PRP Records

Probable Primes Top 10000

(212140 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 ?
9751(2^169969-1017)/3551165Lelio R Paula01/2012
97525*10^51163-751164Dmitry Domanov11/2010
9753(73*10^51162-1)/951163Robert Price01/2015
9754L(244779)+P(244779)51156Robert Price12/2017
9755(22*10^51154+383)/951155Robert Price11/2017
97562^169899+6351145Lelio R Paula05/2009
97572^169898+51351145Lelio R Paula05/2009
97593^107186-1238851141Enzo Doria02/2013
9758(299*10^51139+1)/351141Robert Price11/2017
9760(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
97613*6^65715-751137Lelio R Paula09/2014
9762116^24768+11551133Norbert Schneider10/2013
976335^33113-402651129Enzo Doria03/2013
9764(13*2^169830-1)/8447751121Lelio R Paula01/2014
9765(46*10^51111-1)/951112Serge Batalov10/2014
976615^43452-3451104Lelio R Paula01/2013
97672^169750-13751100Lelio R Paula01/2011
97682^169739+9406551097Lelio R Paula10/2011
976915^43442-2651092Lelio R Paula01/2013
97705^73096-1700651092Enzo Doria02/2013
977110^51091+7160151092Patrick De Geest07/2017
977210^51091-70151091Robert Price06/2017
9773(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
97742^169706-27055151087Gary Barnes08/2009
9775(2^169696+5)/2151083Lelio R Paula01/2012
9776(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
977711^49051-876051082Enzo Doria02/2013
9778(24737*2^169672+1)/2751080Lelio R Paula05/2014
9779(14*10^51079+229)/951080Robert Price11/2017
97802^169677+1609551078Lelio R Paula05/2009
97812^169659-13551073Lelio R Paula01/2011
97822^169638-11318351067Enzo Doria07/2014
9783(29*2^169622-1)/234653118551054Lelio R Paula01/2014
9784(10^51054+17)/951054Robert Price10/2014
97858329^13022-13022^832951054Norbert Schneider07/2017
9786(24737*2^169577+1)/551052Lelio R Paula05/2014
978711^49021-7851051Lelio R Paula01/2013
978818^40669+6151051Lelio R Paula01/2013
978914038^4327+4327^1403851045Hans Havermann02/2016
97902^169555-15951042Lelio R Paula01/2011
979191^26054-251041Lelio R Paula08/2013
9792Phi(101775,10)/162840151034Makoto Kamada05/2015
97937559^13158-13158^755951033Norbert Schneider11/2017
979497*10^51027-351029Robert Price01/2017
97952^169499-264751025Yves Minet07/2014
97965*6^65567+751022Lelio R Paula09/2014
979714763^2858+2858^1476351022Hans Havermann08/2015
979824^36966-147751021Enzo Doria03/2013
9799(78557*2^169464+1)/16052751014Lelio R Paula06/2014
9800(34*10^51008-43)/951009Ray Chandler09/2010
980110^51004+12842751005Patrick De Geest08/2009
980310^51004-11351004Milton L. Brown12/2008
980210^51003+1695151004Patrick De Geest08/2009
980410^51003-7960151003Milton L. Brown12/2008
980510^51003-8083151003Milton L. Brown12/2008
980610^51002+887751003Patrick De Geest08/2009
980810^51002-1054151002Milton L. Brown11/2008
980710^51001+5205151002Patrick De Geest08/2009
980910^51001-15868751001Milton L. Brown10/2008
98102*10^51000+9351001Robert Price07/2016
981110^51000+18825151001Patrick De Geest10/2017
981210^51000-3128951000Patrick De Geest10/2017
9814(2^169416+5)/350999Lelio R Paula01/2012
9813(49*10^50998+41)/950999Robert Price07/2015
981513292^6867+6867^1329250999Hans Havermann02/2016
9816(35*10^50997-71)/950998Robert Price05/2015
98176^65536+2*97878-150997Jiahao He05/2017
981829^34871-28^3487150996Robert Price09/2012
981976^27112-7550993Norbert Schneider11/2012
9820(70^27631-1)/6950981Richard Fischer08/2017
9821(12451^12451+1345)/2^2/19/89/139/697750980Makoto Morimoto07/2016
982210736^12645-12645^1073650971Norbert Schneider12/2016
9823(1017*2^169315-1)/971550968Lelio R Paula03/2015
98247^60309-6^(60309+1)50968Robert Price06/2016
98262^169267+9950955Lelio R Paula07/2009
98255*2^169264+350955Lelio R Paula02/2014
9827t(192517)50950Robert Price08/2014
982810^50943+62445150944Robert Price03/2015
982910^50943+5440950944Patrick De Geest02/2016
983010^50943-10055950943Patrick De Geest03/2016
98312^169206-364550937Lelio R Paula05/2009
98322^169196-11257750934Enzo Doria06/2014
983320^39146-348350931Enzo Doria03/2013
983410^50929+1684950930Patrick De Geest01/2012
