PRP Records

Probable Primes Top 10000

(291192 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 ?
1751(29*10^175236+31)/3175237Robert Price04/2021
17522^582072-1848599175222Enzo Doria08/2015
1753(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
1754(2^581871-15)/7175160Stefano Morozzi08/2022
1755(5*10^175117-311)/9175117Robert Price12/2021
1756(220221^32768+1)/2175075Serge Batalov03/2018
17572^581560+1874911175068Enzo Doria06/2016
1758(25*10^174987-97)/9174988Robert Price01/2022
1759(75^93307-1)/74174955Paul Bourdelais09/2017
1760(47*10^174790+493)/9174791Robert Price03/2019
17612^580528-114035174757Enzo Doria11/2014
1762(19*10^174754+737)/9174755Robert Price07/2018
1763(35*10^174704-377)/9174705Robert Price07/2018
1764(49*10^174681+293)/9174682Robert Price03/2021
17656*10^174681+11174682Robert Price07/2022
17663*10^174665-97174666Robert Price07/2018
17672^580046-459161174612Enzo Doria05/2015
17682^579992-39779174595Enzo Doria09/2015
1769(29*10^174481-149)/3174482Robert Price08/2022
1770(4*10^174423+101)/3174424Robert Price11/2021
1771(2^579371-17)/3174408Stefano Morozzi08/2022
1772(2*10^174301-71)/3174301Robert Price12/2017
177314^152048+3174267Paul Bourdelais12/2020
1774(2^578696+1)/257174203Lelio R Paula09/2015
17752^578656-1851809174193Enzo Doria08/2015
17762^578583-113917174171Enzo Doria10/2014
17772^578434-83174126Yves Minet07/2017
177815^148048-2174118Robert Price06/2015
17795*10^174101+81174102Robert Price03/2019
17802^578346+2794249174100Enzo Doria03/2016
178110^173947+1372429173948Patrick De Geest08/2021
178310^173947-500000001173947Robert Price12/2020
178210^173947-286391173947Patrick De Geest08/2021
17845*10^173904-13173905Robert Price01/2019
1785(8*10^173862-59)/3173863Robert Price08/2021
1786(71*10^173854-287)/9173855Robert Price09/2019
1787(43*10^173826+101)/9173827Robert Price11/2018
17882*10^173809-87173810Robert Price04/2018
1789(2^577372-23)/7173806Stefano Morozzi08/2022
1790(L!41532)/2173772Serge Batalov07/2017
17912^577146-49877173739Enzo Doria10/2015
17922^576889+49727173661Enzo Doria09/2016
1793(167*10^173571-17)/3173573Robert Price03/2020
179437803^37916+37916^37803173562Norbert Schneider06/2022
17955*10^173534+29173535Robert Price12/2020
1796(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
17974*10^173509+99173510Robert Price12/2020
1798(13*10^173467-37)/3173468Robert Price01/2019
17992^576016-113919173399Enzo Doria11/2014
18002^575911-1849387173367Enzo Doria08/2015
18012^575614+9173278Stefano Morozzi04/2021
1802(16*10^173251+107)/3173252Robert Price03/2019
18032^575196-114053173152Enzo Doria11/2014
18047*10^173135-53173136Robert Price06/2020
1805(301*10^173047+23)/9173049Robert Price06/2021
18062^574591-115387172970Enzo Doria07/2015
1807(202*10^172940-13)/9172942Robert Price01/2020
180845^104608+104608^45172940Norbert Schneider06/2021
18092^574328+81121172890Enzo Doria07/2016
1810(115*10^172862-1)/3172864Serge Batalov12/2014
18113*10^172812+13172813Robert Price07/2018
18124*5^247217-9172798Lelio R Paula10/2015
18136*10^172772-31172773Robert Price07/2020
181469061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
1815(34*10^172693-547)/9172694Robert Price03/2021
18165*10^172692+57172693Robert Price12/2018
18172^573668-2782319172692Enzo Doria09/2015
18182^573444-1855109172624Enzo Doria09/2015
1819(14*10^172532-29)/3172533Robert Price09/2021
18203^361608+2172531Robert Price08/2014
1821(54^99563+1)/55172481Paul Bourdelais11/2017
18222^572592-114893172368Enzo Doria05/2015
18234*10^172354-39172355Robert Price09/2020
182437535^37674+37674^37535172338Norbert Schneider05/2022
1825(11*10^172322-119)/9172323Robert Price11/2021
18265^246497-4^246497172295Jean-Louis Charton11/2008
1827(38^109037-1)/37172254Paul Bourdelais10/2017
1828(4*10^172241+89)/3172242Robert Price08/2021
18293*10^172219+73172220Robert Price08/2018
1830A352736(15)172032Kellen Shenton05/2022
1831(36^110503+1)/37171975Lelio R Paula04/2017
18328*10^171934+71171935Robert Price05/2022
