PRP Records

Probable Primes Top 10000

(255312 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 ?
12514*5^247217-9172798Lelio R Paula10/2015
125269061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
12535*10^172692+57172693Robert Price12/2018
12542^573668-2782319172692Enzo Doria09/2015
12552^573444-1855109172624Enzo Doria09/2015
12563^361608+2172531Robert Price08/2014
1257(54^99563+1)/55172481Paul Bourdelais11/2017
12582^572592-114893172368Enzo Doria05/2015
12595^246497-4^246497172295Jean-Louis Charton11/2008
1260(38^109037-1)/37172254Paul Bourdelais10/2017
12613*10^172219+73172220Robert Price08/2018
1262(36^110503+1)/37171975Lelio R Paula04/2017
1263(22*10^171929-73)/3171930Robert Price04/2019
12644*10^171891-63171892Robert Price10/2018
12652^570980-2782289171883Enzo Doria09/2015
1266(25*10^171849-37)/3171850Robert Price10/2019
1267(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
12687*10^171535-99171536Robert Price06/2019
12692^569563-1854607171456Enzo Doria09/2015
12703*10^171391+59171392Robert Price08/2018
1271(13*10^171306-37)/3171307Robert Price01/2019
12728*10^171296+87171297Robert Price10/2019
1273(55^98419-1)/54171284Paul Bourdelais12/2017
12742^568642+1876129171179Enzo Doria07/2016
1275(46*10^170932+143)/9170933Robert Price01/2019
1276(58*10^170842+221)/9170843Robert Price02/2017
12773*10^170800+73170801Robert Price08/2018
127811^164009-270170798Enzo Doria10/2012
12792*10^170767+41170768Robert Price05/2018
12803^357706-112358170670Enzo Doria07/2014
1281TheodorusPrime(170657)170657Eric W. Weisstein08/2013
12822^566871+1876163170646Enzo Doria07/2016
1283(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
12842^566496+7170533Donovan Johnson07/2006
1285(7^201653+1)/8170416Paul Bourdelais02/2010
12862^565183-352021170138Enzo Doria07/2015
12872^565143-114457170125Enzo Doria02/2015
12882^564976-49869170075Enzo Doria10/2015
12892^564526-351401169940Enzo Doria07/2015
12904*10^169759+19169760Robert Price10/2018
129121^128327-20^128327169677Jean-Louis Charton11/2014
1292(4*10^169559+83)/3169560Robert Price02/2018
12932^562749+2793047169405Enzo Doria02/2016
1294(154*10^169337-1)/9169339Serge Batalov12/2014
1295(56*10^169311+691)/9169312Robert Price05/2019
12962^562369-29503169290Enzo Doria08/2015
1297(22*10^169019+383)/9169020Robert Price05/2018
12985*10^168807+87168808Robert Price02/2019
12992^560405-39943168699Enzo Doria09/2015
1300(23*10^168608-83)/3168609Robert Price08/2019
13012^559686-350471168483Enzo Doria06/2015
13022^559672-1855889168479Enzo Doria09/2015
1303(5*10^168379-473)/9168379Robert Price01/2018
13042^559000-59939168276Enzo Doria11/2015
1305(16*10^168181+41)/3168182Robert Price03/2019
1306(19*10^168173+77)/3168174Robert Price05/2019
13072^558640-114149168168Enzo Doria12/2014
13082^558498-1849277168125Enzo Doria08/2015
13092^558476-1850249168119Enzo Doria08/2015
1310(7*10^168067+71)/3168068Robert Price05/2018
13112^558150-1852211168020Enzo Doria08/2015
13122^558125-113661168013Enzo Doria09/2014
1313393^64747-392^64747167980Jean-Louis Charton08/2012
1314(13*10^167911+179)/3167912Robert Price11/2018
1315(26*10^167861-167)/3167862Robert Price10/2019
131639^105456+2167788Robert Price04/2015
1317(28^115877-1)/27167691Paul Bourdelais12/2017
131810^167639+121911167640Patrick De Geest07/2018
131910^167639-8001167639Robert Price03/2018
13202^556504-462059167525Enzo Doria07/2015
13215*10^167510+9167511Robert Price08/2015
13222^555343+1874333167175Enzo Doria06/2016
13232^555210-461261167135Enzo Doria07/2015
13242^554372+1880527166883Enzo Doria11/2016
13252^554299+72173166861Enzo Doria04/2016
13262^554037-2797063166782Enzo Doria03/2016
1327(49*10^166721-139)/9166722Robert Price03/2019
13282^553484-29819166616Enzo Doria08/2015
13292^553383-2784217166585Enzo Doria10/2015
13302^553069+76427166491Enzo Doria05/2016
13312*10^166458+51166459Robert Price05/2018
1332589^60089-588^60089166454Jean-Louis Charton09/2012
