PRP Records

Probable Primes Top 10000

(291910 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(100^90089+1)/101180176Paul Bourdelais08/2017
1752(29*10^180072+691)/9180073Robert Price08/2021
1753(59*10^180038+157)/9180039Robert Price12/2021
175495*10^180019-9180021Robert Price01/2022
17556*10^179970+91179971Robert Price05/2019
1756(4*10^179963-79)/3179964Robert Price02/2018
1757(403*10^179944-43)/9179946Robert Price06/2021
1758Gamma-Prime(179849)179849Eric W. Weisstein06/2011
17592^597424-1859729179843Enzo Doria11/2015
1760Phi(180683,10)179760Maksym Voznyy09/2015
1761(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
1762(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
1763(29*10^179697+223)/9179698Robert Price09/2018
17642^596884+73179680Stefano Morozzi04/2021
1765(11*10^179679+13)/3179680Robert Price03/2022
1766(68*10^179656+7)/3179658Robert Price01/2020
1767(10^179643+173)/3179643Robert Price05/2021
17682^596690-461261179622Enzo Doria07/2015
17692^596684-113939179620Enzo Doria10/2014
17702*10^179602+63179603Robert Price05/2018
1771(25*10^179488-403)/9179489Robert Price01/2021
17727*10^179460+99179461Robert Price05/2021
17733^375887-112696179344Enzo Doria07/2014
17744*10^179265-71179266Robert Price12/2018
17752*10^179193+83179194Robert Price12/2021
17762^595144-1850429179157Enzo Doria08/2015
17772^595122-5179150Stefano Morozzi07/2022
17783*10^179138+89179139Robert Price10/2018
1779(52*10^179062-133)/9179063Robert Price09/2021
17802^594531+82253178972Enzo Doria09/2016
1781(664*10^178939-61)/9178941Robert Price09/2021
17822^594260-2787899178891Enzo Doria11/2015
1783(14*10^178822+67)/9178823Robert Price05/2022
1784(29*10^178732-119)/9178733Robert Price12/2021
17852^593631+101381178701Jorge Menendez04/2018
178610^178695+136719178696Patrick De Geest05/2016
178710^178695-71178695Serge Batalov12/2014
1788(2*10^178649-161)/3178649Robert Price12/2020
1789(691^62903-1)/690178609Michael Stocker05/2020
1790(2^148330+1)^4-2178608Cletus Emmanuel12/2003
17912^593222-14145178578Jorge Menendez10/2017
17927*10^178566+33178567Robert Price06/2020
17932^593178+1867219178565Enzo Doria03/2016
1794(38*10^178456+151)/9178457Robert Price03/2022
1795(302*10^178369+13)/9178371Robert Price02/2020
1796(26*10^178296-113)/3178297Robert Price06/2020
1797(18^142031-1)/17178287Paul Bourdelais03/2010
1798(13*10^178233+137)/3178234Robert Price06/2021
1799(5*10^178206+91)/3178207Robert Price04/2018
18002^591872-291929178172Enzo Doria07/2015
18012^591682-286871178115Enzo Doria07/2015
18024*10^178091+9178092Robert Price05/2015
1803410747#+478483178007Makoto Morimoto02/2016
18043*10^177872+73177873Robert Price08/2018
18052^590762-396765177838Enzo Doria08/2013
1806(136*10^177754-1)/9177756Serge Batalov12/2014
1807ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
1808Smr(37765)177719Eric W. Weisstein12/2021
1809(266*10^177577-11)/3177579Robert Price04/2020
1810(11*10^177466-113)/3177467Robert Price10/2018
18113*10^177373-97177374Robert Price07/2018
18122^589204+1881151177369Enzo Doria11/2016
18132^589132-69479177347Enzo Doria01/2016
1814(101*10^177302-17)/3177304Robert Price02/2020
18152^588912-113519177281Enzo Doria08/2014
1816(682*10^177266-7)/9177268Robert Price08/2021
181715^150706+2177245Robert Price06/2015
18182^588194-1861001177065Enzo Doria11/2015
18195*10^177016-37177017Robert Price11/2021
1820(23*10^176964-47)/3176965Robert Price09/2019
182120530^41031+41031^20530176942Norbert Schneider07/2022
1822(19*10^176932+521)/9176933Robert Price05/2018
1823(8*10^176908+43)/3176909Robert Price06/2018
1824(85*10^176900+203)/9176901Robert Price09/2020
18252^587560-113699176874Enzo Doria09/2014
182620596^40995+40995^20596176844Norbert Schneider07/2022
1827(101*10^176815-17)/3176817Robert Price02/2020
1828(25*10^176715-37)/3176716Robert Price10/2019
18295^252763-12862176674Enzo Doria05/2014
183038442^38531+38531^38442176658Norbert Schneider09/2022
18312^586804+81721176646Enzo Doria08/2016
1832(10^176584+77)/3176584Robert Price01/2018
