PRP Records

Probable Primes Top 10000

(252402 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 ?
92512^183980+7524155384Enzo Doria04/2016
925210^55372+3755373Robert Price01/2011
925310^55372-4996755372Patrick De Geest12/2012
9254(13*10^55367+17)/355368Robert Price06/2015
92552*6^71150+755366Lelio R Paula09/2014
925619^43296-6255365Lelio R Paula02/2013
925719^43295+1055364Lelio R Paula02/2013
9258(29*10^55362-11)/955363Robert Price04/2015
9259(37*10^55359+53)/955360Robert Price05/2015
926019^43283+7255349Lelio R Paula02/2013
92612^183800-6555330Lelio R Paula03/2011
926221001^12801-11055329Enzo Doria07/2012
926333^36433-32^3643355325Robert Price04/2012
9264(17*2^183729+1)/14555308Lelio R Paula07/2012
92659932^13837-13837^993255307Norbert Schneider11/2018
92679^57952+8^(57952-1)55301Robert Price03/2016
926614872^5229+5229^1487255301Hans Havermann08/2016
926861^30972-255296Lelio R Paula08/2013
92692^183671-11253755291Enzo Doria06/2014
9270(2^183687+7)/49793974555287Lelio R Paula02/2012
92713^115873+5655286Lelio R Paula10/2012
927213^49629-8455284Lelio R Paula01/2013
92732^183632-555279Henri Lifchitz08/2005
927413981^8988+8988^1398155277Hans Havermann07/2016
927510688^13719-13719^1068855273Norbert Schneider09/2018
9276(5*2^183585+1)/1355265Lelio R Paula07/2012
92772^183576+17155262Lelio R Paula03/2011
927813^49604+8255257Lelio R Paula01/2013
9279(11*10^55254+1)/355255Erik Branger03/2014
928012609^13474-13474^1260955253Norbert Schneider05/2018
92813^115802-2655252Lelio R Paula10/2012
92822^183534-364555250Lelio R Paula01/2011
9283(15*2^183533-1)/11355249Lelio R Paula01/2014
92845^79032-1376655241Enzo Doria02/2013
92858*3^115759-755232Lelio R Paula03/2014
92866^70974-13755229Lelio R Paula10/2012
92872^183466+52428755229Paul Underwood08/2018
92882^183446-11307355223Enzo Doria07/2014
92892^183441+57729457555222Lelio R Paula03/2013
92905^79000-655219Lelio R Paula10/2012
92912^183413-90155213Yves Minet01/2012
929219^43168-5055202Lelio R Paula02/2013
92932^183340+1968355191Lelio R Paula02/2012
92946^70923+3555189Lelio R Paula10/2012
92952^183317-403555184Lelio R Paula01/2011
92962^183284-1555174Lelio R Paula03/2011
92972^183255+14955166Lelio R Paula02/2011
92984*10^55165+8755166Robert Price05/2016
9300(3^115574+4)/6303755139Lelio R Paula03/2012
92992^183165-11233355139Enzo Doria06/2014
9301(109^27061-1)/10855133Richard Fischer09/2017
93022^183142+85555132Lelio R Paula01/2011
9303(49*10^55129+383)/955130Robert Price04/2017
93042^183019+25525555095Lelio R Paula01/2011
9305(10^55084-19)/955084Robert Price10/2017
93063*10^55077+755078Erik Branger11/2013
9307(62*10^55075-71)/955076Robert Price09/2015
930827499!2-3255070Robert Price10/2015
930915307^3958+3958^1530755067Hans Havermann08/2016
9310155^25137-15455059Norbert Schneider12/2018
931170^29836-6955051Norbert Schneider10/2012
931218^43854-8355049Lelio R Paula02/2013
93137^65126+5855038Lelio R Paula10/2012
93142^182827-161555037Lelio R Paula11/2009
93157*10^55030-955031Dmitry Domanov11/2010
93169027^13912-13912^902755030Norbert Schneider08/2018
93172^182768-405555019Yves Minet02/2018
93186^70702+2355017Lelio R Paula10/2012
9319(23*2^182753+1)/15155014Lelio R Paula07/2012
93202^182743-161555012Lelio R Paula11/2009
9321(24737*2^182736+1)/39955011Lelio R Paula05/2014
93223^115280-956855003Enzo Doria02/2013
93232^182656-1284954985Enzo Doria10/2012
932412791^13388-13388^1279154984Norbert Schneider03/2018
93259*19^42995+1654981Curtis Bright05/2015
93262^182627+2842554977Lelio R Paula11/2009
93272^182597-11305354968Enzo Doria07/2014
9328(3^115213+2)/3090672554964Lelio R Paula03/2012
93292^182581-197554963Yves Minet09/2012
9330(2*10^54960-179)/354960Robert Price11/2017
933127449!!-1654959Robert Price06/2015
9332(22*10^54958-73)/354959Robert Price09/2017
93344^91283-3^9128354958Jean-Louis Charton01/2004
