PRP Records

Probable Primes Top 10000

(295461 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(2^704548-19)/3212090Stefano Morozzi08/2022
17522^704110-2792441211959Enzo Doria02/2016
17532^704084+28531211951Enzo Doria02/2024
17542^703943-1862947211908Enzo Doria12/2015
1755(60^119083+1)/61211746Paul Bourdelais10/2018
1756(184*10^211682-1)/3211684Robert Price12/2022
1757(10^211610-91)/9211610Serge Batalov12/2014
1758227^89797+2211565Lelio R Paula08/2012
17592^702194-3211382Paul Bourdelais03/2012
17602^702064+1874911211343Enzo Doria07/2016
17612^701968-113873211314Enzo Doria10/2014
1762(14*10^211262-41)/9211263Serge Batalov01/2023
17632^701713-113779211237Enzo Doria09/2014
17642^701616-216803211208Enzo Doria01/2024
17652^701449-25201211158Enzo Doria09/2013
17662^701403-2786977211144Enzo Doria11/2015
17672^701189-25423211079Enzo Doria09/2013
17682^701162-459161211071Enzo Doria05/2015
17692^700793+219407210960Enzo Doria03/2024
1770(24^152783-1)/23210872Paul Bourdelais04/2018
17712^700400+9385210842Lelio R Paula01/2014
17722^700304-17210813Stefano Morozzi07/2022
17732^700131+1874693210761Enzo Doria06/2016
1774(2^700095+225414)/2210750Stefano Morozzi04/2020
1775(2^700090+278254)/2210748Stefano Morozzi04/2020
1776(2^700075+303666)/2210744Stefano Morozzi04/2020
1777(2^700073+75882)/2210743Stefano Morozzi04/2020
1778(2^700074+328890)/2210743Stefano Morozzi04/2020
1779(2^700052+79162)/2210737Stefano Morozzi04/2020
1780(2^700052+304458)/2210737Stefano Morozzi04/2020
1781(2^700048+376578)/2210736Stefano Morozzi04/2020
178211^202357-1140210734Enzo Doria12/2012
1783(2^700021+25874)/2210728Stefano Morozzi04/2020
1784(2^700018+377518)/2210727Stefano Morozzi04/2020
17852^699999+300729210721Norman Luhn09/2023
1786(238*10^210712-1)/3210714Robert Price09/2023
17872^699740+25210643Stefano Morozzi05/2021
1788(23*10^210525-143)/3210526Robert Price12/2023
17892^698929-2788423210399Enzo Doria11/2015
1790(5^300893+4^300893)/9210315Jean-Louis Charton11/2011
17912^698316+1878601210215Enzo Doria08/2016
179234*10^210097-9210099Robert Price05/2023
1793(19*10^210011-49)/3210012Robert Price06/2023
17946*10^209846-91209847Robert Price05/2023
17952^697036+1878751209829Enzo Doria08/2016
17962^696813+28607209762Enzo Doria02/2024
1797(238*10^209715-1)/3209717Robert Price09/2023
17986^269407+5209640Paul Bourdelais02/2021
1799(2^696343-1)/11141489/36009913139329209600Tony Prest / Never Odd Or Even02/2014
18002^696254-115151209594Enzo Doria06/2015
1801(35^135623+1)/36209410Paul Bourdelais07/2018
18027*10^209161+39209162Robert Price01/2023
18032^694633+1887257209106Enzo Doria05/2017
1804fibonacci(999790)-4208944Jon Grantham08/2023
18052^693959+180923208903Enzo Doria07/2016
1806(2^693747-11)/3208839Stefano Morozzi08/2022
18072^693462-1847561208753Enzo Doria07/2015
18082^690890-59981207979Enzo Doria11/2015
1809(38^131591+1)/39207884Paul Bourdelais07/2018
18103*2^690484+5207857Jon Grantham07/2023
18112^690163+1877063207760Enzo Doria07/2016
18127^245608-2207563Paul Bourdelais01/2021
1813(67*10^207556+23)/9207557Serge Batalov01/2023
18142^689286-29381207496Enzo Doria08/2015
