PRP Records

Probable Primes Top 10000

(280932 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 ?
12512^613033-114621184542Enzo Doria05/2015
1252(9^193247+1)/10184404Paul Bourdelais02/2010
12532^612341-1604809184334Enzo Doria05/2015
1254(2^611999-1)/18464214225958267477777390354183184199Dario Alpern06/2017
1255(14*10^184150+37)/3184151Robert Price12/2018
12562^611731-4837184150Yves Minet08/2018
12573*10^184124-7184125Robert Price08/2015
12582^611628-24537184119Enzo Doria08/2013
12593*10^184110+13184111Robert Price07/2018
12602^611460+71881184068Enzo Doria04/2016
12614*10^184004-63184005Robert Price10/2018
12622^610982-1867301183924Enzo Doria03/2016
12633*10^183872-49183873Robert Price07/2018
12642^610597+1178897183809Enzo Doria05/2016
1265(65*10^183768-29)/9183769Robert Price01/2021
1266(17*10^183764+31)/3183765Robert Price01/2019
1267(28*10^183760-1)/9183761Serge Batalov10/2014
12682^610401+1277183750Lelio R Paula07/2013
12692^610356-1849019183736Enzo Doria08/2015
1270(63^102103+1)/64183717Paul Bourdelais10/2017
127123*10^183710-7183712Robert Price02/2020
1272(2^610289+1)/(3*528882550291)183704Gord Palameta08/2018
1273(4*10^183659+149)/9183659Robert Price04/2018
12742^609846-1834251183582Enzo Doria07/2015
127510^183546+1547323183547Patrick De Geest02/2021
127710^183546-800000001183546Robert Price09/2020
127610^183546-584297183546Patrick De Geest02/2021
1278(23*10^183477-71)/3183478Robert Price07/2020
127911^176176-240183469Enzo Doria11/2012
1280(41^113749+1)/42183451Paul Bourdelais11/2017
12816*10^183429+53183430Robert Price05/2020
1282(28*10^183403+191)/3183404Robert Price02/2020
1283(101^91463+1)/102183320Paul Bourdelais11/2017
12842^608965-113989183317Enzo Doria10/2014
1285A005165(43592)183312Serge Batalov07/2017
1286(61*10^183294+119)/9183295Robert Price05/2019
12872^608814-461261183272Enzo Doria06/2015
1288(163*10^183227-1)/9183229Serge Batalov12/2014
12892^608541-608541^2183190Henri Lifchitz02/2018
12902^608293+143807183115Enzo Doria10/2016
12912^608164-462419183076Enzo Doria08/2015
12922^607950-1862303183012Enzo Doria12/2015
1293(46*10^182896+683)/9182897Robert Price03/2019
1294(2*10^182787+73)/3182787Robert Price09/2020
12952^607101+1871987182756Enzo Doria05/2016
12962^606869-69175182686Enzo Doria11/2015
1297(23*10^182666-71)/3182667Robert Price07/2020
12983*10^182614-11182615Robert Price07/2018
12992^606560-357182593Enzo Doria05/2014
130066*10^182420+7182422Robert Price07/2020
13012^605687+1866983182330Enzo Doria03/2016
13022^605655-114445182321Enzo Doria02/2015
130394*10^182291-3182293Robert Price05/2020
1304(20^140053+1)/21182212Paul Bourdelais04/2010
1305(14*10^182177-221)/9182178Robert Price04/2018
13062^605174-112751182176Enzo Doria06/2014
13072^604761+1874507182052Enzo Doria06/2016
13082^604705+1871957182035Enzo Doria05/2016
1309(14*10^182000+229)/9182001Robert Price03/2018
1310(10^181996+41)/3181996Robert Price12/2017
1311(5*10^181950-101)/3181951Robert Price04/2018
13122^603915+75233181797Enzo Doria04/2016
13137*10^181594-57181595Robert Price06/2020
1314(194*10^181369-11)/3181371Robert Price09/2020
131511^174145-360181354Enzo Doria10/2012
13162^602351-396765181326Enzo Doria08/2013
13176*10^181306+17181307Robert Price04/2019
1318(286*10^181220-1)/3181222Robert Price11/2020
13192^601957-113833181208Enzo Doria09/2014
132066^99581-65^99581181193Robert Price09/2013
132110^181182+383973181183Patrick De Geest04/2016
132210^181182-21181182Serge Batalov12/2014
1323(5*10^181127-29)/3181128Robert Price03/2018
13242^601521-29143181076Enzo Doria07/2015
13252^601442-2797811181053Enzo Doria04/2016
132644*10^181029+3181031Robert Price04/2020
13275*10^180992-9180993Robert Price05/2015
132810^180979+79477180980Patrick De Geest04/2016
132910^180979+107739180980Patrick De Geest04/2016
133010^180979-11180979Serge Batalov12/2014
13312^601023-113851180926Enzo Doria10/2014
1332(23*10^180862-143)/3180863Robert Price12/2019
13333*10^180852+29180853Robert Price05/2018
