PRP Records

Probable Primes Top 10000

(280932 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 ?
5001(8*10^102541+49)/3102542Robert Price05/2020
5002(536*10^102533-23)/9102535Robert Price02/2020
50032^340547-108897102515Enzo Doria03/2014
5004(2^340536+778)/2102512Stefano Morozzi09/2020
500525592^10119+10119^25592102500Hans Havermann02/2019
50067^121268+82102484Lelio R Paula10/2016
5007(6883*2^340443-1)/162401102483Lelio R Paula05/2015
50082^340434-5955102481Lelio R Paula11/2016
5009(7*10^102480-19)/3102481Robert Price10/2020
5010(2^340381+47)/7102465Lelio R Paula12/2013
5011111^50095+110102461Norbert Schneider04/2017
50122^340291-20301102438Enzo Doria06/2013
501312^94915+89102431Lelio R Paula10/2016
501424466^15349+15349^24466102417Hans Havermann03/2019
50152^340208-20373102413Enzo Doria06/2013
50166^131598-17273102404Enzo Doria02/2013
5017(2^340132+1182)/2102390Stefano Morozzi09/2020
5018(2^340133+1166)/2102390Stefano Morozzi09/2020
50192^340115-21181102385Enzo Doria06/2013
5020(55459*2^340090+1)/1591102379Lelio R Paula07/2014
5021(2^340064+3630)/2102370Stefano Morozzi09/2020
502289^52511-88^52511102365Robert Price06/2015
50233^214539-112756102362Enzo Doria07/2014
502423159^23450-23450^23159102353Norbert Schneider12/2019
50252^340000-19877102351Enzo Doria06/2013
50262^339990-114845102348Enzo Doria05/2015
5027(3^214516-2)/51383102346Lelio R Paula12/2013
502820^78661-99102341Lelio R Paula09/2016
50292^339951-19585102336Enzo Doria05/2013
5030(13*2^339943+1)/45102333Lelio R Paula12/2013
5031(236282#+121441)/(121441*25499429)102332Makoto Morimoto08/2020
50325*10^102323-91102324Robert Price03/2021
50342^339889+29327102317Yves Minet06/2010
5033(167*10^102315-17)/3102317Robert Price03/2020
503526348^7641+7641^26348102314Hans Havermann03/2019
5036Phi(239414,10)/6333218543102303Makoto Kamada08/2019
50372^339834-109493102301Enzo Doria04/2014
5038(16*10^102299-19)/3102300Robert Price02/2019
5039(11^98221-5^98221)/6102286Robert Price01/2013
50403^214365+1820102279Lelio R Paula10/2016
504131978^1579+1579^31978102278Hans Havermann03/2019
5042(11*2^339705-1)/183102261Lelio R Paula03/2014
50432^339694-16995102259Lelio R Paula09/2016
5044(56*10^102255+691)/9102256Robert Price05/2019
5045122^49008+121102249Norbert Schneider10/2018
5046(2^339652+3178)/2102246Stefano Morozzi09/2020
50477^120985-38102245Lelio R Paula10/2016
504810^102244+122961102245Patrick De Geest12/2016
504910^102244-27102244Lelio R Paula09/2016
50507^120982-62102242Lelio R Paula10/2016
5051(2^339640+2670)/2102242Stefano Morozzi09/2020
50524*6^131382-5102236Lelio R Paula11/2014
5053(2^339607+3290)/2102232Stefano Morozzi02/2021
50542^339586-1091102226Yves Minet11/2012
505511^98161-3072000102225Enzo Doria12/2012
50569*7^120961-4102225Lelio R Paula11/2014
50575*3^214250+2102224Serge Batalov10/2010
505812^94713-59102213Lelio R Paula10/2016
505912^94705+89102204Lelio R Paula10/2016
50602^339407-177102172Lelio R Paula08/2011
50614*10^102163-57102164Robert Price10/2018
50622^339355+65102157Lelio R Paula07/2011
5063(28*10^102142-31)/3102143Robert Price12/2019
5064(2^339323+47)/880715102141Lelio R Paula12/2013
5065(2^339268+1758)/2102130Stefano Morozzi09/2020
5066s(178551)102122Robert Price05/2020
5067(2^339175+2790)/2102102Stefano Morozzi02/2021
50702^339168+21102100Lelio R Paula07/2011
50682^339167-108807102100Enzo Doria03/2014
5069(2^339169+42)/2102100Stefano Morozzi09/2020
50712^339156+163102097Lelio R Paula08/2011
5072(2^339149+746)/2102094Stefano Morozzi09/2020
5073(25*10^102076-67)/3102077Robert Price06/2019
50742^339081-4543102074Yves Minet03/2019
50752*10^102062+77102063Robert Price08/2020
507624327^15668+15668^24327102053Hans Havermann02/2019
507725080^11711+11711^25080102041Hans Havermann02/2019
5078(2^338982-7)/1754517102038Lelio R Paula12/2013
50792^338891-18885102017Enzo Doria05/2013
50808*10^102000+51102001Robert Price08/2019
5081(2^338832+642)/2101999Stefano Morozzi09/2020
50822^338829-113239101998Enzo Doria07/2014
50832^338828-113297101998Enzo Doria07/2014
50842^338796+93101988Donovan Johnson06/2008
5085lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
508625295^10744+10744^25295101969Hans Havermann01/2019
