PRP Records

Probable Primes Top 10000

(252675 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 ?
95012^184044-11126955403Enzo Doria05/2014
950214051^8766+8766^1405155401Hans Havermann07/2016
950398^27819+27819^9855394Serge Batalov05/2014
9504(178*10^55390-7)/955392Robert Price08/2017
950558046^9+9^5804655390Andrey Kulsha02/2004
95067^65536+2*59232-255385Jiahao He07/2017
95072^183980+7524155384Enzo Doria04/2016
950810^55372+3755373Robert Price01/2011
950910^55372-4996755372Patrick De Geest12/2012
9510(13*10^55367+17)/355368Robert Price06/2015
95112*6^71150+755366Lelio R Paula09/2014
951219^43296-6255365Lelio R Paula02/2013
951319^43295+1055364Lelio R Paula02/2013
9514(29*10^55362-11)/955363Robert Price04/2015
9515(37*10^55359+53)/955360Robert Price05/2015
951619^43283+7255349Lelio R Paula02/2013
95172^183800-6555330Lelio R Paula03/2011
951821001^12801-11055329Enzo Doria07/2012
951933^36433-32^3643355325Robert Price04/2012
9520(17*2^183729+1)/14555308Lelio R Paula07/2012
95219932^13837-13837^993255307Norbert Schneider11/2018
95239^57952+8^(57952-1)55301Robert Price03/2016
952214872^5229+5229^1487255301Hans Havermann08/2016
952461^30972-255296Lelio R Paula08/2013
95252^183671-11253755291Enzo Doria06/2014
9526(2^183687+7)/49793974555287Lelio R Paula02/2012
95273^115873+5655286Lelio R Paula10/2012
952813^49629-8455284Lelio R Paula01/2013
95292^183632-555279Henri Lifchitz08/2005
953013981^8988+8988^1398155277Hans Havermann07/2016
953110688^13719-13719^1068855273Norbert Schneider09/2018
9532(5*2^183585+1)/1355265Lelio R Paula07/2012
95332^183576+17155262Lelio R Paula03/2011
953413^49604+8255257Lelio R Paula01/2013
9535(11*10^55254+1)/355255Erik Branger03/2014
953612609^13474-13474^1260955253Norbert Schneider05/2018
95373^115802-2655252Lelio R Paula10/2012
95382^183534-364555250Lelio R Paula01/2011
9539(15*2^183533-1)/11355249Lelio R Paula01/2014
95405^79032-1376655241Enzo Doria02/2013
95418*3^115759-755232Lelio R Paula03/2014
95426^70974-13755229Lelio R Paula10/2012
95432^183466+52428755229Paul Underwood08/2018
95442^183446-11307355223Enzo Doria07/2014
95452^183441+57729457555222Lelio R Paula03/2013
95465^79000-655219Lelio R Paula10/2012
95472^183413-90155213Yves Minet01/2012
954819^43168-5055202Lelio R Paula02/2013
95492^183340+1968355191Lelio R Paula02/2012
95506^70923+3555189Lelio R Paula10/2012
95512^183317-403555184Lelio R Paula01/2011
95522^183284-1555174Lelio R Paula03/2011
95532^183255+14955166Lelio R Paula02/2011
95544*10^55165+8755166Robert Price05/2016
9555(3^115574+4)/6303755139Lelio R Paula03/2012
95562^183165-11233355139Enzo Doria06/2014
9557(109^27061-1)/10855133Richard Fischer09/2017
95582^183142+85555132Lelio R Paula01/2011
9559(49*10^55129+383)/955130Robert Price04/2017
95602^183019+25525555095Lelio R Paula01/2011
9561(10^55084-19)/955084Robert Price10/2017
95623*10^55077+755078Erik Branger11/2013
9563(62*10^55075-71)/955076Robert Price09/2015
956427499!2-3255070Robert Price10/2015
956515307^3958+3958^1530755067Hans Havermann08/2016
9566155^25137-15455059Norbert Schneider12/2018
956770^29836-6955051Norbert Schneider10/2012
956818^43854-8355049Lelio R Paula02/2013
95697^65126+5855038Lelio R Paula10/2012
95702^182827-161555037Lelio R Paula11/2009
95717*10^55030-955031Dmitry Domanov11/2010
95729027^13912-13912^902755030Norbert Schneider08/2018
95732^182768-405555019Yves Minet02/2018
95746^70702+2355017Lelio R Paula10/2012
9575(23*2^182753+1)/15155014Lelio R Paula07/2012
95762^182743-161555012Lelio R Paula11/2009
9577(24737*2^182736+1)/39955011Lelio R Paula05/2014
95783^115280-956855003Enzo Doria02/2013
95792^182656-1284954985Enzo Doria10/2012
958012791^13388-13388^1279154984Norbert Schneider03/2018
95819*19^42995+1654981Curtis Bright05/2015
95822^182627+2842554977Lelio R Paula11/2009
95832^182597-11305354968Enzo Doria07/2014
9584(3^115213+2)/3090672554964Lelio R Paula03/2012
