PRP Records

Probable Primes Top 10000

(294627 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
17516*10^203365+53203366Robert Price09/2023
175210247^50678-50678^10247203250Norbert Schneider03/2022
17532^674627-25161203083Enzo Doria09/2013
17542^674603-69337203076Enzo Doria12/2015
1755(182*10^203048+1)/3203050Robert Price09/2023
17562^674459+74213203033Enzo Doria04/2016
17572^674116-458879202930Enzo Doria04/2015
17582^674076-114755202918Enzo Doria04/2015
17595^289937-4^289937202658Jean-Louis Charton03/2013
1760(2^673184-7)/3202649Stefano Morozzi08/2022
1761(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
17622^672773+219407202525Enzo Doria03/2024
17632^672556-1835519202460Enzo Doria04/2015
1764(7*10^202267+179)/3202268Robert Price02/2023
17652^671446-351401202126Enzo Doria07/2015
17662^671373+77747202104Enzo Doria05/2016
1767(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
176898*10^202021-9202023Robert Price05/2023
17692^670726-114845201909Enzo Doria05/2015
17702^670539-25045201853Enzo Doria09/2013
177110^201801-93201801Robert Price02/2023
177243284^43519-43519^43284201769Norbert Schneider08/2018
17732^670213+282317201755Enzo Doria09/2016
17742^670133+89201731Stefano Morozzi05/2021
17752^669854-113501201647Enzo Doria08/2014
17762^669718+81619201606Enzo Doria08/2016
1777(299*10^201547-17)/3201549Robert Price02/2023
1778(145*10^201504-1)/9201506Serge Batalov12/2014
17792^668938-1839821201371Enzo Doria06/2015
17802^668492+1879303201237Enzo Doria08/2016
17817*10^201140-87201141Robert Price03/2023
17826^258413-5^258413201085Jean-Louis Charton03/2013
178310194^50161-50161^10194201063Norbert Schneider09/2020
17842^667894+1875589201057Enzo Doria06/2016
17852^667569-1836559200959Enzo Doria05/2015
1786(172*10^200746-1)/9200748Serge Batalov12/2014
17872^666430+782569200616Enzo Doria10/2016
1788(13*10^200610-43)/3200611Robert Price08/2023
1789(8*10^200408-11)/3200409Robert Price07/2023
1790(19*10^200260+101)/3200261Robert Price06/2023
1791(86^103471+1)/87200163Paul Bourdelais05/2018
1792(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
1793103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
1794103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
1795numbpart(32235776596)200002Serge Batalov04/2017
1796(10^200001+149)/3200001Serge Batalov12/2014
179710^200000+571791200001Patrick De Geest08/2019
1798(3^419180-621444)/3200000Stefano Morozzi06/2019
1799(3^419180-1941384)/3200000Stefano Morozzi08/2019
180010^200000-45557200000Patrick De Geest08/2019
1802(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
18012593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
1803(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
1804(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
1805(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
1806(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
180792*10^199980-9199982Robert Price12/2021
1808(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
1809(85*10^199951-139)/9199952Robert Price08/2021
1810(10^199926+7)/29/373/2339199919Alfred Reich08/2021
18112^663838+25819199836Enzo Doria11/2023
181223*10^199833-9199835Robert Price10/2021
1813fibonacci(956176)-4199829Jon Grantham08/2023
1814(299*10^199801-17)/3199803Robert Price04/2020
18156*10^199788+77199789Robert Price06/2020
1816(23*10^199615+37)/3199616Robert Price02/2022
1817(17*10^199607-167)/3199608Robert Price05/2022
18182^663020-933075199589Paul Bourdelais06/2021
18192^663007+29963199585Enzo Doria03/2024
18203*2^662703-5199494Jon Grantham07/2023
1821(14*10^199447+73)/3199448Robert Price12/2018
1822(2^662424-15)/7199409Stefano Morozzi08/2022
18232^662194+22189199341Enzo Doria09/2023
18242^662103-29287199313Enzo Doria08/2015
1825(2*10^199283+457)/9199283Robert Price01/2018
1826(10^199248-19)/9199248Robert Price01/2018
1827(83*10^199213+529)/9199214Robert Price12/2021
1828(194*10^199146-17)/3199148Robert Price09/2020
1829(151*10^199003-1)/3199005Robert Price03/2020
