PRP Records

Probable Primes Top 10000

(202622 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 ?
10012^577146-49877173739Enzo Doria10/2015
10022^576889+49727173661Enzo Doria09/2016
1003(2^576551-1)/4612409/64758208321/242584327930759173528Dario Alpern06/2014
10042^576016-113919173399Enzo Doria11/2014
10052^575911-1849387173367Enzo Doria08/2015
10062^575196-114053173152Enzo Doria11/2014
10072^574591-115387172970Enzo Doria07/2015
10082^574328+81121172890Enzo Doria07/2016
1009(115*10^172862-1)/3172864Serge Batalov12/2014
10104*5^247217-9172798Lelio R Paula10/2015
101169061#+(467617#)/(69061#)172766Makoto Morimoto10/2017
10122^573668-2782319172692Enzo Doria09/2015
10132^573444-1855109172624Enzo Doria09/2015
10143^361608+2172531Robert Price08/2014
1015(54^99563+1)/55172481Paul Bourdelais11/2017
10162^572592-114893172368Enzo Doria05/2015
10175^246497-4^246497172295Jean-Louis Charton11/2008
1018(38^109037-1)/37172254Paul Bourdelais10/2017
1019(36^110503+1)/37171975Lelio R Paula04/2017
10202^570980-2782289171883Enzo Doria09/2015
1021(2^(12*47563+13)-9)/7171818Kevin Acres11/2013
10222^569563-1854607171456Enzo Doria09/2015
1023(55^98419-1)/54171284Paul Bourdelais12/2017
10242^568642+1876129171179Enzo Doria07/2016
1025(58*10^170842+221)/9170843Robert Price02/2017
102611^164009-270170798Enzo Doria10/2012
10273^357706-112358170670Enzo Doria07/2014
1028TheodorusPrime(170657)170657Eric W. Weisstein08/2013
10292^566871+1876163170646Enzo Doria07/2016
1030(10657#+(404267#)/(10657#))/(1675379)170624Makoto Morimoto10/2017
10312^566496+7170533Donovan Johnson07/2006
1032(7^201653+1)/8170416Paul Bourdelais02/2010
10332^565183-352021170138Enzo Doria07/2015
10342^565143-114457170125Enzo Doria02/2015
10352^564976-49869170075Enzo Doria10/2015
10362^564526-351401169940Enzo Doria07/2015
103721^128327-20^128327169677Jean-Louis Charton11/2014
1038(4*10^169559+83)/3169560Robert Price02/2018
10392^562749+2793047169405Enzo Doria02/2016
1040(154*10^169337-1)/9169339Serge Batalov12/2014
10412^562369-29503169290Enzo Doria08/2015
10422^560405-39943168699Enzo Doria09/2015
10432^559686-350471168483Enzo Doria06/2015
10442^559672-1855889168479Enzo Doria09/2015
1045(5*10^168379-473)/9168379Robert Price01/2018
10462^559000-59939168276Enzo Doria11/2015
10472^558640-114149168168Enzo Doria12/2014
10482^558498-1849277168125Enzo Doria08/2015
10492^558476-1850249168119Enzo Doria08/2015
10502^558150-1852211168020Enzo Doria08/2015
10512^558125-113661168013Enzo Doria09/2014
1052393^64747-392^64747167980Jean-Louis Charton08/2012
105339^105456+2167788Robert Price04/2015
1054(28^115877-1)/27167691Paul Bourdelais12/2017
10552^556504-462059167525Enzo Doria07/2015
10565*10^167510+9167511Robert Price08/2015
10572^555343+1874333167175Enzo Doria06/2016
10582^555210-461261167135Enzo Doria07/2015
10592^554372+1880527166883Enzo Doria11/2016
10602^554299+72173166861Enzo Doria04/2016
10612^554037-2797063166782Enzo Doria03/2016
10622^553484-29819166616Enzo Doria08/2015
10632^553383-2784217166585Enzo Doria10/2015
10642^553069+76427166491Enzo Doria05/2016
1065589^60089-588^60089166454Jean-Louis Charton09/2012
106611^159756-2424166369Mike Oakes06/2010
10672^552649-361275166364Enzo Doria05/2014
10682^552628-113669166358Enzo Doria09/2014
106910^166324-801166324Robert Price02/2018
10702^552137+1879397166210Enzo Doria09/2016
1071(23^121949-1)/22166061Paul Bourdelais10/2017
10722^551542+19249166031Payam Samidoost08/2002
10732^551535-23821166029Enzo Doria08/2013
10742^551507-23557166021Enzo Doria08/2013
10757*10^165916-3165917Robert Price08/2015
107681^86837-80^86837165728Robert Price01/2015
10772^550270-69551165648Enzo Doria12/2015
10782^550000-23625165567Enzo Doria08/2013
10792^549675-1852057165469Enzo Doria08/2015
1080-tau(103^14938)165374Nik Lygeros / Olivier Rozier10/2013
1081(28*10^165358-1)/9165359Serge Batalov10/2014
