2016
12222^636011-1860847191459Enzo Doria11/2015
12232^635926-1860611191433Enzo Doria11/2015
12243*10^191152-7191153Robert Price08/2015
12252^634883-1865677191119Enzo Doria02/2016
12262^634801+1871957191095Enzo Doria05/2016
1227(35*10^191073+1)/9191074Serge Batalov07/2010
12289*10^191018-41191019Robert Price08/2020
12292^634470-59861190995Enzo Doria11/2015
12302^634368-29519190964Enzo Doria08/2015
12312^634188-350609190910Enzo Doria06/2015
1232(65*10^190899+493)/9190900Robert Price08/2021
1233(62*10^190795-413)/9190796Robert Price09/2021
1234(26*10^190789-131)/3190790Robert Price10/2019
1235(13*10^190732-61)/3190733Robert Price11/2018
1236(7*10^190683+143)/3190684Robert Price03/2018
12372^633088-113879190579Enzo Doria10/2014
12382^633064+1874911190572Enzo Doria06/2016
1239(43*10^190547+83)/9190548Robert Price11/2018
124099*10^190543+7190545Robert Price05/2021
1241(299*10^190533+1)/3190535Robert Price04/2020
1242(1744*10^190519-1747)/3190522Robert Price12/2020
12432^632795-351205190491Enzo Doria06/2015
1244(16*10^190420-19)/3190421Robert Price02/2019
1245(43*10^190351+101)/9190352Robert Price11/2018
12462^632156+78391190298Enzo Doria06/2016
124797*10^190295-3190297Robert Price05/2020
12482^632082-1851971190276Enzo Doria08/2015
12492^632020+1880311190257Enzo Doria09/2016
1250(5*10^190242-77)/9190242Robert Price04/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 01 2021 22:29 (Time in France)

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