PRP Records

Probable Primes Top 10000

(293016 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 ?
17512^609846-1834251183582Enzo Doria07/2015
175210^183546+1547323183547Patrick De Geest02/2021
175410^183546-800000001183546Robert Price09/2020
175310^183546-584297183546Patrick De Geest02/2021
17557*10^183511+39183512Robert Price01/2023
1756(23*10^183477-71)/3183478Robert Price07/2020
175711^176176-240183469Enzo Doria11/2012
1758(41^113749+1)/42183451Paul Bourdelais11/2017
17596*10^183429+53183430Robert Price05/2020
1760(28*10^183403+191)/3183404Robert Price02/2020
1761(101^91463+1)/102183320Paul Bourdelais11/2017
17622^608965-113989183317Enzo Doria10/2014
1763A005165(43592)183312Serge Batalov07/2017
1764(61*10^183294+119)/9183295Robert Price05/2019
17652^608814-461261183272Enzo Doria06/2015
1766(163*10^183227-1)/9183229Serge Batalov12/2014
17672^608541-608541^2183190Henri Lifchitz02/2018
17682^608293+143807183115Enzo Doria10/2016
17692^608164-462419183076Enzo Doria08/2015
17702^607950-1862303183012Enzo Doria12/2015
1771(46*10^182896+683)/9182897Robert Price03/2019
1772(2*10^182787+73)/3182787Robert Price09/2020
17732^607101+1871987182756Enzo Doria05/2016
17742^606869-69175182686Enzo Doria11/2015
17758*10^182671+71182672Robert Price05/2022
1776(23*10^182666-71)/3182667Robert Price07/2020
17773*10^182614-11182615Robert Price07/2018
17782^606560-357182593Enzo Doria05/2014
177966*10^182420+7182422Robert Price07/2020
17802^605687+1866983182330Enzo Doria03/2016
17812^605655-114445182321Enzo Doria02/2015
178294*10^182291-3182293Robert Price05/2020
1783(20^140053+1)/21182212Paul Bourdelais04/2010
1784(14*10^182177-221)/9182178Robert Price04/2018
17852^605174-112751182176Enzo Doria06/2014
17862^604761+1874507182052Enzo Doria06/2016
17872^604705+1871957182035Enzo Doria05/2016
1788(14*10^182000+229)/9182001Robert Price03/2018
1789(10^181996+41)/3181996Robert Price12/2017
1790(17*10^181979+91)/9181980Robert Price02/2022
1791(5*10^181950-101)/3181951Robert Price04/2018
17922^603915+75233181797Enzo Doria04/2016
179339470^39537+39537^39470181723Norbert Schneider12/2022
1794(10^181710+7)/563747/2019847181698Alfred Reich08/2021
17957*10^181594-57181595Robert Price06/2020
17968*10^181580+29181581Robert Price11/2021
1797(83*10^181544+61)/9181545Serge Batalov01/2023
1798(2*10^181457+7)/9181457Rytis Slatkevicius01/2023
17993*10^181445+23181446Robert Price03/2022
1800(194*10^181369-11)/3181371Robert Price09/2020
180111^174145-360181354Enzo Doria10/2012
18022^602351-396765181326Enzo Doria08/2013
18036*10^181306+17181307Robert Price04/2019
1804(286*10^181220-1)/3181222Robert Price11/2020
18052^601957-113833181208Enzo Doria09/2014
180666^99581-65^99581181193Robert Price09/2013
180710^181182+383973181183Patrick De Geest04/2016
180810^181182-21181182Serge Batalov12/2014
1809(797*10^181171-41)/9181173Robert Price04/2022
1810(5*10^181127-29)/3181128Robert Price03/2018
18112^601521-29143181076Enzo Doria07/2015
18122^601442-2797811181053Enzo Doria04/2016
181344*10^181029+3181031Robert Price04/2020
18145*10^180992-9180993Robert Price05/2015
181510^180979+79477180980Patrick De Geest04/2016
181610^180979+107739180980Patrick De Geest04/2016
181710^180979-11180979Serge Batalov12/2014
18182^601023-113851180926Enzo Doria10/2014
1819(23*10^180862-143)/3180863Robert Price12/2019
18203*10^180852+29180853Robert Price05/2018
1821(277*10^180782-7)/9180784Robert Price02/2022
1822(8*10^180725-629)/9180725Robert Price01/2022
1823(79*10^180710-1)/3180712Robert Price02/2020
18242^600300-1852559180709Enzo Doria08/2015
1825(2*10^180706-77)/3180706Robert Price02/2021
1826(10^180689+71)/9180689Serge Batalov07/2015
18272^600209+76487180681Enzo Doria05/2016
1828(8*10^180536-269)/9180536Robert Price09/2021
18292^599702-369885180529Enzo Doria11/2013
1830Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
1831(2951*29^123418-3)/4180490Curtis Bright05/2015
1832(29*10^180432-17)/3180433Robert Price09/2019
18334*10^180360+93180361Robert Price08/2018
