PRP Records

Probable Primes Top 10000

(294613 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 ?
1751(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
17522^672773+219407202525Enzo Doria03/2024
17532^672556-1835519202460Enzo Doria04/2015
1754(7*10^202267+179)/3202268Robert Price02/2023
17552^671446-351401202126Enzo Doria07/2015
17562^671373+77747202104Enzo Doria05/2016
1757(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
175898*10^202021-9202023Robert Price05/2023
17592^670726-114845201909Enzo Doria05/2015
17602^670539-25045201853Enzo Doria09/2013
176110^201801-93201801Robert Price02/2023
176243284^43519-43519^43284201769Norbert Schneider08/2018
17632^670213+282317201755Enzo Doria09/2016
17642^670133+89201731Stefano Morozzi05/2021
17652^669854-113501201647Enzo Doria08/2014
17662^669718+81619201606Enzo Doria08/2016
1767(299*10^201547-17)/3201549Robert Price02/2023
1768(145*10^201504-1)/9201506Serge Batalov12/2014
17692^668938-1839821201371Enzo Doria06/2015
17702^668492+1879303201237Enzo Doria08/2016
17717*10^201140-87201141Robert Price03/2023
17726^258413-5^258413201085Jean-Louis Charton03/2013
177310194^50161-50161^10194201063Norbert Schneider09/2020
17742^667894+1875589201057Enzo Doria06/2016
17752^667569-1836559200959Enzo Doria05/2015
1776(172*10^200746-1)/9200748Serge Batalov12/2014
17772^666430+782569200616Enzo Doria10/2016
1778(13*10^200610-43)/3200611Robert Price08/2023
1779(8*10^200408-11)/3200409Robert Price07/2023
1780(19*10^200260+101)/3200261Robert Price06/2023
1781(86^103471+1)/87200163Paul Bourdelais05/2018
1782(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
1783103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
1784103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
1785numbpart(32235776596)200002Serge Batalov04/2017
1786(10^200001+149)/3200001Serge Batalov12/2014
178710^200000+571791200001Patrick De Geest08/2019
1788(3^419180-621444)/3200000Stefano Morozzi06/2019
1789(3^419180-1941384)/3200000Stefano Morozzi08/2019
179010^200000-45557200000Patrick De Geest08/2019
1791(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
17922593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
1793(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
1794(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
1795(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
1796(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
179792*10^199980-9199982Robert Price12/2021
1798(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
1799(85*10^199951-139)/9199952Robert Price08/2021
1800(10^199926+7)/29/373/2339199919Alfred Reich08/2021
18012^663838+25819199836Enzo Doria11/2023
180223*10^199833-9199835Robert Price10/2021
1803fibonacci(956176)-4199829Jon Grantham08/2023
1804(299*10^199801-17)/3199803Robert Price04/2020
18056*10^199788+77199789Robert Price06/2020
1806(23*10^199615+37)/3199616Robert Price02/2022
1807(17*10^199607-167)/3199608Robert Price05/2022
18082^663020-933075199589Paul Bourdelais06/2021
18092^663007+29963199585Enzo Doria03/2024
18103*2^662703-5199494Jon Grantham07/2023
1811(14*10^199447+73)/3199448Robert Price12/2018
1812(2^662424-15)/7199409Stefano Morozzi08/2022
18132^662194+22189199341Enzo Doria09/2023
18142^662103-29287199313Enzo Doria08/2015
1815(2*10^199283+457)/9199283Robert Price01/2018
1816(10^199248-19)/9199248Robert Price01/2018
1817(83*10^199213+529)/9199214Robert Price12/2021
1818(194*10^199146-17)/3199148Robert Price09/2020
1819(151*10^199003-1)/3199005Robert Price03/2020
18209*10^198946-73198947Robert Price01/2021
182145*10^198931-7198933Robert Price07/2020
18222^660482-2891198825Yves Minet05/2016
18232^659589-21198557Stefano Morozzi07/2022
18242^659583+1879223198555Enzo Doria08/2016
1825(53*10^198529+1)/9198530Serge Batalov07/2010
1826(49*10^198403+311)/9198404Robert Price06/2019
182796*10^198376-7198378Robert Price03/2021
1828(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
18292^658828-29819198327Enzo Doria08/2015
