PRP Records

Probable Primes Top 10000

(191107 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 (> 30000) Who ? When ?
10012^570980-2782289171883Enzo Doria09/2015
1002(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
10032^569563-1854607171456Enzo Doria09/2015
10042^568642+1876129171179Enzo Doria07/2016
1005(58*10^170842+221)/9170843Robert Price02/2017
100611^164009-270170798Enzo Doria10/2012
10073^357706-112358170670Enzo Doria07/2014
1008TheodorusPrime(170657)170657Eric W. Weisstein08/2013
10092^566871+1876163170646Enzo Doria07/2016
1010(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
10112^566496+7170533Donovan Johnson07/2006
1012(7^201653+1)/8170416Paul Bourdelais02/2010
10132^565183-352021170138Enzo Doria07/2015
10142^565143-114457170125Enzo Doria02/2015
10152^564976-49869170075Enzo Doria10/2015
10162^564526-351401169940Enzo Doria07/2015
101721^128327-20^128327169677Jean-Louis Charton11/2014
10182^562749+2793047169405Enzo Doria02/2016
1019(154*10^169337-1)/9169339Serge Batalov12/2014
10202^562369-29503169290Enzo Doria08/2015
10212^560405-39943168699Enzo Doria09/2015
10222^559686-350471168483Enzo Doria06/2015
10232^559672-1855889168479Enzo Doria09/2015
10242^559000-59939168276Enzo Doria11/2015
10252^558640-114149168168Enzo Doria12/2014
10262^558498-1849277168125Enzo Doria08/2015
10272^558476-1850249168119Enzo Doria08/2015
10282^558150-1852211168020Enzo Doria08/2015
10292^558125-113661168013Enzo Doria09/2014
1030393^64747-392^64747167980Jean-Louis Charton08/2012
103139^105456+2167788Robert Price04/2015
10322^556504-462059167525Enzo Doria07/2015
10335*10^167510+9167511Robert Price08/2015
10342^555343+1874333167175Enzo Doria06/2016
10352^555210-461261167135Enzo Doria07/2015
10362^554372+1880527166883Enzo Doria11/2016
10372^554299+72173166861Enzo Doria04/2016
10382^554037-2797063166782Enzo Doria03/2016
10392^553484-29819166616Enzo Doria08/2015
10402^553383-2784217166585Enzo Doria10/2015
10412^553069+76427166491Enzo Doria05/2016
1042589^60089-588^60089166454Jean-Louis Charton09/2012
104311^159756-2424166369Mike Oakes06/2010
10442^552649-361275166364Enzo Doria05/2014
10452^552628-113669166358Enzo Doria09/2014
10462^552137+1879397166210Enzo Doria09/2016
1047(23^121949-1)/22166061Paul Bourdelais10/2017
10482^551542+19249166031Payam Samidoost08/2002
10492^551535-23821166029Enzo Doria08/2013
10502^551507-23557166021Enzo Doria08/2013
10517*10^165916-3165917Robert Price08/2015
105281^86837-80^86837165728Robert Price01/2015
10532^550270-69551165648Enzo Doria12/2015
10542^550000-23625165567Enzo Doria08/2013
10552^549675-1852057165469Enzo Doria08/2015
1056-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1057(28*10^165358-1)/9165359Serge Batalov10/2014
10582^549278+1879669165350Enzo Doria09/2016
10592^549252-351269165342Enzo Doria06/2015
10602^549049+2797607165281Enzo Doria04/2016
1061(44^100511-1)/43165184Paul Bourdelais11/2017
10622^547178-1856501164717Enzo Doria10/2015
106311^158160-60164707Enzo Doria07/2012
10642^546398-59201164483Enzo Doria10/2015
10652^546332-114893164463Enzo Doria05/2015
10662^545958+1876189164350Enzo Doria07/2016
10672^545878-49841164326Enzo Doria10/2015
10682^545668-4019164263Yves Minet04/2017
1069(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
10702^545185+76757164118Enzo Doria05/2016
10712^545076-114329164085Enzo Doria01/2015
1072(29^112153+1)/30164011Lelio R Paula03/2017
10732^544757+1874777163989Enzo Doria06/2016
10742^544444-457199163894Enzo Doria01/2015
10752^544264-343529163840Enzo Doria07/2015
10767*10^163780+9163781Robert Price09/2015
10772^543989+2793047163758Enzo Doria02/2016
10782^542870-69551163421Enzo Doria12/2015
10792^542395+72533163278Enzo Doria04/2016
10802^542072-3683163180Yves Minet03/2017
10812^541779-1867357163092Enzo Doria04/2016
10828*10^162924+9162925Robert Price12/2015
10832^540905+81557162829Enzo Doria08/2016