18152^689122-114521207447Enzo Doria04/2015
18169*10^207254-89207255Robert Price02/2023
18172^688373+6077207221Enzo Doria02/2016
18182^688201+1875527207170Enzo Doria07/2016
1819(42^127609+1)/43207140Paul Bourdelais07/2018
18202^687938+213589207090Enzo Doria10/2023
18212^687619+81563206994Enzo Doria08/2016
18223*10^206927+37206928Robert Price08/2023
18232^687383+21803206923Enzo Doria09/2023
18242^686572-1845299206679Enzo Doria07/2015
1825(21^156217-1)/20206552Paul Bourdelais04/2010
1826(2^685739+1)/(3*87774593)206420Gord Palameta08/2018
18272^685578+3206380Paul Bourdelais04/2012
18282^685078+218599206230Enzo Doria01/2024
18292^684836-49349206157Enzo Doria10/2015
1830(73^110603-1)/72206088Paul Bourdelais06/2018
18312^684163-2790967205954Enzo Doria12/2015
1832326^81943-325^81943205941Jean-Louis Charton07/2012
1833(2^684127-1)/23765203727205933Jens K. Andersen04/2009
1834(68*10^205510+13)/9205511Serge Batalov01/2023
18354^341233-3^341233205443Jean-Louis Charton01/2006
18362^682414+215029205428Enzo Doria11/2023
1837(963^68821-1)/962205334Jinyuan Wang01/2024
1838(43*10^205183-421)/9205184Robert Price10/2023
18392^681545+467205166Lelio R Paula11/2013
18402^681306+81049205094Enzo Doria07/2016
18412^680697+1877057204911Enzo Doria07/2016
18422^680415+71783204826Enzo Doria04/2016
184310^204764-8001204764Robert Price03/2023
1844(26*10^204730-77)/3204731Robert Price03/2023
18452^679860-459995204659Enzo Doria06/2015
18462^679593+1879547204578Enzo Doria09/2016
18472^678899+220073204369Enzo Doria03/2024
18482^678753+21677204326Enzo Doria08/2023
18492^678651+1875023204295Enzo Doria07/2016
18502^678561+678561204268Henri Lifchitz05/2006
18515*3^427884+2^427884204154Jon Grantham08/2023
18522^678101-114043204129Enzo Doria11/2014
18532^678028+1875631204107Enzo Doria06/2016
18542^677721+28607204015Enzo Doria01/2024
1855(19*10^203798-7)/3203799Robert Price12/2023
18562^676992-59783203795Enzo Doria10/2015
18572^676972+1866871203789Enzo Doria03/2016
18582^676815+22583203742Enzo Doria09/2023
18592^676761-9203726Robert Price01/2017
18602^676592-23203675Stefano Morozzi07/2022
18612^676563-2792407203666Enzo Doria02/2016
18622^676306-114713203589Enzo Doria04/2015
1863(2^675977-1)/(1686378749257*7171117283326998925471)203456Dario Alpern07/2015
18646*10^203365+53203366Robert Price09/2023
186510247^50678-50678^10247203250Norbert Schneider03/2022
18662^674627-25161203083Enzo Doria09/2013
18672^674603-69337203076Enzo Doria12/2015
1868(182*10^203048+1)/3203050Robert Price09/2023
18692^674459+74213203033Enzo Doria04/2016
18702^674116-458879202930Enzo Doria04/2015
18712^674076-114755202918Enzo Doria04/2015
18725^289937-4^289937202658Jean-Louis Charton03/2013
18735^289926-289926^5202650Henri Lifchitz07/2024
1874(2^673184-7)/3202649Stefano Morozzi08/2022
1875(467617#+14534)/(2^2*13*43)202603Makoto Morimoto06/2019
1876(155^92479-1)/154202558Anonymous06/2024
18772^672773+219407202525Enzo Doria03/2024
18782^672556-1835519202460Enzo Doria04/2015
1879(7*10^202267+179)/3202268Robert Price02/2023
18802^671446-351401202126Enzo Doria07/2015