983610^50929-5150929Robert Price05/2011
98357^60264+4850929Lelio R Paula10/2012
98372^169167+129950925Lelio R Paula05/2009
983810103^12717-10050925Enzo Doria07/2012
98393^106721-13050919Lelio R Paula07/2012
984118225^622+622^1822550917Anatoly F. Selevich11/2006
9840(10223*2^169138+1)/111350917Lelio R Paula05/2014
98426057^13462-13462^605750917Norbert Schneider04/2018
98437*2^169125+950913Lelio R Paula02/2014
9844(47*2^169123+1)/2950912Lelio R Paula03/2015
984520^39131+9350911Lelio R Paula01/2013
9846(21*27^35567-94921)/2650910Curtis Bright05/2015
9847(7*2^169124-1)/954950909Lelio R Paula01/2014
9848(12433^12433+809)/2/3/1150907Makoto Morimoto07/2016
984913693^5212+5212^1369350897Hans Havermann02/2016
98507*5^72813+650895Lelio R Paula09/2014
98515*10^50890-8150891Robert Price04/2017
98523^106656-1202850888Enzo Doria02/2013
9853(2^169028+3)/25950881Lelio R Paula01/2012
98542^169000-112750875Yves Minet05/2013
985519^39780+1650869Lelio R Paula01/2013
9856(19*2^168960+1)/550863Lelio R Paula07/2012
9857(-lucasV(1,2,337937)-2)/(3^2*11)50863Mike Oakes02/2017
985911^48840+4650862Lelio R Paula01/2013
9858(5*10^50861-107)/350862Robert Price01/2017
986020^39087-420350854Enzo Doria03/2013
9861(12421^12421+1339)/2^4/5/43/15750848Makoto Morimoto07/2016
98622^168907-54444750847Paul Bourdelais11/2012
986319312^429+429^1931250839Anatoly F. Selevich12/2006
98645^72716-1322650827Enzo Doria02/2013
98652^168823+102550821Lelio R Paula01/2009
98667*10^50818-8950819Robert Price01/2017
98682^168811+15015*16881150818Henri Lifchitz02/2005
98672^168813-283350818Yves Minet09/2014
9870(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
98697022^13211-13211^702250816Norbert Schneider12/2017
98712^168795+538550813Lelio R Paula05/2009
98727670^13079-13079^767050810Norbert Schneider09/2017
98734*3^106483+550806Lelio R Paula03/2014
987413^45606+450803Lelio R Paula01/2013
987513^45606-3850803Lelio R Paula01/2013
98762^168746+5890550798Lelio R Paula05/2009
9877(16*10^50795-43)/950796Robert Price02/2015
9878gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
98797*10^50789-4750790Robert Price02/2017
98802^168717-72952350789Paul Bourdelais11/2012
9881(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9882(21*2^168652-1)/21550769Lelio R Paula01/2014
98832^168629+1290950763Lelio R Paula01/2011
98849328^12787+12787^932850762Norbert Schneider01/2016
98852^168627+7311350762Enzo Doria04/2016
98862^168623+4733350761Yves Minet02/2010
9887(8*10^50750-101)/350751Robert Price10/2017
9888(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9889(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
98903*10^50727-3150728Robert Price10/2017
98916152^13387-13387^615250724Norbert Schneider03/2018
98928544^12901-12901^854450723Norbert Schneider05/2017
9893(17^41221+1)/1850720Paul Bourdelais03/2010
989410^50711+750712Jason Earls12/2007
989510^50711-31796950711Patrick De Geest04/2009
9897(17^41213+3^41213)/2050710Robert Price08/2013
9896(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
989847779!4+102450708Robert Price08/2017
99002^168431-15950703Lelio R Paula01/2011
9899(7*10^50702-1)/350703Erik Branger03/2014
9901117216#-p(117216)50700Henri Lifchitz03/2007
9902(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
9903(13*2^168352-1)/47750678Lelio R Paula01/2014
99048*10^50675+3950676Robert Price01/2017
9905(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
990614415^3274+3274^1441550670Hans Havermann05/2016
9907(12379^12379+282)/1750663Makoto Morimoto07/2016
99095^72480-1712650662Enzo Doria02/2013
9908(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
99103^106143+250644Mike Oakes11/2009
99119178^12777-12777^917850633Norbert Schneider02/2017
9912(2*10^50603-41)/350603Robert Price01/2017
9913(12^46889-1)/1150601Paul Bourdelais09/2008
99142^168068-189350594Yves Minet09/2012
99152^168057+841550591Lelio R Paula11/2011
99164*10^50579+950580Robert Price05/2015
99172^168019-9439550579Lelio R Paula07/2011
99182^168019+7421350579Enzo Doria04/2016