1833(11*10^171933+601)/9171934Robert Price02/2022
1834(22*10^171929-73)/3171930Robert Price04/2019
1835(49*10^171892-319)/9171893Robert Price10/2021
18364*10^171891-63171892Robert Price10/2018
183767*10^171882-9171884Robert Price03/2021
18382^570980-2782289171883Enzo Doria09/2015
1839(25*10^171849-37)/3171850Robert Price10/2019
184010^171832+387909171833Patrick De Geest08/2021
184110^171832-10001171832Robert Price02/2021
1843(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
1842(2^570769-9)/7171818Stefano Morozzi08/2022
1844(74*10^171651-29)/9171652Robert Price06/2022
1845(536*10^171601-23)/9171603Robert Price02/2020
18467*10^171535-99171536Robert Price06/2019
1847(28*10^171534+101)/3171535Robert Price09/2020
18482^569563-1854607171456Enzo Doria09/2015
18493*10^171391+59171392Robert Price08/2018
1850(13*10^171306-37)/3171307Robert Price01/2019
18518*10^171296+87171297Robert Price10/2019
1852(55^98419-1)/54171284Paul Bourdelais12/2017
1853(29*10^171275+67)/3171276Robert Price12/2019
1854(457*10^171248-7)/9171250Robert Price09/2022
1855(194*10^171193+1)/3171195Robert Price01/2022
18562^568642+1876129171179Enzo Doria07/2016
18574*10^171146-47171147Robert Price10/2021
1858(19*10^170970+131)/3170971Robert Price06/2020
1859(46*10^170932+143)/9170933Robert Price01/2019
1860(79*10^170901-1)/3170903Robert Price02/2020
1861(58*10^170842+221)/9170843Robert Price02/2017
1862(29*10^170830+583)/9170831Robert Price06/2021
18633*10^170800+73170801Robert Price08/2018
1864(29*10^170799-119)/9170800Robert Price12/2021
186511^164009-270170798Enzo Doria10/2012
18662*10^170767+41170768Robert Price05/2018
18673^357706-112358170670Enzo Doria07/2014
1868TheodorusPrime(170657)170657Eric W. Weisstein08/2013
18692^566871+1876163170646Enzo Doria07/2016
1870(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
18712^566496+7170533Donovan Johnson07/2006
1872(7^201653+1)/8170416Paul Bourdelais02/2010
18737*10^170348+33170349Robert Price06/2020
18742^565183-352021170138Enzo Doria07/2015
18752^565143-114457170125Enzo Doria02/2015
18762^564976-49869170075Enzo Doria10/2015
1877(7*10^169944+23)/3169945Robert Price06/2020
1878(37*10^169943+251)/9169944Robert Price09/2021
18792^564526-351401169940Enzo Doria07/2015
18804*10^169759+19169760Robert Price10/2018
1881(2^563903-13)/5169752Stefano Morozzi08/2022
188221^128327-20^128327169677Jean-Louis Charton11/2014
18832^563583+89169656Stefano Morozzi04/2021
1884(4*10^169559+83)/3169560Robert Price02/2018
1885(194*10^169461-17)/3169463Robert Price09/2020
18862^562749+2793047169405Enzo Doria02/2016
1887(154*10^169337-1)/9169339Serge Batalov12/2014
1888(109*10^169337+11)/3169339Robert Price06/2022
1889(56*10^169311+691)/9169312Robert Price05/2019
18902^562369-29503169290Enzo Doria08/2015
1891(17*10^169283+19)/9169284Robert Price03/2021
189210^169074-5000000001169074Robert Price09/2022
18938*10^169071+59169072Robert Price11/2021
1894(10^169044+173)/3169044Robert Price05/2021
1895(22*10^169019+383)/9169020Robert Price05/2018
1896(64*10^168935+143)/9168936Robert Price05/2021
1897(22*10^168906+47)/3168907Robert Price06/2021
18985*10^168807+87168808Robert Price02/2019
1899(77*10^168803-149)/9168804Robert Price03/2022
19004*10^168788-47168789Robert Price10/2021
1901(154*10^168781+17)/9168783Robert Price06/2022
1902(418*10^168751-31)/9168753Robert Price05/2022
1903(29*10^168711+691)/9168712Robert Price08/2021
19042^560405-39943168699Enzo Doria09/2015
1905(397*10^168634+17)/9168636Robert Price03/2022
190689*10^168614-7168616Robert Price04/2020
1907(23*10^168608-83)/3168609Robert Price08/2019
1908(94*10^168541+11)/3168543Robert Price04/2020
19092^559686-350471168483Enzo Doria06/2015
19102^559672-1855889168479Enzo Doria09/2015
1911(5*10^168379-473)/9168379Robert Price01/2018
19122^559000-59939168276Enzo Doria11/2015
1913(16*10^168181+41)/3168182Robert Price03/2019
1914(19*10^168173+77)/3168174Robert Price05/2019
1915(74*10^168170+529)/9168171Robert Price02/2022
19162^558640-114149168168Enzo Doria12/2014