10842^540628-2939162746Yves Minet09/2014
1085919^54919-918^54919162743Jean-Louis Charton01/2013
10863^340694-112960162553Enzo Doria07/2014
10872^539807-114081162499Enzo Doria12/2014
10882^539654-114893162453Enzo Doria05/2015
10892^539617-1851583162441Enzo Doria08/2015
10902^539346+81049162360Enzo Doria07/2016
10912^539220-115499162322Enzo Doria07/2015
10922^539217-113713162321Enzo Doria09/2014
10939^170099-8^170099162316Jean-Louis Charton05/2005
1094(115*10^162153-1)/3162155Serge Batalov12/2014
1095(10^162138+11)/3162138Serge Batalov07/2015
10962^538473-112723162097Enzo Doria06/2014
10972^538157+79337162002Enzo Doria06/2016
10982^538136-114749161996Enzo Doria05/2015
10992^538104+1531161986Lelio R Paula01/2013
1100(9*29^110727-1199)/14161927Curtis Bright05/2015
11012^537815-22737161899Enzo Doria07/2013
11022^537804-39839161896Enzo Doria09/2015
11032^537458-59201161791Enzo Doria10/2015
11042^537209-49849161717Enzo Doria10/2015
11052^536937+1879397161635Enzo Doria09/2016
11062^536569-22881161524Enzo Doria07/2013
11077*10^161192-9161193Robert Price10/2015
11082^535269-113803161133Enzo Doria09/2014
11092^535205-23295161113Enzo Doria08/2013
1110(89^82609+1)/90161036Paul Bourdelais10/2017
11112^534359-23229160859Enzo Doria08/2013
111267^88037-66^88037160763Robert Price10/2013
11132^533948-1852559160735Enzo Doria08/2015
11142^533665-23335160650Enzo Doria08/2013
11153^336353-2^336353160482Mike Oakes10/2007
11162^532253+1868417160225Enzo Doria04/2016
11172^532108-291989160181Enzo Doria07/2015
11182^531110-1853771159881Enzo Doria09/2015
11192^530992-1845299159845Enzo Doria07/2015
1120(136*10^159736-1)/9159738Serge Batalov12/2014
11212^530417-113833159672Enzo Doria09/2014
11222^530406-69701159669Enzo Doria02/2016
1123(24^115597-1)/23159547Paul Bourdelais09/2017
11242^528944-461315159229Enzo Doria07/2015
11252^528620-113879159131Enzo Doria10/2014
11262^528000-23307158944Enzo Doria08/2013
11272^527817+1876817158889Enzo Doria07/2016
11282^527774-49451158876Enzo Doria10/2015
11292^527745-291553158868Enzo Doria07/2015
11302^527644-1856999158837Enzo Doria10/2015
1131(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
11322^527573-1863253158816Enzo Doria12/2015
11332^527553-23401158810Enzo Doria08/2013
113411^152420-210158730Enzo Doria09/2012
11352^527052-69059158659Enzo Doria11/2015
11362^526849-113233158598Enzo Doria07/2014
1137(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
11382^526658-3551158540Yves Minet03/2017
11392^526375-23115158455Enzo Doria08/2013
11402^526028-112793158351Enzo Doria07/2014
11412^525690-9221158249Lelio R Paula01/2013
11422*10^158242-7158243Robert Price10/2015
11432^525186-1857431158097Enzo Doria10/2015
11442^524515-23245157895Enzo Doria08/2013
11452^524499-109087157890Enzo Doria04/2014
11462^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
11472^524288+189093157827Makoto Morimoto01/2016
1148(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
1149(10^157792+359)/9157792Serge Batalov12/2014
11502^523924+1876591157717Enzo Doria07/2016
1151(46^94841+1)/47157696Robert Price01/2014
11522^523774+77839157672Enzo Doria05/2016
11532^523587+2799143157616Enzo Doria04/2016
11542^523371+1872113157551Enzo Doria05/2016
11552^522535-351457157299Enzo Doria07/2015
11562^522226+2799079157206Enzo Doria04/2016
11572^522134-1849451157178Enzo Doria08/2015
11582^521401-29593156958Enzo Doria08/2015
11592^521348-23397156942Enzo Doria08/2013
116065^86522+64156857Lelio R Paula04/2016
11618^173687-7^173687156855Jean-Louis Charton09/2004
11622^520977-1858183156830Enzo Doria10/2015
11632^520314-1849481156631Enzo Doria08/2015
1164(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
116553^90679-52^90679156356Robert Price01/2013
11662^519106-59141156267Enzo Doria10/2015
11672^519053+6077156251Enzo Doria02/2016
11682^518968-1860989156225Enzo Doria11/2015