18342^598942+80779180300Enzo Doria07/2016
1835(38*10^180296+403)/9180297Robert Price10/2018
1836(85*10^180241+77)/9180242Robert Price07/2022
18372^598591-1844797180194Enzo Doria06/2015
1838(100^90089+1)/101180176Paul Bourdelais08/2017
1839(29*10^180072+691)/9180073Robert Price08/2021
1840(59*10^180038+157)/9180039Robert Price12/2021
184195*10^180019-9180021Robert Price01/2022
18426*10^179970+91179971Robert Price05/2019
1843(4*10^179963-79)/3179964Robert Price02/2018
1844(403*10^179944-43)/9179946Robert Price06/2021
1845Gamma-Prime(179849)179849Eric W. Weisstein06/2011
18462^597424-1859729179843Enzo Doria11/2015
1847Phi(180683,10)179760Maksym Voznyy09/2015
1848(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
1849(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
1850(29*10^179697+223)/9179698Robert Price09/2018
18512^596884+73179680Stefano Morozzi04/2021
1852(11*10^179679+13)/3179680Robert Price03/2022
1853(68*10^179656+7)/3179658Robert Price01/2020
1854(10^179643+173)/3179643Robert Price05/2021
18552^596690-461261179622Enzo Doria07/2015
18562^596684-113939179620Enzo Doria10/2014
18572*10^179602+63179603Robert Price05/2018
1858(25*10^179488-403)/9179489Robert Price01/2021
18597*10^179460+99179461Robert Price05/2021
18603^375887-112696179344Enzo Doria07/2014
18614*10^179265-71179266Robert Price12/2018
18622*10^179193+83179194Robert Price12/2021
18632^595144-1850429179157Enzo Doria08/2015
18642^595122-5179150Stefano Morozzi07/2022
18653*10^179138+89179139Robert Price10/2018
1866(52*10^179062-133)/9179063Robert Price09/2021
18672^594531+82253178972Enzo Doria09/2016
1868(664*10^178939-61)/9178941Robert Price09/2021
18692^594260-2787899178891Enzo Doria11/2015
1870(14*10^178822+67)/9178823Robert Price05/2022
1871(29*10^178732-119)/9178733Robert Price12/2021
18722^593631+101381178701Jorge Menendez04/2018
187310^178695+136719178696Patrick De Geest05/2016
187410^178695-71178695Serge Batalov12/2014
1875(2*10^178649-161)/3178649Robert Price12/2020
1876(691^62903-1)/690178609Michael Stocker05/2020
1877(2^148330+1)^4-2178608Cletus Emmanuel12/2003
18782^593222-14145178578Jorge Menendez10/2017
18797*10^178566+33178567Robert Price06/2020
18802^593178+1867219178565Enzo Doria03/2016
1881(38*10^178456+151)/9178457Robert Price03/2022
1882(302*10^178369+13)/9178371Robert Price02/2020
1883(26*10^178296-113)/3178297Robert Price06/2020
1884(18^142031-1)/17178287Paul Bourdelais03/2010
1885(13*10^178233+137)/3178234Robert Price06/2021
1886(5*10^178206+91)/3178207Robert Price04/2018
18872^591872-291929178172Enzo Doria07/2015
18882^591682-286871178115Enzo Doria07/2015
18894*10^178091+9178092Robert Price05/2015
1890410747#+478483178007Makoto Morimoto02/2016
18913*10^177872+73177873Robert Price08/2018
18922^590762-396765177838Enzo Doria08/2013
1893(136*10^177754-1)/9177756Serge Batalov12/2014
1895ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
1894Smr(37765)177719Eric W. Weisstein12/2021
1896(266*10^177577-11)/3177579Robert Price04/2020
1897(11*10^177466-113)/3177467Robert Price10/2018
18983*10^177373-97177374Robert Price07/2018
18992^589204+1881151177369Enzo Doria11/2016
19002^589132-69479177347Enzo Doria01/2016
1901(101*10^177302-17)/3177304Robert Price02/2020
19022^588912-113519177281Enzo Doria08/2014
1903(682*10^177266-7)/9177268Robert Price08/2021
190415^150706+2177245Robert Price06/2015
19052^588194-1861001177065Enzo Doria11/2015
19065*10^177016-37177017Robert Price11/2021
1907(23*10^176964-47)/3176965Robert Price09/2019
190820530^41031+41031^20530176942Norbert Schneider07/2022
1909(19*10^176932+521)/9176933Robert Price05/2018
1910(8*10^176908+43)/3176909Robert Price06/2018
1911(85*10^176900+203)/9176901Robert Price09/2020
19122^587560-113699176874Enzo Doria09/2014
191320596^40995+40995^20596176844Norbert Schneider07/2022
1914(101*10^176815-17)/3176817Robert Price02/2020
1915(25*10^176715-37)/3176716Robert Price10/2019
19165^252763-12862176674Enzo Doria05/2014
191738442^38531+38531^38442176658Norbert Schneider09/2022