18309*10^198946-73198947Robert Price01/2021
183145*10^198931-7198933Robert Price07/2020
18322^660482-2891198825Yves Minet05/2016
18332^659589-21198557Stefano Morozzi07/2022
18342^659583+1879223198555Enzo Doria08/2016
1835(53*10^198529+1)/9198530Serge Batalov07/2010
1836(49*10^198403+311)/9198404Robert Price06/2019
183796*10^198376-7198378Robert Price03/2021
1838(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
18392^658828-29819198327Enzo Doria08/2015
18402^658776-2791229198312Enzo Doria01/2016
1841(35*10^198294-377)/9198295Robert Price07/2018
1842(4*10^198268+137)/3198269Robert Price03/2018
18432^658544-1854029198242Enzo Doria09/2015
1844(62*10^198229-233)/9198230Robert Price02/2022
1845(26*10^198200-41)/3198201Robert Price02/2022
1846(157^90239-1)/156198154Alexander Zhirkov06/2016
18472^657815+26213198023Enzo Doria12/2023
18482*10^197959-37197960Robert Price11/2021
1849(232*10^197897+17)/3197899Robert Price04/2021
1850(4*10^197778+173)/3197779Robert Price02/2018
18512^656763+211373197706Enzo Doria08/2023
185278*10^197702-7197704Robert Price10/2020
1853(17*10^197640-23)/3197641Robert Price03/2021
1854(29*10^197629-77)/3197630Robert Price02/2020
18552^656462+1874419197615Enzo Doria06/2016
1856(89^101363+1)/90197595Paul Bourdelais11/2017
18572^655893-344563197444Enzo Doria07/2015
18582^655875+71333197439Enzo Doria04/2016
18592^655845-9197430Robert Price01/2017
1860(299*10^197426+1)/3197428Robert Price04/2020
18612^655682-1849121197380Enzo Doria08/2015
18624*10^197268-89197269Robert Price11/2018
1863(11*10^197198-89)/3197199Robert Price05/2021
18642^655045-49603197189Enzo Doria10/2015
18652^655000-2784089197175Enzo Doria10/2015
1866(18^157051-1)/17197141Paul Bourdelais03/2010
1867(4*10^197061+41)/9197061Serge Batalov11/2022
1868(154*10^197005+17)/9197007Robert Price06/2022
18692^654400-39719196995Enzo Doria09/2015
1870(5^281807-2^281807)/3196975Jon Grantham08/2023
1871(14*10^196965-221)/9196966Robert Price04/2018
18722^654216-459995196939Enzo Doria06/2015
1873(17*10^196921+31)/3196922Robert Price01/2019
1874(14*10^196885-89)/3196886Robert Price05/2020
18753*10^196881-59196882Robert Price09/2018
18762^653851+82295196829Enzo Doria09/2016
1877(38*10^196792+691)/9196793Robert Price10/2018
1878(65*10^196768+493)/9196769Robert Price08/2021
18802^653636-29429196765Enzo Doria08/2015
18792^653638-11196765Stefano Morozzi07/2022
18812^653601-69673196754Enzo Doria02/2016
1882(44*10^196684+1)/9196685Serge Batalov07/2010
18832^652786-1852571196509Enzo Doria08/2015
18842^652752-1325196498Yves Minet07/2015
18852^652470-1859141196414Enzo Doria10/2015
18862^652346+29329196376Enzo Doria02/2024
18872^652307+1877483196364Enzo Doria08/2016
18882^652293-115273196360Enzo Doria06/2015
1889(47*10^196281+403)/9196282Robert Price03/2019
18902^652025+218027196280Enzo Doria01/2024
18912^652004+23961196273Enzo Doria10/2023
1892(7*10^196125-31)/3196126Robert Price12/2021
189333^129128+129128^33196083Norbert Schneider06/2022
18946*10^196070+73196071Robert Price04/2019
18952^651218-1868201196037Enzo Doria04/2016
18962^651047-49687195985Enzo Doria10/2015
189710^195968-700001195968Robert Price08/2021
1898fibonacci(937485)+3195923Jon Grantham08/2023
1899(29*10^195875-197)/3195876Robert Price08/2021
1900(25*10^195808-97)/9195809Robert Price01/2022
19012^650285-2785333195756Enzo Doria10/2015
1902(10^195732+7)/18089/49605893195721Alfred Reich08/2021
1903(69^106397-1)/68195647Paul Bourdelais10/2017
19042^649811+1877573195613Enzo Doria08/2016
19052^649662-170531195568Hans Havermann10/2018
19062^649586+182839195545Enzo Doria11/2016
19072^649537-1867363195531Enzo Doria04/2016
19082^649536-1861499195530Enzo Doria12/2015
19092^649493+25907195517Enzo Doria11/2023
1910(103*10^195478-1)/3195480Serge Batalov12/2014
19112^649102-59351195400Enzo Doria10/2015
1912(2*10^195399+529)/9195399Robert Price01/2018
1913(202*10^195383-13)/9195385Robert Price01/2020
19142^648988+1178971195365Enzo Doria06/2016
19152^648975-114319195361Enzo Doria02/2015