11692^518931-2782297156214Enzo Doria09/2015
11702^518608-2939156117Yves Minet09/2014
117110*27^109005+697156027Curtis Bright05/2015
11722^517967-113485155924Enzo Doria08/2014
11732^517698+4429155843Lelio R Paula01/2013
11742^517543-113257155796Enzo Doria07/2014
117531^104309-30^104309155563Henri Lifchitz08/2013
11762^516742-39851155555Enzo Doria09/2015
11772^516440+1878421155464Enzo Doria08/2016
11782^515863-1867237155291Enzo Doria03/2016
11792^515786-461861155268Enzo Doria07/2015
11802^515644-113247155225Enzo Doria07/2014
11812^515227-114997155099Enzo Doria06/2015
1182EPrime(155025)155025Eric W. Weisstein10/2010
1183(115*10^154869-1)/3154871Serge Batalov12/2014
11842^514361+78167154839Enzo Doria05/2016
11852^514281-115033154815Enzo Doria06/2015
11862^514194-3311154788Yves Minet12/2014
11872^513437+1879337154560Enzo Doria09/2016
11882^513306-113201154521Enzo Doria07/2014
11892^513042-113787154442Enzo Doria09/2014
11902^512628-114053154317Enzo Doria11/2014
11912^512529-49783154287Enzo Doria10/2015
11922^512315-115297154223Enzo Doria06/2015
11932^512168+79561154178Enzo Doria06/2016
11942^511658-114371154025Enzo Doria02/2015
1195(57^87719+1)/58154022Paul Bourdelais11/2017
11962^511580-1846679154001Enzo Doria07/2015
11972^511541-113713153990Enzo Doria09/2014
11982^511077-112723153850Enzo Doria06/2014
119969^83653-68^83653153826Robert Price12/2013
12002^510963-113707153816Enzo Doria09/2014
1201(154*10^153810-1)/9153812Serge Batalov12/2014
1202(181*25^109991-75077)/8153763Curtis Bright05/2015
12032*10^153746-3153747Robert Price07/2015
12042^510626+1179379153714Enzo Doria05/2016
12052^510420+81121153652Enzo Doria07/2016
1206(197*7^181761-1)/2153608Karsten Bonath05/2017
12072^509894-459161153494Enzo Doria05/2015
12082^509841+71657153478Enzo Doria04/2016
12092^509533-1846723153385Enzo Doria07/2015
12102^509468-39989153366Enzo Doria09/2015
121170^83117-69^83117153360Robert Price01/2014
1212(112*10^153025-1)/3153027Serge Batalov12/2014
12132^508174-1855151152976Enzo Doria09/2015
12142^508160-1864829152972Enzo Doria01/2016
12152^507857-1848199152881Enzo Doria07/2015
12162^507638-115361152815Enzo Doria07/2015
12172^507551-114025152789Enzo Doria11/2014
1218(6^196337+1)/7152780Paul Bourdelais02/2010
12192^506451-22339152457Enzo Doria07/2013
12202^505995-113185152320Enzo Doria07/2014
1221578^55117-577^55117152230Jean-Louis Charton08/2012
12222^505431-505431152150Henri Lifchitz04/2005
12232^505053+73097152037Enzo Doria04/2016
1224350377#+797581151937Nicolas PALAU08/2017
12252^504618-343991151906Enzo Doria07/2015
12262^504212-461939151783Enzo Doria07/2015
12272^504054-2231151736Yves Minet10/2011
12282^503361-39883151527Enzo Doria09/2015
12292^503225+382667151486Enzo Doria10/2016
12302^502769+1877567151349Enzo Doria08/2016
12312^502576-4019151291Yves Minet10/2011
12322^502290-2792501151205Enzo Doria02/2016
12332^502181+1868417151172Enzo Doria04/2016
12342^501781-1850503151052Enzo Doria08/2015
12352^501627-991151005Yves Minet02/2014
12362^501577-115333150990Enzo Doria07/2015
12378*10^150975+3150976Robert Price08/2015
12382^501512-113669150971Enzo Doria09/2014
1239(12^139739+1)/13150803Paul Bourdelais09/2011
1240(31^101111-1)/30150792Alexander Zhirkov11/2010
12412^500899-500899150786Henri Lifchitz04/2005
12422^500832+1876801150766Enzo Doria07/2016
12432^500699+1884953150726Enzo Doria02/2017
1244(2^500527+lucasV(1,2,500527)+1)/4150674Mike Oakes11/2016
12452^500337-71101150617Enzo Doria04/2016
12462^500160+80071150564Enzo Doria06/2016
1248(10^150551-1)/9/385207015049/57498437921/7808738631274081150512Maksym Voznyy08/2014
1247(10^150551-1)/1556587827131683185788921941743157225041150512Robert Price07/2016
12492^499861-29503150474Enzo Doria08/2015
12502^499653-113533150411Enzo Doria08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

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