19172^558498-1849277168125Enzo Doria08/2015
19182^558476-1850249168119Enzo Doria08/2015
1919(7*10^168067+71)/3168068Robert Price05/2018
19202^558150-1852211168020Enzo Doria08/2015
19212^558125-113661168013Enzo Doria09/2014
1922393^64747-392^64747167980Jean-Louis Charton08/2012
1923(13*10^167911+179)/3167912Robert Price11/2018
1924(26*10^167861-167)/3167862Robert Price10/2019
192539^105456+2167788Robert Price04/2015
1926(28^115877-1)/27167691Paul Bourdelais12/2017
19276*10^167662-13167663Robert Price07/2022
192810^167639+121911167640Patrick De Geest07/2018
192910^167639-8001167639Robert Price03/2018
19302^556504-462059167525Enzo Doria07/2015
1931(88*10^167522-637)/9167523Robert Price11/2020
19325*10^167510+9167511Robert Price08/2015
19337*10^167437-93167438Robert Price08/2020
193411^160663+6167314Paul Bourdelais02/2021
1935(7*10^167308-493)/9167308Robert Price04/2021
19362^555343+1874333167175Enzo Doria06/2016
19372^555210-461261167135Enzo Doria07/2015
19389*10^166996+59166997Robert Price01/2020
1939(68*10^166976-329)/9166977Robert Price03/2021
1940(64*10^166901+683)/9166902Robert Price06/2022
19412^554372+1880527166883Enzo Doria11/2016
19422^554299+72173166861Enzo Doria04/2016
1943(185*10^166837+7)/3166839Robert Price03/2020
1944(14*10^166813+139)/9166814Robert Price11/2021
19452^554037-2797063166782Enzo Doria03/2016
1946(49*10^166721-139)/9166722Robert Price03/2019
19472*10^166646+69166647Robert Price06/2020
19482^553484-29819166616Enzo Doria08/2015
1949(188*10^166611+7)/3166613Robert Price03/2020
19502^553383-2784217166585Enzo Doria10/2015
19512^553069+76427166491Enzo Doria05/2016
19522*10^166458+51166459Robert Price05/2018
1953589^60089-588^60089166454Jean-Louis Charton09/2012
195411^159756-2424166369Mike Oakes06/2010
19552^552649-361275166364Enzo Doria05/2014
19562^552628-113669166358Enzo Doria09/2014
1957(19*10^166325+137)/3166326Robert Price03/2022
195810^166324+550603166325Patrick De Geest07/2018
195910^166324-801166324Robert Price02/2018
1960(85*10^166297-1)/3166299Robert Price02/2020
19618*10^166227+87166228Robert Price10/2019
19622^552137+1879397166210Enzo Doria09/2016
1963(103*10^166126+11)/3166128Robert Price01/2021
1964(22*10^166077+179)/3166078Robert Price02/2022
1965(23^121949-1)/22166061Paul Bourdelais10/2017
19662^551542+19249166031Payam Samidoost08/2002
19672^551535-23821166029Enzo Doria08/2013
19682^551507-23557166021Enzo Doria08/2013
196910^165947-7000000001165947Robert Price12/2021
19704*10^165938-47165939Robert Price10/2021
19717*10^165916-3165917Robert Price08/2015
1972(29*10^165796+67)/3165797Robert Price12/2019
197381^86837-80^86837165728Robert Price01/2015
1974(71*10^165663-539)/9165664Robert Price07/2019
19752^550270-69551165648Enzo Doria12/2015
1976(202*10^165569-13)/9165571Robert Price01/2020
19772^550000-23625165567Enzo Doria08/2013
19782^549675-1852057165469Enzo Doria08/2015
1979(529*10^165394-7)/9165396Robert Price08/2021
1980-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1981(28*10^165358-1)/9165359Serge Batalov10/2014
19822^549278+1879669165350Enzo Doria09/2016
1983(7*10^165350-439)/9165350Robert Price02/2018
19842^549252-351269165342Enzo Doria06/2015
198567*10^165327-9165329Robert Price03/2021
1987(14*10^165282+73)/3165283Robert Price12/2018
1986(8*10^165283-629)/9165283Robert Price01/2022
19882^549049+2797607165281Enzo Doria04/2016
1989(218*10^165258+7)/9165260Robert Price06/2022
1990(7*10^165239+107)/3165240Robert Price02/2018
1991(44^100511-1)/43165184Paul Bourdelais11/2017
1992(7*10^165134+107)/3165135Robert Price02/2018
1993(301*10^165082+23)/9165084Robert Price06/2021
1994(23*10^165060-83)/3165061Robert Price08/2019
1995(76*10^164984+77)/9164985Robert Price10/2019
1996(4*10^164929-211)/9164929Robert Price03/2022
199710^164878-500001164878Robert Price03/2022
19989*10^164791-89164792Robert Price04/2020
19992^547178-1856501164717Enzo Doria10/2015
200011^158160-60164707Enzo Doria07/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!