93332^182565+10754958Lelio R Paula11/2009
93352^182560+205354957Lelio R Paula12/2010
9336126892#-p(126892)54927Henri Lifchitz12/2018
93372^182451-18245154924Henri Lifchitz10/2004
93382^182444+8154922Henri Lifchitz10/2005
93392^182433+7410554918Enzo Doria04/2016
934020^42206-524354912Enzo Doria03/2013
93412^182394+8554907Lelio R Paula02/2011
93422^182374-11228754901Enzo Doria06/2014
9344(47^32833-33^32833)/1454899Serge Batalov12/2016
934310188^13697-13697^1018854899Norbert Schneider09/2018
93452^182363-11316754897Enzo Doria07/2014
93462^182359-11222154896Enzo Doria06/2014
9347(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
9348(17*2^182274+1)/146754869Lelio R Paula01/2012
934918^43698-554853Lelio R Paula02/2013
93502^182209-189354851Yves Minet09/2012
93512^182194-344354846Yves Minet12/2016
935215023^4468+4468^1502354836Hans Havermann08/2016
93532^182135+9014354829Yves Minet10/2010
93542^182119+7433354824Enzo Doria04/2016
935514289^6860+6860^1428954818Hans Havermann08/2016
93563^114892-114892^354818Norbert Schneider03/2017
93572^182070-4735554809Lelio R Paula01/2011
93583^114869+7654807Lelio R Paula10/2012
93598^60681-60681^854801Norbert Schneider12/2016
93601897^16710+16710^189754777Serge Batalov05/2014
9361Phi(61868,59)54776Enzo Doria04/2012
9362113^26679+254775Lelio R Paula05/2013
93633^114789-7454769Lelio R Paula10/2012
936415^46567+9854768Lelio R Paula02/2013
9365(2*10^54767-71)/354767Robert Price01/2017
9366(298*10^54765-7)/354767Robert Price06/2017
9367(21*2^181931-1)/16999754763Lelio R Paula01/2014
93682^181913+2954762Henri Lifchitz06/2005
9369(31*10^54761-121)/954762Robert Price06/2016
93702^181887+18954754Lelio R Paula02/2011
93712^181874+181874^2-154750Robert Price04/2014
9372(2^181865+9)/733954743Lelio R Paula02/2012
93735^78314-9254740Lelio R Paula10/2012
9374(163*10^54727-1)/954729Serge Batalov12/2014
937515^46531+7454725Lelio R Paula02/2013
9376277^22400-34854712Enzo Doria07/2012
93776^70302+10154706Lelio R Paula10/2012
93783^114622-1040854689Enzo Doria02/2013
9380(23*2^181674+1)/48954688Lelio R Paula01/2012
93792^181669-155154688Yves Minet08/2012
9381(57352^11491-1)/5735154676Serge Batalov04/2015
9382(31*2^181629-1)/1073472154671Lelio R Paula01/2014
9383(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
938413^49073+4654665Lelio R Paula01/2013
9385(57042^11491-1)/5704154649Serge Batalov04/2015
938720^42000+7354644Lelio R Paula02/2013
9386(67607*2^181517+1)/165554644Lelio R Paula05/2014
938833*10^54634+754636Robert Price07/2016
938920^41988+6154628Lelio R Paula01/2013
939020^41988-812354628Enzo Doria03/2013
93922^181420+2118154613Yves Minet03/2011
93919854^13675-13675^985454613Norbert Schneider08/2018
9393(19*10^54608+161)/954609Robert Price07/2016
939419^42696-2454598Lelio R Paula02/2013
9395(44*10^54596-503)/954597Robert Price10/2017
9396(74*10^54583+61)/954584Robert Price10/2015
93972^181316-9439554582Lelio R Paula09/2011
939814751^5006+5006^1475154572Hans Havermann08/2016
939914^47609+3954567Lelio R Paula02/2013
940012696^13295-13295^1269654559Norbert Schneider01/2018
9401(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
94033^114327-7454548Lelio R Paula10/2012
9402(44*10^54547-161)/954548Robert Price11/2017
9404gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
9405(17*10^54537-47)/354538Robert Price05/2017
94062^181155-1155*18115554534Henri Lifchitz02/2005
9407Phi(61672,83)54533Enzo Doria05/2012
9408(2*10^54527-197)/354527Robert Price11/2017
94099*2^181128+754526Lelio R Paula03/2014
941089*10^54518-754520Robert Price03/2017
94112^181090-11324754514Enzo Doria07/2014
941214031^7670+7670^1403154508Hans Havermann08/2016
941314210^6849+6849^1421054505Hans Havermann08/2016
94142^181043-19954500Lelio R Paula02/2011
941512^50499+554498Lelio R Paula01/2013
941612^50491+554489Lelio R Paula01/2013
94176^70016-14554484Lelio R Paula10/2012