1916(11*10^195350-137)/9195351Robert Price01/2018
19172^648619-24835195254Enzo Doria09/2013
19185*10^195250-21195251Robert Price12/2021
1919(14*10^195234-83)/3195235Robert Price12/2018
19205*10^195221+81195222Robert Price03/2019
192110^195143-5001195143Robert Price12/2021
19222^648190-24737195125Enzo Doria09/2013
1923(57^111119+1)/58195110Paul Bourdelais10/2017
1924(29*10^195098-197)/3195099Robert Price08/2021
192510^195060+89701195061Patrick De Geest02/2021
192710^195060-40000000001195060Robert Price09/2020
192610^195060-110337195060Patrick De Geest02/2021
192856*10^195032-3195034Robert Price03/2020
192911^187185-90194934Enzo Doria09/2012
19302^647468+220141194908Enzo Doria03/2024
1931(86*10^194818-437)/9194819Robert Price03/2021
19322^647068+77281194787Enzo Doria05/2016
19332*10^194716-93194717Robert Price12/2021
193415^165559-14^165559194713Jean-Louis Charton03/2011
1935F(931517)194676Henri Lifchitz09/2008
19364*10^194668+49194669Robert Price01/2019
19372^646589+1179407194643Enzo Doria06/2016
19382^646289-114621194553Enzo Doria05/2015
19392^646236-39659194537Enzo Doria09/2015
1940(16*10^194536+53)/3194537Robert Price03/2019
19412^646161-59833194514Enzo Doria11/2015
1942(17*10^194502+31)/3194503Robert Price01/2019
1943(19*10^194428+287)/9194429Robert Price10/2021
19442*10^194413+3194414Robert Price07/2015
19452^645360-1848599194273Enzo Doria08/2015
194622470^44641+44641^22470194260Norbert Schneider08/2023
1947(112*10^194150-1)/3194152Serge Batalov12/2014
1948Phi(293127,10)194041Makoto Kamada12/2023
19492*10^193981-43193982Robert Price04/2018
19502^644382+75169193979Enzo Doria04/2016
19512^644304-1861409193955Enzo Doria11/2015
1952(29*10^193950-23)/3193951Robert Price03/2022
19535*10^193907-9193908Robert Price05/2015
19542^644043+1876703193877Enzo Doria07/2016
19552*10^193841-63193842Robert Price01/2022
19562^643735+1879733193784Enzo Doria09/2016
1957(5^277183+1)/6193742Paul Bourdelais07/2010
19589*10^193712+71193713Robert Price08/2020
19592^643216-286565193628Enzo Doria07/2015
19602^643204+215011193624Enzo Doria11/2023
196110^193566+1126339193567Patrick De Geest09/2022
196310^193566-10000000001193566Robert Price04/2021
196210^193566-454041193566Patrick De Geest08/2021
19652^642888-24965193529Enzo Doria09/2013
19642^642889+25367193529Enzo Doria11/2023
19662^642448-114825193397Enzo Doria05/2015
19672^642437-1856623193393Enzo Doria10/2015
19682^642039-59797193273Enzo Doria11/2015
19692^641987+39193258Jon Grantham08/2023
197010^193230+513861193231Patrick De Geest07/2018
197110^193230-8001193230Robert Price03/2018
1972(62*10^193225-233)/9193226Robert Price02/2022
19732^641692-286349193169Enzo Doria07/2015
19742^641690-24737193168Enzo Doria09/2013
197522268^44421+44421^22268193129Norbert Schneider06/2023
19762^641514+1876549193115Enzo Doria07/2016
19772^640888-2785619192927Enzo Doria10/2015
19782^640874-2783741192923Enzo Doria09/2015
197910^192922+192207192923Patrick De Geest08/2021
198010^192922-7001192922Robert Price04/2021
19812^640854+25192917Stefano Morozzi05/2021
198234*10^192868-9192870Robert Price06/2020
1983(46*10^192841+683)/9192842Robert Price03/2019
19842^640181+467192714Lelio R Paula08/2013
19852^640072+27541192681Enzo Doria01/2024
19862^639536-1850249192520Enzo Doria08/2015
198740714<>40712<>...<>1086421357911<>...<>40711<>40713192464Hans Havermann12/2019
19885*10^192422-43192423Robert Price01/2019
19892^639110-2792441192392Enzo Doria02/2016
19902^638955-29827192345Enzo Doria08/2015
199115^163539+14192337Alfred Reich10/2023
19922^638713-2784223192272Enzo Doria10/2015
1993(10^192216+7)/149192214Alfred Reich07/2021
19942^638490-113507192205Enzo Doria08/2014
19952^638189-39943192115Enzo Doria09/2015
19962^638110+1877119192091Enzo Doria07/2016
19972^638066-2785211192078Enzo Doria10/2015
1998(35*10^191973-341)/9191974Robert Price08/2021
1999(112*10^191900+17)/3191902Robert Price03/2020
20002^637475-115309191900Enzo Doria07/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!