133311^159756-2424166369Mike Oakes06/2010
13342^552649-361275166364Enzo Doria05/2014
13352^552628-113669166358Enzo Doria09/2014
133610^166324+550603166325Patrick De Geest07/2018
133710^166324-801166324Robert Price02/2018
13388*10^166227+87166228Robert Price10/2019
13392^552137+1879397166210Enzo Doria09/2016
1340(23^121949-1)/22166061Paul Bourdelais10/2017
13412^551542+19249166031Payam Samidoost08/2002
13422^551535-23821166029Enzo Doria08/2013
13432^551507-23557166021Enzo Doria08/2013
13447*10^165916-3165917Robert Price08/2015
134581^86837-80^86837165728Robert Price01/2015
1346(71*10^165663-539)/9165664Robert Price07/2019
13472^550270-69551165648Enzo Doria12/2015
13482^550000-23625165567Enzo Doria08/2013
13492^549675-1852057165469Enzo Doria08/2015
1350-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1351(28*10^165358-1)/9165359Serge Batalov10/2014
13532^549278+1879669165350Enzo Doria09/2016
1352(7*10^165350-439)/9165350Robert Price02/2018
13542^549252-351269165342Enzo Doria06/2015
1355(14*10^165282+73)/3165283Robert Price12/2018
13562^549049+2797607165281Enzo Doria04/2016
1357(7*10^165239+107)/3165240Robert Price02/2018
1358(44^100511-1)/43165184Paul Bourdelais11/2017
1359(7*10^165134+107)/3165135Robert Price02/2018
1360(23*10^165060-83)/3165061Robert Price08/2019
1361(76*10^164984+77)/9164985Robert Price10/2019
13622^547178-1856501164717Enzo Doria10/2015
136311^158160-60164707Enzo Doria07/2012
1364(26*10^164643-167)/3164644Robert Price10/2019
13652^546398-59201164483Enzo Doria10/2015
13662^546332-114893164463Enzo Doria05/2015
13672^545958+1876189164350Enzo Doria07/2016
13682^545878-49841164326Enzo Doria10/2015
1369(10^164284+77)/3164284Robert Price01/2018
13702^545668-4019164263Yves Minet04/2017
1371(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
1372(16*10^164122+197)/3164123Robert Price04/2019
13732^545185+76757164118Enzo Doria05/2016
13742^545076-114329164085Enzo Doria01/2015
1375(2*10^164043-143)/3164043Robert Price03/2018
1376(29^112153+1)/30164011Lelio R Paula03/2017
13772^544757+1874777163989Enzo Doria06/2016
13782^544444-457199163894Enzo Doria01/2015
13792^544264-343529163840Enzo Doria07/2015
13807*10^163780+9163781Robert Price09/2015
13812^543989+2793047163758Enzo Doria02/2016
13822^542870-69551163421Enzo Doria12/2015
13832^542395+72533163278Enzo Doria04/2016
13842^542072-3683163180Yves Minet03/2017
13852^541779-1867357163092Enzo Doria04/2016
13868*10^162924+9162925Robert Price12/2015
13872^540905+81557162829Enzo Doria08/2016
13882^540628-2939162746Yves Minet09/2014
1389919^54919-918^54919162743Jean-Louis Charton01/2013
13903*10^162620-59162621Robert Price09/2018
13913^340694-112960162553Enzo Doria07/2014
13922^539807-114081162499Enzo Doria12/2014
13932^539654-114893162453Enzo Doria05/2015
13942^539617-1851583162441Enzo Doria08/2015
13952^539346+81049162360Enzo Doria07/2016
13962^539220-115499162322Enzo Doria07/2015
13972^539217-113713162321Enzo Doria09/2014
13989^170099-8^170099162316Jean-Louis Charton05/2005
1399(115*10^162153-1)/3162155Serge Batalov12/2014
1400(10^162138+11)/3162138Serge Batalov07/2015
14012^538473-112723162097Enzo Doria06/2014
14022^538157+79337162002Enzo Doria06/2016
14032^538136-114749161996Enzo Doria05/2015
14042^538104+1531161986Lelio R Paula01/2013
1405(9*29^110727-1199)/14161927Curtis Bright05/2015
14062^537815-22737161899Enzo Doria07/2013
14072^537804-39839161896Enzo Doria09/2015
14082^537458-59201161791Enzo Doria10/2015
14092*10^161766+51161767Robert Price05/2018
14102^537209-49849161717Enzo Doria10/2015
1411(58*10^161691+329)/9161692Robert Price05/2019
14122^536937+1879397161635Enzo Doria09/2016
14132^536569-22881161524Enzo Doria07/2013
141410^161253+573493161254Patrick De Geest07/2018
141510^161253-8001161253Robert Price03/2018
14167*10^161192-9161193Robert Price10/2015
14172^535269-113803161133Enzo Doria09/2014
14182^535205-23295161113Enzo Doria08/2013