1334(79*10^180710-1)/3180712Robert Price02/2020
13352^600300-1852559180709Enzo Doria08/2015
1336(2*10^180706-77)/3180706Robert Price02/2021
1337(10^180689+71)/9180689Serge Batalov07/2015
13382^600209+76487180681Enzo Doria05/2016
13392^599702-369885180529Enzo Doria11/2013
1340Tau(643^11688)180524Nik Lygeros / Olivier Rozier05/2015
1341(2951*29^123418-3)/4180490Curtis Bright05/2015
1342(29*10^180432-17)/3180433Robert Price09/2019
13434*10^180360+93180361Robert Price08/2018
13442^598942+80779180300Enzo Doria07/2016
1345(38*10^180296+403)/9180297Robert Price10/2018
13462^598591-1844797180194Enzo Doria06/2015
1347(100^90089+1)/101180176Paul Bourdelais08/2017
13486*10^179970+91179971Robert Price05/2019
1349(4*10^179963-79)/3179964Robert Price02/2018
1350Gamma-Prime(179849)179849Eric W. Weisstein06/2011
13512^597424-1859729179843Enzo Doria11/2015
1352Phi(180683,10)179760Maksym Voznyy09/2015
1353(10^180683-1)*9/(10^643-1)/(10^281-1)179760Robert Price07/2016
1354(3^376657-2^376657)/22301107657179701Mike Oakes04/2017
1355(29*10^179697+223)/9179698Robert Price09/2018
1356(68*10^179656+7)/3179658Robert Price01/2020
13572^596690-461261179622Enzo Doria07/2015
13582^596684-113939179620Enzo Doria10/2014
13592*10^179602+63179603Robert Price05/2018
1360(25*10^179488-403)/9179489Robert Price01/2021
13613^375887-112696179344Enzo Doria07/2014
13624*10^179265-71179266Robert Price12/2018
13632^595144-1850429179157Enzo Doria08/2015
13643*10^179138+89179139Robert Price10/2018
13652^594531+82253178972Enzo Doria09/2016
13662^594260-2787899178891Enzo Doria11/2015
13672^593631+101381178701Jorge Menendez04/2018
136810^178695+136719178696Patrick De Geest05/2016
136910^178695-71178695Serge Batalov12/2014
1370(2*10^178649-161)/3178649Robert Price12/2020
1371(691^62903-1)/690178609Michael Stocker05/2020
1372(2^148330+1)^4-2178608Cletus Emmanuel12/2003
13732^593222-14145178578Jorge Menendez10/2017
13747*10^178566+33178567Robert Price06/2020
13752^593178+1867219178565Enzo Doria03/2016
1376(302*10^178369+13)/9178371Robert Price02/2020
1377(26*10^178296-113)/3178297Robert Price06/2020
1378(18^142031-1)/17178287Paul Bourdelais03/2010
1379(5*10^178206+91)/3178207Robert Price04/2018
13802^591872-291929178172Enzo Doria07/2015
13812^591682-286871178115Enzo Doria07/2015
13824*10^178091+9178092Robert Price05/2015
1383410747#+478483178007Makoto Morimoto02/2016
13843*10^177872+73177873Robert Price08/2018
13852^590762-396765177838Enzo Doria08/2013
1386(136*10^177754-1)/9177756Serge Batalov12/2014
1387ReverseConsecutiveIntegerPrime(37765)177719Eric W. Weisstein04/2010
1388(266*10^177577-11)/3177579Robert Price04/2020
1389(11*10^177466-113)/3177467Robert Price10/2018
13903*10^177373-97177374Robert Price07/2018
13912^589204+1881151177369Enzo Doria11/2016
13922^589132-69479177347Enzo Doria01/2016
1393(101*10^177302-17)/3177304Robert Price02/2020
13942^588912-113519177281Enzo Doria08/2014
139515^150706+2177245Robert Price06/2015
13962^588194-1861001177065Enzo Doria11/2015
1397(23*10^176964-47)/3176965Robert Price09/2019
1398(19*10^176932+521)/9176933Robert Price05/2018
1399(8*10^176908+43)/3176909Robert Price06/2018
1400(85*10^176900+203)/9176901Robert Price09/2020
14012^587560-113699176874Enzo Doria09/2014
1402(101*10^176815-17)/3176817Robert Price02/2020
1403(25*10^176715-37)/3176716Robert Price10/2019
14045^252763-12862176674Enzo Doria05/2014
14052^586804+81721176646Enzo Doria08/2016
1406(10^176584+77)/3176584Robert Price01/2018
14072^586570+1874419176576Enzo Doria06/2016
14082^585994-3311176402Yves Minet12/2014
14098*10^176383-81176384Robert Price02/2021
14102^585832-112799176354Enzo Doria07/2014
14112^585336-461039176204Enzo Doria06/2015
1412(25*10^176164+143)/3176165Robert Price08/2020
14132^585095-1848127176132Enzo Doria08/2015
14146*10^176092+77176093Robert Price06/2020
14152^584950-115451176088Enzo Doria07/2015
14162^584671-3697176004Yves Minet03/2017