18812^671373+77747202104Enzo Doria05/2016
1882(2*10^202059+7)/9202059Rytis Slatkevicius01/2023
188398*10^202021-9202023Robert Price05/2023
18842^670726-114845201909Enzo Doria05/2015
18852^670539-25045201853Enzo Doria09/2013
188610^201801-93201801Robert Price02/2023
188743284^43519-43519^43284201769Norbert Schneider08/2018
18882^670213+282317201755Enzo Doria09/2016
18892^670133+89201731Stefano Morozzi05/2021
18902^669854-113501201647Enzo Doria08/2014
18912^669718+81619201606Enzo Doria08/2016
1892(299*10^201547-17)/3201549Robert Price02/2023
1893(145*10^201504-1)/9201506Serge Batalov12/2014
18942^668938-1839821201371Enzo Doria06/2015
1895(198^87623-1)/197201239Anonymous06/2024
18962^668492+1879303201237Enzo Doria08/2016
18977*10^201140-87201141Robert Price03/2023
18986^258413-5^258413201085Jean-Louis Charton03/2013
189910194^50161-50161^10194201063Norbert Schneider09/2020
19002^667894+1875589201057Enzo Doria06/2016
19012^667569-1836559200959Enzo Doria05/2015
1902(172*10^200746-1)/9200748Serge Batalov12/2014
1903(166^90407-1)/165200712Anonymous06/2024
19042^666430+782569200616Enzo Doria10/2016
1905(13*10^200610-43)/3200611Robert Price08/2023
1906(8*10^200408-11)/3200409Robert Price07/2023
1907(19*10^200260+101)/3200261Robert Price06/2023
190843183^43183+4^4200167Serge Batalov04/2024
1909(86^103471+1)/87200163Paul Bourdelais05/2018
1910(10^(2*100072+1)+36*10^100072-1)/9200145Robert Price09/2023
19112^664778+34789200119Enzo Doria07/2024
1912103*(10^100000+20110)^2-4707*(10^100000+20110)+50383200003Robert Price05/2017
1913103*(10^100000+33798)^2-4707*(10^100000+33798)+50383200003Robert Price01/2018
1914numbpart(32235776596)200002Serge Batalov04/2017
1915(10^200001+149)/3200001Serge Batalov12/2014
191610^200000+571791200001Patrick De Geest08/2019
1917(3^419180-621444)/3200000Stefano Morozzi06/2019
1918(3^419180-1941384)/3200000Stefano Morozzi08/2019
191910^200000-45557200000Patrick De Geest08/2019
1920(10^200000-1)/9-10^58838200000Akihiko Yoshida04/2020
19212593604092947240127723272^8192+2593604092947240127722755^8192200000Youcef Lemsafer01/2023
1922(2593604092947240127723019^8192+2593604092947240127723011^8192)/2199999Youcef Lemsafer01/2023
1923(2593604092947240127723087^8192+2593604092947240127722984^8192)/147457199994Youcef Lemsafer01/2023
1924(2593604092947240127723229^8192+2593604092947240127723171^8192)/15032745986199989Youcef Lemsafer01/2023
1925(2593604092947240127723215^8192+2593604092947240127722938^8192)/12728329863169199986Youcef Lemsafer01/2023
192692*10^199980-9199982Robert Price12/2021
1927(2593604092947240127723216^8192+2593604092947240127723163^8192)/20172788859482903707649199977Youcef Lemsafer01/2023
1928(85*10^199951-139)/9199952Robert Price08/2021
1929(10^199926+7)/29/373/2339199919Alfred Reich08/2021
19302^663838+25819199836Enzo Doria11/2023
193123*10^199833-9199835Robert Price10/2021
1932fibonacci(956176)-4199829Jon Grantham08/2023
1933(299*10^199801-17)/3199803Robert Price04/2020
19346*10^199788+77199789Robert Price06/2020
1935(23*10^199615+37)/3199616Robert Price02/2022
1936(17*10^199607-167)/3199608Robert Price05/2022