508725712^9243+9243^25712101969Hans Havermann01/2019
5088(71^55079-1)/70101964Paul Bourdelais08/2017
50892^338682-19865101954Enzo Doria06/2013
5090(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
5091(2^338666+3154)/2101949Stefano Morozzi09/2020
509228594^3673+3673^28594101939Hans Havermann02/2019
5093(2^338587+2306)/2101925Stefano Morozzi02/2021
50942^338568+37101920Lelio R Paula07/2011
50952^338559-1858777101917Enzo Doria04/2016
5096(9*2^338520+1)/365101904Lelio R Paula12/2013
509724502^14419+14419^24502101903Hans Havermann01/2019
50982^338497-17041101898Enzo Doria05/2013
50992^338475+54615101892Lelio R Paula10/2016
51002^338426-19797101877Enzo Doria06/2013
51012^338368-20369101859Enzo Doria06/2013
51022^338366+74179101859Enzo Doria04/2016
510327088^5755+5755^27088101853Hans Havermann01/2019
51042^338280-19745101833Enzo Doria06/2013
5105(2^338242+2782)/2101821Stefano Morozzi02/2021
5106(3*2^338236-1)/347101818Lelio R Paula03/2014
51076^130841+103101815Lelio R Paula10/2016
51082^338122-20117101785Enzo Doria06/2013
5109(2^338139+5)/905333101785Lelio R Paula12/2013
511035^65917-7092101781Enzo Doria03/2013
51112^338010-19833101752Enzo Doria06/2013
51123^213215-76101730Lelio R Paula09/2016
511323907^17998+17998^23907101730Hans Havermann01/2019
511410^101728+154953101729Patrick De Geest02/2020
51172^337930+63101728Lelio R Paula07/2011
511510^101728-987654321101728Robert Price12/2019
511610^101728-60741101728Patrick De Geest02/2020
51182^337920+1869661101725Enzo Doria05/2016
511924116^16509+16509^24116101715Hans Havermann01/2019
5120(2^337875+3174)/2101711Stefano Morozzi09/2020
51212^337859-19645101706Enzo Doria05/2013
51222^337754+1869169101675Enzo Doria05/2016
51233*10^101657-37101658Robert Price07/2018
5124(31*2^337677-1)/593101650Lelio R Paula03/2014
512511^97605-24101646Lelio R Paula10/2016
5126(2^337624+3606)/2101635Stefano Morozzi09/2020
51278^112539-112539101633Robert Price01/2014
5128(2^337575+1818)/2101620Stefano Morozzi02/2021
512925694^9003+9003^25694101605Hans Havermann12/2018
51302^337515-19869101603Enzo Doria06/2013
51312^337473+719101590Lelio R Paula08/2011
5132(2^337485-509203)/656647157101585Lelio R Paula12/2013
51342^337452-108815101584Enzo Doria03/2014
51332^337453+1185101584Lelio R Paula09/2016
51352^337410-113561101571Enzo Doria08/2014
51362^337387+855101564Lelio R Paula09/2016
51372^337367-17295101558Lelio R Paula09/2016
51382^337342-109035101551Enzo Doria04/2014
513923703^19238+19238^23703101548Hans Havermann12/2018
5140(26*10^101537-167)/3101538Robert Price10/2019
51412^337267-19101528Lelio R Paula07/2011
5142(2^337259+1766)/2101525Stefano Morozzi09/2020
5143(2^337257+2306)/2101525Stefano Morozzi02/2021
5144(2^337195+2646)/2101506Stefano Morozzi09/2020
51452^337183-19989101503Enzo Doria06/2013
51462^337149+72425101492Enzo Doria04/2016
514724041^16642+16642^24041101483Hans Havermann12/2018
514833982^969+969^33982101482Hans Havermann12/2018
51492^337101-20241101478Enzo Doria06/2013
51502^337035-20001101458Enzo Doria06/2013
5151(7*10^101456+89)/3101457Robert Price08/2020
51522^337017-16995101453Lelio R Paula09/2016
51532^336979-115315101441Enzo Doria06/2015
51542^336970-20885101439Enzo Doria06/2013
51552^336958+79101435Lelio R Paula10/2009
51562^336942+169101430Lelio R Paula10/2009
5157(15185*2^336894-1)/7939101416Lelio R Paula05/2015
51584*10^101415-89101416Robert Price11/2018
5159(14*10^101410-89)/3101411Robert Price05/2020
51602^336871+257463101409Tony Prest / Never Odd Or Even04/2016
51612^336871+318105101409Tony Prest / Never Odd Or Even04/2016
51622^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
51632^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
51642^336871+389273101409Tony Prest / Never Odd Or Even04/2016
51652^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
51662^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
51672^336871+586905101409Tony Prest / Never Odd Or Even04/2016
51682^336871+674571101409Tony Prest / Never Odd Or Even04/2016
51692^336871+707009101409Tony Prest / Never Odd Or Even04/2016
51702^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
51712^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