95852^182581-197554963Yves Minet09/2012
9586(2*10^54960-179)/354960Robert Price11/2017
958727449!!-1654959Robert Price06/2015
9588(22*10^54958-73)/354959Robert Price09/2017
95904^91283-3^9128354958Jean-Louis Charton01/2004
95892^182565+10754958Lelio R Paula11/2009
95912^182560+205354957Lelio R Paula12/2010
9592126892#-p(126892)54927Henri Lifchitz12/2018
95932^182451-18245154924Henri Lifchitz10/2004
95942^182444+8154922Henri Lifchitz10/2005
95957589^14154-14154^758954921Norbert Schneider01/2019
95962^182433+7410554918Enzo Doria04/2016
959720^42206-524354912Enzo Doria03/2013
95982^182394+8554907Lelio R Paula02/2011
95992^182374-11228754901Enzo Doria06/2014
9600(47^32833-33^32833)/1454899Serge Batalov12/2016
960110188^13697-13697^1018854899Norbert Schneider09/2018
96022^182363-11316754897Enzo Doria07/2014
96032^182359-11222154896Enzo Doria06/2014
9604(F(1905)^139-F(1904)^139)/F(1903)54893Wayne Halsdorf05/2010
9605(17*2^182274+1)/146754869Lelio R Paula01/2012
960618^43698-554853Lelio R Paula02/2013
96072^182209-189354851Yves Minet09/2012
96082^182194-344354846Yves Minet12/2016
960915023^4468+4468^1502354836Hans Havermann08/2016
96102^182135+9014354829Yves Minet10/2010
96112^182119+7433354824Enzo Doria04/2016
961214289^6860+6860^1428954818Hans Havermann08/2016
96133^114892-114892^354818Norbert Schneider03/2017
96142^182070-4735554809Lelio R Paula01/2011
96153^114869+7654807Lelio R Paula10/2012
96168^60681-60681^854801Norbert Schneider12/2016
96171897^16710+16710^189754777Serge Batalov05/2014
9618Phi(61868,59)54776Enzo Doria04/2012
9619113^26679+254775Lelio R Paula05/2013
96203^114789-7454769Lelio R Paula10/2012
962115^46567+9854768Lelio R Paula02/2013
9622(2*10^54767-71)/354767Robert Price01/2017
9623(298*10^54765-7)/354767Robert Price06/2017
9624(21*2^181931-1)/16999754763Lelio R Paula01/2014
96262^181913+2954762Henri Lifchitz06/2005
9625(31*10^54761-121)/954762Robert Price06/2016
96272^181887+18954754Lelio R Paula02/2011
96282^181874+181874^2-154750Robert Price04/2014
9629(2^181865+9)/733954743Lelio R Paula02/2012
96305^78314-9254740Lelio R Paula10/2012
9631(163*10^54727-1)/954729Serge Batalov12/2014
963215^46531+7454725Lelio R Paula02/2013
9633277^22400-34854712Enzo Doria07/2012
96346^70302+10154706Lelio R Paula10/2012
96353^114622-1040854689Enzo Doria02/2013
9637(23*2^181674+1)/48954688Lelio R Paula01/2012
96362^181669-155154688Yves Minet08/2012
9638(57352^11491-1)/5735154676Serge Batalov04/2015
9639(31*2^181629-1)/1073472154671Lelio R Paula01/2014
9640(F(1048)^251-F(1047)^251)/F(1046)54668Wayne Halsdorf05/2010
964113^49073+4654665Lelio R Paula01/2013
9642(57042^11491-1)/5704154649Serge Batalov04/2015
964420^42000+7354644Lelio R Paula02/2013
9643(67607*2^181517+1)/165554644Lelio R Paula05/2014
964533*10^54634+754636Robert Price07/2016
964620^41988+6154628Lelio R Paula01/2013
964720^41988-812354628Enzo Doria03/2013
96482^181420+2118154613Yves Minet03/2011
96499854^13675-13675^985454613Norbert Schneider08/2018
9650(19*10^54608+161)/954609Robert Price07/2016
965119^42696-2454598Lelio R Paula02/2013
9652(44*10^54596-503)/954597Robert Price10/2017
9653(74*10^54583+61)/954584Robert Price10/2015
96542^181316-9439554582Lelio R Paula09/2011
965514751^5006+5006^1475154572Hans Havermann08/2016
965614^47609+3954567Lelio R Paula02/2013
965712696^13295-13295^1269654559Norbert Schneider01/2018
9658(2^124979+lucasV(2,-2,124979)+1)/354552Paul Vanderveen12/2017
96603^114327-7454548Lelio R Paula10/2012
9659(44*10^54547-161)/954548Robert Price11/2017
9661gcd(V(995625),5*F(199125)*(F(199125)-1)+1)54546Serge Batalov04/2015
9662(17*10^54537-47)/354538Robert Price05/2017
96632^181155-1155*18115554534Henri Lifchitz02/2005
9664Phi(61672,83)54533Enzo Doria05/2012
9665(2*10^54527-197)/354527Robert Price11/2017
96669*2^181128+754526Lelio R Paula03/2014
966789*10^54518-754520Robert Price03/2017