1417(13*10^175965-37)/3175966Robert Price01/2019
14182*10^175860-87175861Robert Price04/2018
1419(86*10^175774-221)/9175775Robert Price09/2019
142010^175608+2971175609Mike Oakes05/2010
142110^175608-55829175608Patrick De Geest09/2013
14222^583051+1879793175516Enzo Doria09/2016
14232^582860-23829175459Enzo Doria08/2013
1424(28*10^175417-67)/3175418Robert Price10/2020
14252^582670-23913175402Enzo Doria08/2013
14262^582573-29563175372Enzo Doria08/2015
14272^582435-1862767175331Enzo Doria12/2015
1428(11*10^175250-149)/3175251Robert Price09/2018
1429(29*10^175236+31)/3175237Robert Price04/2021
14302^582072-1848599175222Enzo Doria08/2015
1431(404267#+465)/(3^4*5^2*31)175208Makoto Morimoto06/2019
1432(220221^32768+1)/2175075Serge Batalov03/2018
14332^581560+1874911175068Enzo Doria06/2016
1434(75^93307-1)/74174955Paul Bourdelais09/2017
1435(47*10^174790+493)/9174791Robert Price03/2019
14362^580528-114035174757Enzo Doria11/2014
1437(19*10^174754+737)/9174755Robert Price07/2018
1438(35*10^174704-377)/9174705Robert Price07/2018
1439(49*10^174681+293)/9174682Robert Price03/2021
14403*10^174665-97174666Robert Price07/2018
14412^580046-459161174612Enzo Doria05/2015
14422^579992-39779174595Enzo Doria09/2015
1443(2*10^174301-71)/3174301Robert Price12/2017
144414^152048+3174267Paul Bourdelais12/2020
1445(2^578696+1)/257174203Lelio R Paula09/2015
14462^578656-1851809174193Enzo Doria08/2015
14472^578583-113917174171Enzo Doria10/2014
14482^578434-83174126Yves Minet07/2017
144915^148048-2174118Robert Price06/2015
14505*10^174101+81174102Robert Price03/2019
14512^578346+2794249174100Enzo Doria03/2016
145210^173947-500000001173947Robert Price12/2020
14535*10^173904-13173905Robert Price01/2019
1454(71*10^173854-287)/9173855Robert Price09/2019
1455(43*10^173826+101)/9173827Robert Price11/2018
14562*10^173809-87173810Robert Price04/2018
1457(L!41532)/2173772Serge Batalov07/2017
14582^577146-49877173739Enzo Doria10/2015
14592^576889+49727173661Enzo Doria09/2016
1460(167*10^173571-17)/3173573Robert Price03/2020
14615*10^173534+29173535Robert Price12/2020
1462(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
14634*10^173509+99173510Robert Price12/2020
1464(13*10^173467-37)/3173468Robert Price01/2019
14652^576016-113919173399Enzo Doria11/2014
14662^575911-1849387173367Enzo Doria08/2015
1467(16*10^173251+107)/3173252Robert Price03/2019
14682^575196-114053173152Enzo Doria11/2014
14697*10^173135-53173136Robert Price06/2020
14702^574591-115387172970Enzo Doria07/2015
1471(202*10^172940-13)/9172942Robert Price01/2020
14722^574328+81121172890Enzo Doria07/2016
1473(115*10^172862-1)/3172864Serge Batalov12/2014
14743*10^172812+13172813Robert Price07/2018
14754*5^247217-9172798Lelio R Paula10/2015
14766*10^172772-31172773Robert Price07/2020
147769061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
1478(34*10^172693-547)/9172694Robert Price03/2021
14795*10^172692+57172693Robert Price12/2018
14802^573668-2782319172692Enzo Doria09/2015
14812^573444-1855109172624Enzo Doria09/2015
14823^361608+2172531Robert Price08/2014
1483(54^99563+1)/55172481Paul Bourdelais11/2017
14842^572592-114893172368Enzo Doria05/2015
14854*10^172354-39172355Robert Price09/2020
14865^246497-4^246497172295Jean-Louis Charton11/2008
1487(38^109037-1)/37172254Paul Bourdelais10/2017
14883*10^172219+73172220Robert Price08/2018
1489(36^110503+1)/37171975Lelio R Paula04/2017
1490(22*10^171929-73)/3171930Robert Price04/2019
14914*10^171891-63171892Robert Price10/2018
149267*10^171882-9171884Robert Price03/2021
14932^570980-2782289171883Enzo Doria09/2015
1494(25*10^171849-37)/3171850Robert Price10/2019
149510^171832-10001171832Robert Price02/2021
1496(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
1497(536*10^171601-23)/9171603Robert Price02/2020
14987*10^171535-99171536Robert Price06/2019
1499(28*10^171534+101)/3171535Robert Price09/2020
15002^569563-1854607171456Enzo Doria09/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!