18302^658776-2791229198312Enzo Doria01/2016
1831(35*10^198294-377)/9198295Robert Price07/2018
1832(4*10^198268+137)/3198269Robert Price03/2018
18332^658544-1854029198242Enzo Doria09/2015
1834(62*10^198229-233)/9198230Robert Price02/2022
1835(26*10^198200-41)/3198201Robert Price02/2022
1836(157^90239-1)/156198154Alexander Zhirkov06/2016
18372^657815+26213198023Enzo Doria12/2023
18382*10^197959-37197960Robert Price11/2021
1839(232*10^197897+17)/3197899Robert Price04/2021
1840(4*10^197778+173)/3197779Robert Price02/2018
18412^656763+211373197706Enzo Doria08/2023
184278*10^197702-7197704Robert Price10/2020
1843(17*10^197640-23)/3197641Robert Price03/2021
1844(29*10^197629-77)/3197630Robert Price02/2020
18452^656462+1874419197615Enzo Doria06/2016
1846(89^101363+1)/90197595Paul Bourdelais11/2017
18472^655893-344563197444Enzo Doria07/2015
18482^655875+71333197439Enzo Doria04/2016
18492^655845-9197430Robert Price01/2017
1850(299*10^197426+1)/3197428Robert Price04/2020
18512^655682-1849121197380Enzo Doria08/2015
18524*10^197268-89197269Robert Price11/2018
1853(11*10^197198-89)/3197199Robert Price05/2021
18542^655045-49603197189Enzo Doria10/2015
18552^655000-2784089197175Enzo Doria10/2015
1856(18^157051-1)/17197141Paul Bourdelais03/2010
1857(4*10^197061+41)/9197061Serge Batalov11/2022
1858(154*10^197005+17)/9197007Robert Price06/2022
18592^654400-39719196995Enzo Doria09/2015
1860(5^281807-2^281807)/3196975Jon Grantham08/2023
1861(14*10^196965-221)/9196966Robert Price04/2018
18622^654216-459995196939Enzo Doria06/2015
1863(17*10^196921+31)/3196922Robert Price01/2019
1864(14*10^196885-89)/3196886Robert Price05/2020
18653*10^196881-59196882Robert Price09/2018
18662^653851+82295196829Enzo Doria09/2016
1867(38*10^196792+691)/9196793Robert Price10/2018
1868(65*10^196768+493)/9196769Robert Price08/2021
18702^653636-29429196765Enzo Doria08/2015
18692^653638-11196765Stefano Morozzi07/2022
18712^653601-69673196754Enzo Doria02/2016
1872(44*10^196684+1)/9196685Serge Batalov07/2010
18732^652786-1852571196509Enzo Doria08/2015
18742^652752-1325196498Yves Minet07/2015
18752^652470-1859141196414Enzo Doria10/2015
18762^652346+29329196376Enzo Doria02/2024
18772^652307+1877483196364Enzo Doria08/2016
18782^652293-115273196360Enzo Doria06/2015
1879(47*10^196281+403)/9196282Robert Price03/2019
18802^652025+218027196280Enzo Doria01/2024
18812^652004+23961196273Enzo Doria10/2023
1882(7*10^196125-31)/3196126Robert Price12/2021
188333^129128+129128^33196083Norbert Schneider06/2022
18846*10^196070+73196071Robert Price04/2019
18852^651218-1868201196037Enzo Doria04/2016
18862^651047-49687195985Enzo Doria10/2015
188710^195968-700001195968Robert Price08/2021
1888fibonacci(937485)+3195923Jon Grantham08/2023
1889(29*10^195875-197)/3195876Robert Price08/2021
1890(25*10^195808-97)/9195809Robert Price01/2022
18912^650285-2785333195756Enzo Doria10/2015
1892(10^195732+7)/18089/49605893195721Alfred Reich08/2021
1893(69^106397-1)/68195647Paul Bourdelais10/2017
18942^649811+1877573195613Enzo Doria08/2016
18952^649662-170531195568Hans Havermann10/2018
18962^649586+182839195545Enzo Doria11/2016
18972^649537-1867363195531Enzo Doria04/2016
18982^649536-1861499195530Enzo Doria12/2015
18992^649493+25907195517Enzo Doria11/2023
1900(103*10^195478-1)/3195480Serge Batalov12/2014
19012^649102-59351195400Enzo Doria10/2015
1902(2*10^195399+529)/9195399Robert Price01/2018
1903(202*10^195383-13)/9195385Robert Price01/2020
19042^648988+1178971195365Enzo Doria06/2016
19052^648975-114319195361Enzo Doria02/2015
1906(11*10^195350-137)/9195351Robert Price01/2018
19072^648619-24835195254Enzo Doria09/2013
19085*10^195250-21195251Robert Price12/2021
1909(14*10^195234-83)/3195235Robert Price12/2018
19105*10^195221+81195222Robert Price03/2019
191110^195143-5001195143Robert Price12/2021
19122^648190-24737195125Enzo Doria09/2013
1913(57^111119+1)/58195110Paul Bourdelais10/2017
1914(29*10^195098-197)/3195099Robert Price08/2021
191510^195060+89701195061Patrick De Geest02/2021