96682^181090-11324754514Enzo Doria07/2014
966914031^7670+7670^1403154508Hans Havermann08/2016
967014210^6849+6849^1421054505Hans Havermann08/2016
96712^181043-19954500Lelio R Paula02/2011
967212^50499+554498Lelio R Paula01/2013
967312^50491+554489Lelio R Paula01/2013
96746^70016-14554484Lelio R Paula10/2012
967511^52313-960054479Enzo Doria02/2013
96762^64459+3^64459+5^64459+7^6445954475Henri Lifchitz08/2001
96772^180946-11104154471Enzo Doria05/2014
9678(64*10^54467+287)/954468Robert Price04/2016
9679(32*10^54458+319)/954459Robert Price10/2017
96805^77907-2*3^7790754455Mike Oakes11/2009
968120^41853-562354453Enzo Doria03/2013
968214^47506-7554448Lelio R Paula02/2013
9683(25*10^54443-67)/354444Robert Price11/2017
96842^180839-11343754438Enzo Doria08/2014
96853^114085+2854433Lelio R Paula10/2012
9686Phi(141230,10)54432Ray Chandler08/2009
96876^69946-5554429Lelio R Paula10/2012
9688p(11796)#/2-102454427Robert Price09/2017
96895*2^180796+354426Lelio R Paula03/2014
9690(23*2^180782-1)/9154421Lelio R Paula01/2014
96919*6^69928-754416Lelio R Paula09/2014
969292^27701-91^2770154399Robert Price08/2015
9693(2^180687-3)*6-754393Gilbert Mozzo04/2016
9694(5*10^54388-11)/354389Erik Branger12/2013
969520^41799-304354382Enzo Doria03/2013
969613860^8387+8387^1386054382Hans Havermann08/2016
9697(F(19)^15017-F(18)^15017)/F(17)54378Wayne Halsdorf05/2010
96987^64329-1854365Lelio R Paula10/2012
96992^180551-96754352Yves Minet01/2012
97009075^13732-13732^907554350Norbert Schneider09/2018
970115^46209-7454347Lelio R Paula02/2013
970210^54345+2973954346Patrick De Geest08/2013
970310^54345-14138154345Patrick De Geest09/2013
9704lucasU(2098,1,16360)-lucasU(2098,1,16359)54342Mike Oakes05/2009
9705177^24171-254336Lelio R Paula10/2017
97062^180496+1554335Lelio R Paula02/2011
97071845^16636+16636^184554334Serge Batalov05/2014
970811^52169-7054329Lelio R Paula01/2013
97092^180446-403154320Yves Minet02/2018
971013693^9262+9262^1369354317Hans Havermann06/2016
97112^180429-11310154315Enzo Doria07/2014
97122^180423-11205154313Enzo Doria05/2014
971316112^2349+2349^1611254312Hans Havermann06/2016
9714(79^28621-1)/7854311Paul Bourdelais08/2017
9715(13^48751+4^48751)/1754305Robert Price05/2013
97162^180370+1291554297Lelio R Paula09/2012
9717(10^54290+41)/354290Robert Price01/2017
971815108^3917+3917^1510854283Hans Havermann06/2016
97192^180317-301954281Yves Minet10/2014
97202^180314+85554280Lelio R Paula10/2009
972119^42425+9454252Lelio R Paula02/2013
97222^180180-100544954240Paul Bourdelais11/2012
97232^180173-277354238Yves Minet07/2014
972413367^11418+11418^1336754238Hans Havermann06/2016
9725427^20614+20614^42754224Norbert Schneider06/2016
97262^180124-8795954223Gary Barnes08/2009
97272^180111-11310154219Enzo Doria07/2014
97282^180102-447554217Yves Minet03/2019
97292^180101-11487154216Enzo Doria05/2015
9730(11*2^180099+1)/5161754212Lelio R Paula07/2012
97322^180070+46554207Lelio R Paula09/2012
973113683^9154+9154^1368354207Hans Havermann06/2016
9733810522513*2^180009-9531*2^9531-154198Jiong Sun12/2003
97342^180014+61354190Jason Earls04/2008
97352^180007+10154188Lelio R Paula02/2011
97362^180001+4187754186Jim Fougeron08/2002
97372^180000+13015354186Jim Fougeron09/2002
97383^113565-7454185Lelio R Paula10/2012
973950^31891-4954182Norbert Schneider07/2014
9740(5*2^179991-1)/1142754180Lelio R Paula01/2014
97413^113548+2654177Lelio R Paula10/2012
9742(lucasV(1,2,360029)-2)/(3^3*522251*725981)54177Mike Oakes04/2017
9743181^23996-254176Lelio R Paula10/2017
97444159^14969-13854173Enzo Doria07/2012
97462^179955+577554172Lelio R Paula10/2009
97452^179953-23131354172Enzo Doria05/2014
97475^77485+654160Lelio R Paula10/2012
974818^43141+8554154Lelio R Paula02/2013
974910^54149+18764754150Patrick De Geest07/2017
975010^54149-80000154149Robert Price06/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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