19372^663020-933075199589Paul Bourdelais06/2021
19382^663007+29963199585Enzo Doria03/2024
19393*2^662703-5199494Jon Grantham07/2023
1940(14*10^199447+73)/3199448Robert Price12/2018
1941(2^662424-15)/7199409Stefano Morozzi08/2022
19422^662194+22189199341Enzo Doria09/2023
19432^662103-29287199313Enzo Doria08/2015
1944(2*10^199283+457)/9199283Robert Price01/2018
1945(10^199248-19)/9199248Robert Price01/2018
1946(83*10^199213+529)/9199214Robert Price12/2021
1947(194*10^199146-17)/3199148Robert Price09/2020
1948(151*10^199003-1)/3199005Robert Price03/2020
19499*10^198946-73198947Robert Price01/2021
195045*10^198931-7198933Robert Price07/2020
19512^660482-2891198825Yves Minet05/2016
19522^659589-21198557Stefano Morozzi07/2022
19532^659583+1879223198555Enzo Doria08/2016
1954(53*10^198529+1)/9198530Serge Batalov07/2010
1955(49*10^198403+311)/9198404Robert Price06/2019
195696*10^198376-7198378Robert Price03/2021
1957(10^198375+7)/59/1201/87589198366Alfred Reich08/2021
19582^658828-29819198327Enzo Doria08/2015
19592^658776-2791229198312Enzo Doria01/2016
1960(35*10^198294-377)/9198295Robert Price07/2018
1961(4*10^198268+137)/3198269Robert Price03/2018
19622^658544-1854029198242Enzo Doria09/2015
1963(62*10^198229-233)/9198230Robert Price02/2022
1964(26*10^198200-41)/3198201Robert Price02/2022
1965(157^90239-1)/156198154Alexander Zhirkov06/2016
19662^657815+26213198023Enzo Doria12/2023
19672*10^197959-37197960Robert Price11/2021
1968(29*10^197941-41)/3197942Tyler Busby03/2024
1969(232*10^197897+17)/3197899Robert Price04/2021
1970(4*10^197778+173)/3197779Robert Price02/2018
19712^656763+211373197706Enzo Doria08/2023
197278*10^197702-7197704Robert Price10/2020
1973(17*10^197640-23)/3197641Robert Price03/2021
1974(29*10^197629-77)/3197630Robert Price02/2020
19752^656462+1874419197615Enzo Doria06/2016
1976(89^101363+1)/90197595Paul Bourdelais11/2017
19772^655893-344563197444Enzo Doria07/2015
19782^655875+71333197439Enzo Doria04/2016
19792^655845-9197430Robert Price01/2017
1980(299*10^197426+1)/3197428Robert Price04/2020
19812^655682-1849121197380Enzo Doria08/2015
19824*10^197268-89197269Robert Price11/2018
1983(11*10^197198-89)/3197199Robert Price05/2021
19842^655045-49603197189Enzo Doria10/2015
19852^655000-2784089197175Enzo Doria10/2015
1986(18^157051-1)/17197141Paul Bourdelais03/2010
1987(4*10^197061+41)/9197061Serge Batalov11/2022
1988(154*10^197005+17)/9197007Robert Price06/2022
19892^654400-39719196995Enzo Doria09/2015
1990(5^281807-2^281807)/3196975Jon Grantham08/2023
1991(14*10^196965-221)/9196966Robert Price04/2018
19922^654216-459995196939Enzo Doria06/2015
1993(17*10^196921+31)/3196922Robert Price01/2019
1994(14*10^196885-89)/3196886Robert Price05/2020
19953*10^196881-59196882Robert Price09/2018
19962^653851+82295196829Enzo Doria09/2016
1997(38*10^196792+691)/9196793Robert Price10/2018
1998(65*10^196768+493)/9196769Robert Price08/2021
20002^653636-29429196765Enzo Doria08/2015
19992^653638-11196765Stefano Morozzi07/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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