1419(89^82609+1)/90161036Paul Bourdelais10/2017
14202^534359-23229160859Enzo Doria08/2013
142167^88037-66^88037160763Robert Price10/2013
14222^533948-1852559160735Enzo Doria08/2015
14232^533665-23335160650Enzo Doria08/2013
1424(19*10^160619+77)/3160620Robert Price05/2019
14253^336353-2^336353160482Mike Oakes10/2007
14262^532253+1868417160225Enzo Doria04/2016
14272^532108-291989160181Enzo Doria07/2015
1428(26*10^160166-131)/3160167Robert Price10/2019
1429(17*10^160143+67)/3160144Robert Price01/2019
1430(19*10^159921-49)/3159922Robert Price05/2019
14312^531110-1853771159881Enzo Doria09/2015
14322^530992-1845299159845Enzo Doria07/2015
1433(136*10^159736-1)/9159738Serge Batalov12/2014
14342^530417-113833159672Enzo Doria09/2014
14352^530406-69701159669Enzo Doria02/2016
14365*10^159656+41159657Robert Price03/2019
14377^188858-188858^7159604Norbert Schneider05/2018
1438(24^115597-1)/23159547Paul Bourdelais09/2017
1439(17*10^159438-377)/9159439Robert Price03/2018
14402^528944-461315159229Enzo Doria07/2015
1441(13*10^159147+161)/3159148Robert Price11/2018
14422^528620-113879159131Enzo Doria10/2014
14432^528000-23307158944Enzo Doria08/2013
1444(29*10^158909+61)/9158910Robert Price08/2018
14452^527817+1876817158889Enzo Doria07/2016
14462^527774-49451158876Enzo Doria10/2015
14472^527745-291553158868Enzo Doria07/2015
14482^527644-1856999158837Enzo Doria10/2015
1449(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
14502^527573-1863253158816Enzo Doria12/2015
14512^527553-23401158810Enzo Doria08/2013
145211^152420-210158730Enzo Doria09/2012
1453(13*10^158694+401)/9158695Robert Price01/2018
14542^527052-69059158659Enzo Doria11/2015
14552^526849-113233158598Enzo Doria07/2014
1456(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
14572^526658-3551158540Yves Minet03/2017
14587*10^158465-11158466Robert Price06/2019
14592^526375-23115158455Enzo Doria08/2013
1460(77*10^158407-293)/9158408Robert Price09/2019
14612^526028-112793158351Enzo Doria07/2014
14622^525690-9221158249Lelio R Paula01/2013
14632*10^158242-7158243Robert Price10/2015
14642^525667-525667^2158242Henri Lifchitz12/2017
14652^525186-1857431158097Enzo Doria10/2015
14662^524515-23245157895Enzo Doria08/2013
14672^524499-109087157890Enzo Doria04/2014
14682^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
14692^524288+189093157827Makoto Morimoto01/2016
1470(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
1471(10^157792+359)/9157792Serge Batalov12/2014
14722^523924+1876591157717Enzo Doria07/2016
1473(17*10^157705+67)/3157706Robert Price01/2019
1474(46^94841+1)/47157696Robert Price01/2014
14752^523774+77839157672Enzo Doria05/2016
14762^523587+2799143157616Enzo Doria04/2016
14772^523371+1872113157551Enzo Doria05/2016
1478(82*10^157319+449)/9157320Robert Price11/2019
14792^522535-351457157299Enzo Doria07/2015
14802^522226+2799079157206Enzo Doria04/2016
14812^522134-1849451157178Enzo Doria08/2015
14824*10^157150+93157151Robert Price08/2018
14832^521401-29593156958Enzo Doria08/2015
14847*10^156956+87156957Robert Price07/2019
14852^521348-23397156942Enzo Doria08/2013
1486(98^78797+1)/99156901Paul Bourdelais12/2017
148765^86522+64156857Lelio R Paula04/2016
14888^173687-7^173687156855Jean-Louis Charton09/2004
14892^520977-1858183156830Enzo Doria10/2015
1490(8*10^156718-101)/3156719Robert Price08/2018
14912^520314-1849481156631Enzo Doria08/2015
1492(13*10^156522+89)/3156523Robert Price09/2018
1493(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
14943*10^156435-97156436Robert Price07/2018
1495(8*10^156371-77)/3156372Robert Price07/2018
149653^90679-52^90679156356Robert Price01/2013
14972^519106-59141156267Enzo Doria10/2015
14982^519053+6077156251Enzo Doria02/2016
14992^518968-1860989156225Enzo Doria11/2015
1500(25*10^156221-7)/9156222Robert Price05/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 14 2019 11:13 (Time in France)

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