10832^549278+1879669165350Enzo Doria09/2016
1082(7*10^165350-439)/9165350Robert Price02/2018
10842^549252-351269165342Enzo Doria06/2015
10852^549049+2797607165281Enzo Doria04/2016
1086(44^100511-1)/43165184Paul Bourdelais11/2017
10872^547178-1856501164717Enzo Doria10/2015
108811^158160-60164707Enzo Doria07/2012
10892^546398-59201164483Enzo Doria10/2015
10902^546332-114893164463Enzo Doria05/2015
10912^545958+1876189164350Enzo Doria07/2016
10922^545878-49841164326Enzo Doria10/2015
1093(10^164284+77)/3164284Robert Price01/2018
10942^545668-4019164263Yves Minet04/2017
1095(13*53^238539*617^9)/10^247183164151Hans Havermann07/2017
10962^545185+76757164118Enzo Doria05/2016
10972^545076-114329164085Enzo Doria01/2015
1098(29^112153+1)/30164011Lelio R Paula03/2017
10992^544757+1874777163989Enzo Doria06/2016
11002^544444-457199163894Enzo Doria01/2015
11012^544264-343529163840Enzo Doria07/2015
11027*10^163780+9163781Robert Price09/2015
11032^543989+2793047163758Enzo Doria02/2016
11042^542870-69551163421Enzo Doria12/2015
11052^542395+72533163278Enzo Doria04/2016
11062^542072-3683163180Yves Minet03/2017
11072^541779-1867357163092Enzo Doria04/2016
11088*10^162924+9162925Robert Price12/2015
11092^540905+81557162829Enzo Doria08/2016
11102^540628-2939162746Yves Minet09/2014
1111919^54919-918^54919162743Jean-Louis Charton01/2013
11123^340694-112960162553Enzo Doria07/2014
11132^539807-114081162499Enzo Doria12/2014
11142^539654-114893162453Enzo Doria05/2015
11152^539617-1851583162441Enzo Doria08/2015
11162^539346+81049162360Enzo Doria07/2016
11172^539220-115499162322Enzo Doria07/2015
11182^539217-113713162321Enzo Doria09/2014
11199^170099-8^170099162316Jean-Louis Charton05/2005
1120(115*10^162153-1)/3162155Serge Batalov12/2014
1121(10^162138+11)/3162138Serge Batalov07/2015
11222^538473-112723162097Enzo Doria06/2014
11232^538157+79337162002Enzo Doria06/2016
11242^538136-114749161996Enzo Doria05/2015
11252^538104+1531161986Lelio R Paula01/2013
1126(9*29^110727-1199)/14161927Curtis Bright05/2015
11272^537815-22737161899Enzo Doria07/2013
11282^537804-39839161896Enzo Doria09/2015
11292^537458-59201161791Enzo Doria10/2015
11302^537209-49849161717Enzo Doria10/2015
11312^536937+1879397161635Enzo Doria09/2016
11322^536569-22881161524Enzo Doria07/2013
11337*10^161192-9161193Robert Price10/2015
11342^535269-113803161133Enzo Doria09/2014
11352^535205-23295161113Enzo Doria08/2013
1136(89^82609+1)/90161036Paul Bourdelais10/2017
11372^534359-23229160859Enzo Doria08/2013
113867^88037-66^88037160763Robert Price10/2013
11392^533948-1852559160735Enzo Doria08/2015
11402^533665-23335160650Enzo Doria08/2013
11413^336353-2^336353160482Mike Oakes10/2007
11422^532253+1868417160225Enzo Doria04/2016
11432^532108-291989160181Enzo Doria07/2015
11442^531110-1853771159881Enzo Doria09/2015
11452^530992-1845299159845Enzo Doria07/2015
1146(136*10^159736-1)/9159738Serge Batalov12/2014
11472^530417-113833159672Enzo Doria09/2014
11482^530406-69701159669Enzo Doria02/2016
1149(24^115597-1)/23159547Paul Bourdelais09/2017
11502^528944-461315159229Enzo Doria07/2015
11512^528620-113879159131Enzo Doria10/2014
11522^528000-23307158944Enzo Doria08/2013
11532^527817+1876817158889Enzo Doria07/2016
11542^527774-49451158876Enzo Doria10/2015
11552^527745-291553158868Enzo Doria07/2015
11562^527644-1856999158837Enzo Doria10/2015
1157(37200^37199-37198^37199)/(2^37199)158822Henri Lifchitz06/2013
11582^527573-1863253158816Enzo Doria12/2015
11592^527553-23401158810Enzo Doria08/2013
116011^152420-210158730Enzo Doria09/2012
1161(13*10^158694+401)/9158695Robert Price01/2018
11622^527052-69059158659Enzo Doria11/2015
11632^526849-113233158598Enzo Doria07/2014
1164(2^526763-lucasV(1,2,526763)+1)/2158572Mike Oakes11/2016
11652^526658-3551158540Yves Minet03/2017
11662^526375-23115158455Enzo Doria08/2013
11672^526028-112793158351Enzo Doria07/2014