9919(47*10^50578+493)/950579Robert Price11/2017
99205925^13406-13406^592550577Norbert Schneider03/2018
99213^106002+7050576Lelio R Paula07/2012
99225*2^167970-950565Lelio R Paula02/2014
9923(58*10^50558-13)/950559Robert Price09/2015
992488*10^50547+750549Robert Price11/2016
99252^167910-11262550546Enzo Doria06/2014
9926(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
99272^167866+1171550533Lelio R Paula05/2009
9928gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
99292^167847-13550527Lelio R Paula01/2011
9930-lucasV(-1,2,335684)50526Mike Oakes01/2017
9931(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
9932(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
99342^167807+7550515Lelio R Paula08/2010
99332^167805+7627750515Enzo Doria04/2016
99358335^12882+12882^833550510Norbert Schneider03/2016
99367*2^167777+950507Lelio R Paula02/2014
993714162^3681+3681^1416250502Hans Havermann05/2016
9938(17*10^50495-11)/350496Robert Price07/2015
99392^167682+8550478Lelio R Paula08/2010
99402^167667-92742750473Paul Bourdelais11/2012
99419737^12654+12654^973750470Norbert Schneider01/2016
9942(9179*2^167644-1)/1750469Lelio R Paula03/2015
994313386^5891+5891^1338650468Hans Havermann05/2016
9944(10^50467-97)/350467Robert Kinser10/2017
9945(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
9946152^23124+15150453Eric Chen04/2018
99475003^13637-15650447Enzo Doria07/2012
99486^64826-2672350445Enzo Doria03/2013
9949(3^105718+7)/3250439Lelio R Paula03/2012
9950(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
995117^40989+5650435Lelio R Paula01/2013
9952(12329^12329+1652)/42150435Makoto Morimoto07/2016
99532*5^72153+750434Lelio R Paula09/2014
9954(3126^14431-1)/312550433Richard Fischer03/2015
99558078^12907-12907^807850432Norbert Schneider05/2017
995639^31694+3850428Norbert Schneider05/2014
9957(7*10^50414-151)/950414Robert Price09/2017
99582^167460+218750411Lelio R Paula11/2011
9959(12323^12323+2709)/2^450409Makoto Morimoto07/2016
996011^48400-771050404Enzo Doria02/2013
99612^167432+5461550403Lelio R Paula05/2009
9962(23*2^167430-1)/416950400Lelio R Paula01/2014
996368677!6-250395Robert Price07/2017
996419^39404+2250389Lelio R Paula01/2013
9965(102^25087-1)/10150388Richard Fischer08/2017
996635^32629-783450382Enzo Doria03/2013
99686^64744+16350381Lelio R Paula06/2012
9967116447#+17465950381Nicolas PALAU09/2016
99702^167353+12950379Lelio R Paula05/2009
996920^38722-113350379Enzo Doria03/2013
99723^105567-1650369Lelio R Paula07/2012
99712^167321-11284950369Enzo Doria06/2014
9973(28*10^50362-43)/350363Robert Price04/2016
997411421^12410-12410^1142150357Norbert Schneider08/2013
99752^167278-206350356Yves Minet03/2013
9976181^22300+22300^18150347Serge Batalov05/2014
99779932^12595-12595^993250343Norbert Schneider12/2016
99788993^12732-12732^899350342Norbert Schneider02/2017
99793*5^72018-450339Lelio R Paula09/2014
99802^167207-11268750335Enzo Doria06/2014
99816^64674-3750327Lelio R Paula06/2012
99822^167177+7480150326Enzo Doria04/2016
998313739^4600+4600^1373950323Hans Havermann10/2015
998411508^12391+12391^1150850320Norbert Schneider06/2014
99852^167132-216350312Yves Minet08/2013
99867^59527-6250307Lelio R Paula06/2012
9987(310027^9161+1)/31002850302Faysal YAtim04/2008
9988(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
99892^167083-11251950297Enzo Doria06/2014
9990272^20659-20659^27250296Norbert Schneider09/2015
999125337!!-1650290Robert Price06/2015
99929722^12611-12611^972250290Norbert Schneider12/2016
9993(15*2^167013+1)/64950275Lelio R Paula07/2012
999419^39315-1250275Lelio R Paula01/2013
99955^71925-3650274Lelio R Paula06/2012
99962^167002+279913950273Enzo Doria04/2016
999710957^12444-12444^1095750270Norbert Schneider07/2013
99988*10^50253-9950254Robert Price02/2017
100005^71894-5450252Lelio R Paula06/2012
9999(127^23887+1)/12850252Richard Fischer04/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 20 2018 08:38 (Time in France)

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