51722^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
51732^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
51742^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
51752^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
51762^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
51772^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
5178(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
5179(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
5180(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
5181(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
518224097^16150+16150^24097101405Hans Havermann12/2018
51832^336842+94065101400Lelio R Paula09/2016
5184(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
5185(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
5186(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
5187(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
5188(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
5189(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
5190(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
519110^101369+203811101370Patrick De Geest11/2016
519210^101369-99101369Lelio R Paula09/2016
5193(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
51942^336701-113563101358Enzo Doria08/2014
519589717!4-512101351Robert Price11/2019
51962^336644-109023101340Enzo Doria04/2014
51972^336601-21081101327Enzo Doria06/2013
519820^77869+63101310Lelio R Paula09/2016
5199(13*2^336523-1)/19101304Lelio R Paula03/2014
52006^130179-137101299Lelio R Paula10/2016
5201(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
5202(24737*2^336485+1)/7285101293Lelio R Paula07/2014
5203(2^336448+9)/497405101276Lelio R Paula12/2013
52042^336369-19753101258Enzo Doria05/2013
520523842^17653+17653^23842101253Hans Havermann11/2018
52072^336350-344291101252Enzo Doria07/2015
5206(17*10^101251-161)/9101252Robert Price02/2021
5208(56*10^101222-47)/9101223Robert Price02/2019
52092^336243-108777101220Enzo Doria03/2014
5210(31*2^336189-1)/19101204Lelio R Paula03/2014
521123535^19954+19954^23535101202Hans Havermann11/2018
5212(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
52132^336150-20393101192Enzo Doria06/2013
521423996^16473+16473^23996101186Hans Havermann11/2018
52152^336112-1865249101180Enzo Doria03/2016
52162^336103-109015101178Enzo Doria04/2014
5217(2^336095+2078)/2101175Stefano Morozzi09/2020
521813^90809-96101157Lelio R Paula10/2016
521926199^7258+7258^26199101150Hans Havermann11/2018
522019^79098-30101147Lelio R Paula10/2016
522119^79095+88101144Lelio R Paula10/2016
522215^85976+32101116Lelio R Paula10/2016
52232^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
5224(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
5225(4^167933+17)/3101106Robert Price02/2017
52272^335858+153101104Lelio R Paula10/2009
5226(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
5228(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
5229(2^335839+2114)/2101098Stefano Morozzi09/2020
5230(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
52316^129918-35101096Lelio R Paula10/2016
5232(2*10^101096-107)/3101096Robert Price11/2020
52333^211885-70101095Lelio R Paula09/2016
5235(29*2^335835-1)/550599101093Lelio R Paula03/2014
5234(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
52362^335818-20033101092Enzo Doria06/2013
52372^335813-110083101090Enzo Doria04/2014
52382^335804+2155101088Lelio R Paula09/2016
5239(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
52402^335784-16145101082Enzo Doria04/2013
524111^97051+62101069Lelio R Paula10/2016
52423*10^101065+11101066Robert Price07/2018
524327820^4293+4293^27820101064Hans Havermann10/2018
5244(2^335714+3750)/2101060Stefano Morozzi01/2021
5245(2^335690+1038)/2101053Stefano Morozzi09/2020
5246(2^335691-3)/26515101049Lelio R Paula12/2013
52472^335658-94395101044Lelio R Paula09/2016
524824514^13215+13215^24514101024Hans Havermann11/2018
52492^335586+169101022Lelio R Paula10/2009
5250(56^57787-1)/55101021Paul Bourdelais08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

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