18332^586570+1874419176576Enzo Doria06/2016
1834(157*10^176482-1)/3176484Robert Price01/2022
18352^585994-3311176402Yves Minet12/2014
18368*10^176383-81176384Robert Price02/2021
1837(23*10^176357+61)/3176358Robert Price01/2022
18382^585832-112799176354Enzo Doria07/2014
1839(29*10^176240+49)/3176241Robert Price09/2021
1840(2^585387-11)/3176219Stefano Morozzi08/2022
18412^585336-461039176204Enzo Doria06/2015
1842(25*10^176164+143)/3176165Robert Price08/2020
18432^585095-1848127176132Enzo Doria08/2015
1844(5*10^176101-311)/9176101Robert Price12/2021
18456*10^176092+77176093Robert Price06/2020
18462^584950-115451176088Enzo Doria07/2015
1847(646*10^176044+11)/9176046Robert Price10/2021
18482^584671-3697176004Yves Minet03/2017
1849(13*10^175965-37)/3175966Robert Price01/2019
18502*10^175860-87175861Robert Price04/2018
1851(86*10^175774-221)/9175775Robert Price09/2019
18529*10^175654+47175655Robert Price01/2022
185310^175608+2971175609Mike Oakes05/2010
185410^175608-55829175608Patrick De Geest09/2013
18552^583051+1879793175516Enzo Doria09/2016
1856(76*10^175514+491)/9175515Robert Price10/2021
18572^582860-23829175459Enzo Doria08/2013
1858(8*10^175428-53)/9175428Serge Batalov11/2022
1859(28*10^175417-67)/3175418Robert Price10/2020
18602^582670-23913175402Enzo Doria08/2013
18612^582573-29563175372Enzo Doria08/2015
18622^582435-1862767175331Enzo Doria12/2015
186310^175295-40000001175295Robert Price07/2022
1864(11*10^175250-149)/3175251Robert Price09/2018
1865(29*10^175236+31)/3175237Robert Price04/2021
18662^582072-1848599175222Enzo Doria08/2015
1867(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
1868Phi(262767,10)/259613797175168Makoto Kamada12/2022
1869(2^581871-15)/7175160Stefano Morozzi08/2022
1870(5*10^175117-311)/9175117Robert Price12/2021
1871(220221^32768+1)/2175075Serge Batalov03/2018
18722^581560+1874911175068Enzo Doria06/2016
1873(25*10^174987-97)/9174988Robert Price01/2022
1874(75^93307-1)/74174955Paul Bourdelais09/2017
1875(47*10^174790+493)/9174791Robert Price03/2019
18762^580528-114035174757Enzo Doria11/2014
1877(19*10^174754+737)/9174755Robert Price07/2018
1878(35*10^174704-377)/9174705Robert Price07/2018
1879(49*10^174681+293)/9174682Robert Price03/2021
18806*10^174681+11174682Robert Price07/2022
18813*10^174665-97174666Robert Price07/2018
18822^580046-459161174612Enzo Doria05/2015
18832^579992-39779174595Enzo Doria09/2015
1884(29*10^174481-149)/3174482Robert Price08/2022
1885(4*10^174423+101)/3174424Robert Price11/2021
1886(2^579371-17)/3174408Stefano Morozzi08/2022
1887(2*10^174301-71)/3174301Robert Price12/2017
188814^152048+3174267Paul Bourdelais12/2020
1889(2^578696+1)/257174203Lelio R Paula09/2015
18902^578656-1851809174193Enzo Doria08/2015
18912^578583-113917174171Enzo Doria10/2014
18922^578434-83174126Yves Minet07/2017
189315^148048-2174118Robert Price06/2015
18945*10^174101+81174102Robert Price03/2019
18952^578346+2794249174100Enzo Doria03/2016
189610^173947+1372429173948Patrick De Geest08/2021
189810^173947-500000001173947Robert Price12/2020
189710^173947-286391173947Patrick De Geest08/2021
18995*10^173904-13173905Robert Price01/2019
1900(8*10^173862-59)/3173863Robert Price08/2021
1901(71*10^173854-287)/9173855Robert Price09/2019
1902(43*10^173826+101)/9173827Robert Price11/2018
19032*10^173809-87173810Robert Price04/2018
1904(2^577372-23)/7173806Stefano Morozzi08/2022
1905(L!41532)/2173772Serge Batalov07/2017
19062^577146-49877173739Enzo Doria10/2015
19072^576889+49727173661Enzo Doria09/2016
1908(167*10^173571-17)/3173573Robert Price03/2020
190937803^37916+37916^37803173562Norbert Schneider06/2022
19105*10^173534+29173535Robert Price12/2020
1911(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
19124*10^173509+99173510Robert Price12/2020
1913(13*10^173467-37)/3173468Robert Price01/2019
19142^576016-113919173399Enzo Doria11/2014
19152^575911-1849387173367Enzo Doria08/2015
1916515^63898+63898^515173280Norbert Schneider12/2022
19172^575614+9173278Stefano Morozzi04/2021
1918(16*10^173251+107)/3173252Robert Price03/2019