19182^586804+81721176646Enzo Doria08/2016
1919(10^176584+77)/3176584Robert Price01/2018
19202^586570+1874419176576Enzo Doria06/2016
1921(157*10^176482-1)/3176484Robert Price01/2022
19222^585994-3311176402Yves Minet12/2014
19238*10^176383-81176384Robert Price02/2021
1924(23*10^176357+61)/3176358Robert Price01/2022
19252^585832-112799176354Enzo Doria07/2014
1926(29*10^176240+49)/3176241Robert Price09/2021
1927(2^585387-11)/3176219Stefano Morozzi08/2022
19282^585336-461039176204Enzo Doria06/2015
1929(25*10^176164+143)/3176165Robert Price08/2020
19302^585095-1848127176132Enzo Doria08/2015
1931(5*10^176101-311)/9176101Robert Price12/2021
19326*10^176092+77176093Robert Price06/2020
19332^584950-115451176088Enzo Doria07/2015
1934(646*10^176044+11)/9176046Robert Price10/2021
19352^584671-3697176004Yves Minet03/2017
1936(13*10^175965-37)/3175966Robert Price01/2019
19372*10^175860-87175861Robert Price04/2018
1938(86*10^175774-221)/9175775Robert Price09/2019
19399*10^175654+47175655Robert Price01/2022
194010^175608+2971175609Mike Oakes05/2010
194110^175608-55829175608Patrick De Geest09/2013
19422^583051+1879793175516Enzo Doria09/2016
1943(76*10^175514+491)/9175515Robert Price10/2021
19442^582860-23829175459Enzo Doria08/2013
1945(8*10^175428-53)/9175428Serge Batalov11/2022
1946(28*10^175417-67)/3175418Robert Price10/2020
19472^582670-23913175402Enzo Doria08/2013
19482^582573-29563175372Enzo Doria08/2015
19492^582435-1862767175331Enzo Doria12/2015
195010^175295-40000001175295Robert Price07/2022
1951(11*10^175250-149)/3175251Robert Price09/2018
1952(29*10^175236+31)/3175237Robert Price04/2021
19532^582072-1848599175222Enzo Doria08/2015
1954(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
1955Phi(262767,10)/259613797175168Makoto Kamada12/2022
1956(2^581871-15)/7175160Stefano Morozzi08/2022
1957(5*10^175117-311)/9175117Robert Price12/2021
1958(220221^32768+1)/2175075Serge Batalov03/2018
19592^581560+1874911175068Enzo Doria06/2016
1960(25*10^174987-97)/9174988Robert Price01/2022
1961(75^93307-1)/74174955Paul Bourdelais09/2017
1962(47*10^174790+493)/9174791Robert Price03/2019
19632^580528-114035174757Enzo Doria11/2014
1964(19*10^174754+737)/9174755Robert Price07/2018
1965(35*10^174704-377)/9174705Robert Price07/2018
1967(49*10^174681+293)/9174682Robert Price03/2021
19666*10^174681+11174682Robert Price07/2022
19683*10^174665-97174666Robert Price07/2018
19692^580046-459161174612Enzo Doria05/2015
19702^579992-39779174595Enzo Doria09/2015
1971(29*10^174481-149)/3174482Robert Price08/2022
1972(4*10^174423+101)/3174424Robert Price11/2021
1973(2^579371-17)/3174408Stefano Morozzi08/2022
1974(2*10^174301-71)/3174301Robert Price12/2017
197514^152048+3174267Paul Bourdelais12/2020
1976(2^578696+1)/257174203Lelio R Paula09/2015
19772^578656-1851809174193Enzo Doria08/2015
19782^578583-113917174171Enzo Doria10/2014
19792^578434-83174126Yves Minet07/2017
198015^148048-2174118Robert Price06/2015
19815*10^174101+81174102Robert Price03/2019
19822^578346+2794249174100Enzo Doria03/2016
198310^173947+1372429173948Patrick De Geest08/2021
198510^173947-500000001173947Robert Price12/2020
198410^173947-286391173947Patrick De Geest08/2021
19865*10^173904-13173905Robert Price01/2019
1987(8*10^173862-59)/3173863Robert Price08/2021
1988(71*10^173854-287)/9173855Robert Price09/2019
1989(43*10^173826+101)/9173827Robert Price11/2018
19902*10^173809-87173810Robert Price04/2018
1991(2^577372-23)/7173806Stefano Morozzi08/2022
1992(L!41532)/2173772Serge Batalov07/2017
19932^577146-49877173739Enzo Doria10/2015
19942^576889+49727173661Enzo Doria09/2016
1995(167*10^173571-17)/3173573Robert Price03/2020
199637803^37916+37916^37803173562Norbert Schneider06/2022
19975*10^173534+29173535Robert Price12/2020
1998(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
19994*10^173509+99173510Robert Price12/2020
2000(13*10^173467-37)/3173468Robert Price01/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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