191710^195060-40000000001195060Robert Price09/2020
191610^195060-110337195060Patrick De Geest02/2021
191856*10^195032-3195034Robert Price03/2020
191911^187185-90194934Enzo Doria09/2012
1920(86*10^194818-437)/9194819Robert Price03/2021
19212^647068+77281194787Enzo Doria05/2016
19222*10^194716-93194717Robert Price12/2021
192315^165559-14^165559194713Jean-Louis Charton03/2011
1924F(931517)194676Henri Lifchitz09/2008
19254*10^194668+49194669Robert Price01/2019
19262^646589+1179407194643Enzo Doria06/2016
19272^646289-114621194553Enzo Doria05/2015
19282^646236-39659194537Enzo Doria09/2015
1929(16*10^194536+53)/3194537Robert Price03/2019
19302^646161-59833194514Enzo Doria11/2015
1931(17*10^194502+31)/3194503Robert Price01/2019
1932(19*10^194428+287)/9194429Robert Price10/2021
19332*10^194413+3194414Robert Price07/2015
19342^645360-1848599194273Enzo Doria08/2015
193522470^44641+44641^22470194260Norbert Schneider08/2023
1936(112*10^194150-1)/3194152Serge Batalov12/2014
1937Phi(293127,10)194041Makoto Kamada12/2023
19382*10^193981-43193982Robert Price04/2018
19392^644382+75169193979Enzo Doria04/2016
19402^644304-1861409193955Enzo Doria11/2015
1941(29*10^193950-23)/3193951Robert Price03/2022
19425*10^193907-9193908Robert Price05/2015
19432^644043+1876703193877Enzo Doria07/2016
19442*10^193841-63193842Robert Price01/2022
19452^643735+1879733193784Enzo Doria09/2016
1946(5^277183+1)/6193742Paul Bourdelais07/2010
19479*10^193712+71193713Robert Price08/2020
19482^643216-286565193628Enzo Doria07/2015
19492^643204+215011193624Enzo Doria11/2023
195010^193566+1126339193567Patrick De Geest09/2022
195210^193566-10000000001193566Robert Price04/2021
195110^193566-454041193566Patrick De Geest08/2021
19542^642888-24965193529Enzo Doria09/2013
19532^642889+25367193529Enzo Doria11/2023
19552^642448-114825193397Enzo Doria05/2015
19562^642437-1856623193393Enzo Doria10/2015
19572^642039-59797193273Enzo Doria11/2015
19582^641987+39193258Jon Grantham08/2023
195910^193230+513861193231Patrick De Geest07/2018
196010^193230-8001193230Robert Price03/2018
1961(62*10^193225-233)/9193226Robert Price02/2022
19622^641692-286349193169Enzo Doria07/2015
19632^641690-24737193168Enzo Doria09/2013
196422268^44421+44421^22268193129Norbert Schneider06/2023
19652^641514+1876549193115Enzo Doria07/2016
19662^640888-2785619192927Enzo Doria10/2015
19672^640874-2783741192923Enzo Doria09/2015
196810^192922+192207192923Patrick De Geest08/2021
196910^192922-7001192922Robert Price04/2021
19702^640854+25192917Stefano Morozzi05/2021
197134*10^192868-9192870Robert Price06/2020
1972(46*10^192841+683)/9192842Robert Price03/2019
19732^640181+467192714Lelio R Paula08/2013
19742^640072+27541192681Enzo Doria01/2024
19752^639536-1850249192520Enzo Doria08/2015
197640714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
19775*10^192422-43192423Robert Price01/2019
19782^639110-2792441192392Enzo Doria02/2016
19792^638955-29827192345Enzo Doria08/2015
198015^163539+14192337Alfred Reich10/2023
19812^638713-2784223192272Enzo Doria10/2015
1982(10^192216+7)/149192214Alfred Reich07/2021
19832^638490-113507192205Enzo Doria08/2014
19842^638189-39943192115Enzo Doria09/2015
19852^638110+1877119192091Enzo Doria07/2016
19862^638066-2785211192078Enzo Doria10/2015
1987(35*10^191973-341)/9191974Robert Price08/2021
1988(112*10^191900+17)/3191902Robert Price03/2020
19892^637475-115309191900Enzo Doria07/2015
1990(68*10^191754-113)/9191755Robert Price03/2021
19912^636930-11191736Stefano Morozzi07/2022
1992(47*10^191732+259)/9191733Robert Price03/2022
19932^636661+1876577191655Enzo Doria07/2016
1994(9^200807-2^200807)/7191618Jon Grantham07/2023
1995(34^125101-1)/33191589Paul Bourdelais11/2017
1996fibonacci(916540)-2191546Jon Grantham08/2023
19972^636177-1855123191509Enzo Doria09/2015
19982^636158-113627191503Enzo Doria08/2014
1999(37*25^136966+63)/4191472Curtis Bright05/2015
20002^636035+79823191466Enzo Doria06/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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