19192^575196-114053173152Enzo Doria11/2014
19207*10^173135-53173136Robert Price06/2020
1921(301*10^173047+23)/9173049Robert Price06/2021
19222^574591-115387172970Enzo Doria07/2015
1923(202*10^172940-13)/9172942Robert Price01/2020
192445^104608+104608^45172940Norbert Schneider06/2021
19252^574328+81121172890Enzo Doria07/2016
1926(115*10^172862-1)/3172864Serge Batalov12/2014
19273*10^172812+13172813Robert Price07/2018
19284*5^247217-9172798Lelio R Paula10/2015
19296*10^172772-31172773Robert Price07/2020
193069061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
1931(34*10^172693-547)/9172694Robert Price03/2021
19325*10^172692+57172693Robert Price12/2018
19332^573668-2782319172692Enzo Doria09/2015
19342^573444-1855109172624Enzo Doria09/2015
1935(14*10^172532-29)/3172533Robert Price09/2021
19363^361608+2172531Robert Price08/2014
1937(54^99563+1)/55172481Paul Bourdelais11/2017
19382^572592-114893172368Enzo Doria05/2015
19394*10^172354-39172355Robert Price09/2020
194037535^37674+37674^37535172338Norbert Schneider05/2022
1941(11*10^172322-119)/9172323Robert Price11/2021
19425^246497-4^246497172295Jean-Louis Charton11/2008
1943(38^109037-1)/37172254Paul Bourdelais10/2017
1944(4*10^172241+89)/3172242Robert Price08/2021
19453*10^172219+73172220Robert Price08/2018
1946A352736(15)172032Kellen Shenton05/2022
1947(36^110503+1)/37171975Lelio R Paula04/2017
19488*10^171934+71171935Robert Price05/2022
1949(11*10^171933+601)/9171934Robert Price02/2022
1950(22*10^171929-73)/3171930Robert Price04/2019
1951(49*10^171892-319)/9171893Robert Price10/2021
19524*10^171891-63171892Robert Price10/2018
195367*10^171882-9171884Robert Price03/2021
19542^570980-2782289171883Enzo Doria09/2015
1955(25*10^171849-37)/3171850Robert Price10/2019
195610^171832+387909171833Patrick De Geest08/2021
195710^171832-10001171832Robert Price02/2021
1959(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
1958(2^570769-9)/7171818Stefano Morozzi08/2022
1960(74*10^171651-29)/9171652Robert Price06/2022
1961(536*10^171601-23)/9171603Robert Price02/2020
19627*10^171535-99171536Robert Price06/2019
1963(28*10^171534+101)/3171535Robert Price09/2020
19642^569563-1854607171456Enzo Doria09/2015
19653*10^171391+59171392Robert Price08/2018
1966(13*10^171306-37)/3171307Robert Price01/2019
19678*10^171296+87171297Robert Price10/2019
1968(55^98419-1)/54171284Paul Bourdelais12/2017
1969(29*10^171275+67)/3171276Robert Price12/2019
1970(457*10^171248-7)/9171250Robert Price09/2022
1971(194*10^171193+1)/3171195Robert Price01/2022
19722^568642+1876129171179Enzo Doria07/2016
19734*10^171146-47171147Robert Price10/2021
1974(19*10^170970+131)/3170971Robert Price06/2020
1975(46*10^170932+143)/9170933Robert Price01/2019
1976(79*10^170901-1)/3170903Robert Price02/2020
1977(58*10^170842+221)/9170843Robert Price02/2017
1978(29*10^170830+583)/9170831Robert Price06/2021
19793*10^170800+73170801Robert Price08/2018
1980(29*10^170799-119)/9170800Robert Price12/2021
198111^164009-270170798Enzo Doria10/2012
19822*10^170767+41170768Robert Price05/2018
19833^357706-112358170670Enzo Doria07/2014
1984TheodorusPrime(170657)170657Eric W. Weisstein08/2013
19852^566871+1876163170646Enzo Doria07/2016
1986(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
19872^566496+7170533Donovan Johnson07/2006
1988(7^201653+1)/8170416Paul Bourdelais02/2010
19897*10^170348+33170349Robert Price06/2020
19902^565183-352021170138Enzo Doria07/2015
19912^565143-114457170125Enzo Doria02/2015
19922^564976-49869170075Enzo Doria10/2015
1993(7*10^169944+23)/3169945Robert Price06/2020
1994(37*10^169943+251)/9169944Robert Price09/2021
19952^564526-351401169940Enzo Doria07/2015
19964*10^169759+19169760Robert Price10/2018
1997(2^563903-13)/5169752Stefano Morozzi08/2022
199821^128327-20^128327169677Jean-Louis Charton11/2014
19992^563583+89169656Stefano Morozzi04/2021
2000(4*10^169559+83)/3169560Robert Price02/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 02 2023 13:22 (Time in France)

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