941811^52313-960054479Enzo Doria02/2013
94192^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
94202^180946-11104154471Enzo Doria05/2014
9421(64*10^54467+287)/954468Robert Price04/2016
9422(32*10^54458+319)/954459Robert Price10/2017
94235^77907-2*3^7790754455Mike Oakes11/2009
942420^41853-562354453Enzo Doria03/2013
942514^47506-7554448Lelio R Paula02/2013
9426(25*10^54443-67)/354444Robert Price11/2017
94272^180839-11343754438Enzo Doria08/2014
94283^114085+2854433Lelio R Paula10/2012
9429Phi(141230,10)54432Ray Chandler08/2009
94306^69946-5554429Lelio R Paula10/2012
9431p(11796)#/2-102454427Robert Price09/2017
94325*2^180796+354426Lelio R Paula03/2014
9433(23*2^180782-1)/9154421Lelio R Paula01/2014
94349*6^69928-754416Lelio R Paula09/2014
943592^27701-91^2770154399Robert Price08/2015
9436(2^180687-3)*6-754393Gilbert Mozzo04/2016
9437(5*10^54388-11)/354389Erik Branger12/2013
943920^41799-304354382Enzo Doria03/2013
943813860^8387+8387^1386054382Hans Havermann08/2016
9440(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
94417^64329-1854365Lelio R Paula10/2012
94422^180551-96754352Yves Minet01/2012
94439075^13732-13732^907554350Norbert Schneider09/2018
944415^46209-7454347Lelio R Paula02/2013
944510^54345+2973954346Patrick De Geest08/2013
944610^54345-14138154345Patrick De Geest09/2013
9447lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
9448177^24171-254336Lelio R Paula10/2017
94492^180496+1554335Lelio R Paula02/2011
94501845^16636+16636^184554334Serge Batalov05/2014
945111^52169-7054329Lelio R Paula01/2013
94522^180446-403154320Yves Minet02/2018
945313693^9262+9262^1369354317Hans Havermann06/2016
94542^180429-11310154315Enzo Doria07/2014
94552^180423-11205154313Enzo Doria05/2014
945616112^2349+2349^1611254312Hans Havermann06/2016
9457(79^28621-1)/7854311Paul Bourdelais08/2017
9458(13^48751+4^48751)/1754305Robert Price05/2013
94592^180370+1291554297Lelio R Paula09/2012
9460(10^54290+41)/354290Robert Price01/2017
946115108^3917+3917^1510854283Hans Havermann06/2016
94622^180317-301954281Yves Minet10/2014
94632^180314+85554280Lelio R Paula10/2009
946419^42425+9454252Lelio R Paula02/2013
94652^180180-100544954240Paul Bourdelais11/2012
94662^180173-277354238Yves Minet07/2014
946713367^11418+11418^1336754238Hans Havermann06/2016
9468427^20614+20614^42754224Norbert Schneider06/2016
94692^180124-8795954223Gary Barnes08/2009
94702^180111-11310154219Enzo Doria07/2014
94712^180101-11487154216Enzo Doria05/2015
9472(11*2^180099+1)/5161754212Lelio R Paula07/2012
94742^180070+46554207Lelio R Paula09/2012
947313683^9154+9154^1368354207Hans Havermann06/2016
9475810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
94762^180014+61354190Jason Earls04/2008
94772^180007+10154188Lelio R Paula02/2011
94782^180001+4187754186Jim Fougeron08/2002
94792^180000+13015354186Jim Fougeron09/2002
94803^113565-7454185Lelio R Paula10/2012
948150^31891-4954182Norbert Schneider07/2014
9482(5*2^179991-1)/1142754180Lelio R Paula01/2014
94843^113548+2654177Lelio R Paula10/2012
9483(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
9485181^23996-254176Lelio R Paula10/2017
94864159^14969-13854173Enzo Doria07/2012
94882^179955+577554172Lelio R Paula10/2009
94872^179953-23131354172Enzo Doria05/2014
94895^77485+654160Lelio R Paula10/2012
949018^43141+8554154Lelio R Paula02/2013
949110^54149+18764754150Patrick De Geest07/2017
94943^113489-34054149Lelio R Paula10/2012
949210^54149-80000154149Robert Price06/2017
949310^54149-3650154149Patrick De Geest07/2017
94957^64070+9054146Lelio R Paula10/2012
949612549^13210-13210^1254954143Norbert Schneider12/2017
949718^43131+7154142Lelio R Paula02/2013
94982^179826-13154134Lelio R Paula02/2011
94992^179815-11273554130Enzo Doria06/2014
95002^179806+7384954127Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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