11682^525690-9221158249Lelio R Paula01/2013
11692*10^158242-7158243Robert Price10/2015
11702^525667-525667^2158242Henri Lifchitz12/2017
11712^525186-1857431158097Enzo Doria10/2015
11722^524515-23245157895Enzo Doria08/2013
11732^524499-109087157890Enzo Doria04/2014
11742^18067*(2^506221+1)-1157827Makoto Morimoto05/2014
11752^524288+189093157827Makoto Morimoto01/2016
1176(2^(2^19)-9333)/(19*23*463*1213*31973)157814Makoto Morimoto09/2017
1177(10^157792+359)/9157792Serge Batalov12/2014
11782^523924+1876591157717Enzo Doria07/2016
1179(46^94841+1)/47157696Robert Price01/2014
11802^523774+77839157672Enzo Doria05/2016
11812^523587+2799143157616Enzo Doria04/2016
11822^523371+1872113157551Enzo Doria05/2016
11832^522535-351457157299Enzo Doria07/2015
11842^522226+2799079157206Enzo Doria04/2016
11852^522134-1849451157178Enzo Doria08/2015
11862^521401-29593156958Enzo Doria08/2015
11872^521348-23397156942Enzo Doria08/2013
1188(98^78797+1)/99156901Paul Bourdelais12/2017
118965^86522+64156857Lelio R Paula04/2016
11908^173687-7^173687156855Jean-Louis Charton09/2004
11912^520977-1858183156830Enzo Doria10/2015
11922^520314-1849481156631Enzo Doria08/2015
1193(2^(6*86654+1)-5)/3156513Kevin Acres12/2013
119453^90679-52^90679156356Robert Price01/2013
11952^519106-59141156267Enzo Doria10/2015
11962^519053+6077156251Enzo Doria02/2016
11972^518968-1860989156225Enzo Doria11/2015
11982^518931-2782297156214Enzo Doria09/2015
11992^518608-2939156117Yves Minet09/2014
120010*27^109005+697156027Curtis Bright05/2015
12012^517967-113485155924Enzo Doria08/2014
12022^517698+4429155843Lelio R Paula01/2013
12032^517543-113257155796Enzo Doria07/2014
120431^104309-30^104309155563Henri Lifchitz08/2013
12052^516742-39851155555Enzo Doria09/2015
12062^516440+1878421155464Enzo Doria08/2016
12072^515863-1867237155291Enzo Doria03/2016
12082^515786-461861155268Enzo Doria07/2015
12092^515644-113247155225Enzo Doria07/2014
12102^515227-114997155099Enzo Doria06/2015
1211EPrime(155025)155025Eric W. Weisstein10/2010
1212(115*10^154869-1)/3154871Serge Batalov12/2014
12132^514361+78167154839Enzo Doria05/2016
12142^514281-115033154815Enzo Doria06/2015
12152^514194-3311154788Yves Minet12/2014
12162^513437+1879337154560Enzo Doria09/2016
12172^513306-113201154521Enzo Doria07/2014
1218(10^154494-13)/3154494Robert Price12/2017
12192^513042-113787154442Enzo Doria09/2014
12202^512628-114053154317Enzo Doria11/2014
12212^512529-49783154287Enzo Doria10/2015
12222^512315-115297154223Enzo Doria06/2015
12232^512168+79561154178Enzo Doria06/2016
12242^511658-114371154025Enzo Doria02/2015
1225(57^87719+1)/58154022Paul Bourdelais11/2017
12262^511580-1846679154001Enzo Doria07/2015
12272^511541-113713153990Enzo Doria09/2014
12282^511077-112723153850Enzo Doria06/2014
122969^83653-68^83653153826Robert Price12/2013
12302^510963-113707153816Enzo Doria09/2014
1231(154*10^153810-1)/9153812Serge Batalov12/2014
1232(181*25^109991-75077)/8153763Curtis Bright05/2015
12332*10^153746-3153747Robert Price07/2015
12342^510626+1179379153714Enzo Doria05/2016
12352^510420+81121153652Enzo Doria07/2016
1236(197*7^181761-1)/2153608Karsten Bonath05/2017
12372^509894-459161153494Enzo Doria05/2015
12382^509841+71657153478Enzo Doria04/2016
12392^509533-1846723153385Enzo Doria07/2015
12402^509468-39989153366Enzo Doria09/2015
124170^83117-69^83117153360Robert Price01/2014
1242(112*10^153025-1)/3153027Serge Batalov12/2014
12432^508174-1855151152976Enzo Doria09/2015
1244181^67757-2152974Lelio R Paula12/2017
12452^508160-1864829152972Enzo Doria01/2016
12462^507857-1848199152881Enzo Doria07/2015
12472^507638-115361152815Enzo Doria07/2015
12482^507551-114025152789Enzo Doria11/2014
1249(6^196337+1)/7152780Paul Bourdelais02/2010
12502^506451-22339152457Enzo Doria07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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