PRP Records

Probable Primes Top 10000

(205869 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 ?
3001(55459*2^340090+1)/1591102379Lelio R Paula07/2014
300289^52511-88^52511102365Robert Price06/2015
30033^214539-112756102362Enzo Doria07/2014
30042^340000-19877102351Enzo Doria06/2013
30052^339990-114845102348Enzo Doria05/2015
3006(3^214516-2)/51383102346Lelio R Paula12/2013
300720^78661-99102341Lelio R Paula09/2016
30082^339951-19585102336Enzo Doria05/2013
3009(13*2^339943+1)/45102333Lelio R Paula12/2013
30102^339889+29327102317Yves Minet06/2010
30112^339834-109493102301Enzo Doria04/2014
3012(11^98221-5^98221)/6102286Robert Price01/2013
30133^214365+1820102279Lelio R Paula10/2016
3014(11*2^339705-1)/183102261Lelio R Paula03/2014
30152^339694-16995102259Lelio R Paula09/2016
30167^120985-38102245Lelio R Paula10/2016
301710^102244+122961102245Patrick De Geest12/2016
301810^102244-27102244Lelio R Paula09/2016
30197^120982-62102242Lelio R Paula10/2016
30204*6^131382-5102236Lelio R Paula11/2014
30212^339586-1091102226Yves Minet11/2012
302211^98161-3072000102225Enzo Doria12/2012
30239*7^120961-4102225Lelio R Paula11/2014
30245*3^214250+2102224Serge Batalov10/2010
302512^94713-59102213Lelio R Paula10/2016
302612^94705+89102204Lelio R Paula10/2016
30272^339407-177102172Lelio R Paula08/2011
30282^339355+65102157Lelio R Paula07/2011
3029(2^339323+47)/880715102141Lelio R Paula12/2013
30302^339168+21102100Lelio R Paula07/2011
30312^339167-108807102100Enzo Doria03/2014
30322^339156+163102097Lelio R Paula08/2011
3033(2^338982-7)/1754517102038Lelio R Paula12/2013
30342^338891-18885102017Enzo Doria05/2013
30352^338829-113239101998Enzo Doria07/2014
30362^338828-113297101998Enzo Doria07/2014
30372^338796+93101988Donovan Johnson06/2008
3038lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
3039(71^55079-1)/70101964Paul Bourdelais08/2017
30412^338682-19865101954Enzo Doria06/2013
3040(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
30422^338568+37101920Lelio R Paula07/2011
30432^338559-1858777101917Enzo Doria04/2016
3044(9*2^338520+1)/365101904Lelio R Paula12/2013
30452^338497-17041101898Enzo Doria05/2013
30462^338475+54615101892Lelio R Paula10/2016
30472^338426-19797101877Enzo Doria06/2013
30482^338368-20369101859Enzo Doria06/2013
30492^338366+74179101859Enzo Doria04/2016
30502^338280-19745101833Enzo Doria06/2013
3051(3*2^338236-1)/347101818Lelio R Paula03/2014
30526^130841+103101815Lelio R Paula10/2016
30542^338122-20117101785Enzo Doria06/2013
3053(2^338139+5)/905333101785Lelio R Paula12/2013
305535^65917-7092101781Enzo Doria03/2013
30562^338010-19833101752Enzo Doria06/2013
30573^213215-76101730Lelio R Paula09/2016
30582^337930+63101728Lelio R Paula07/2011
30592^337920+1869661101725Enzo Doria05/2016
30602^337859-19645101706Enzo Doria05/2013
30612^337754+1869169101675Enzo Doria05/2016
3062(31*2^337677-1)/593101650Lelio R Paula03/2014
306311^97605-24101646Lelio R Paula10/2016
30648^112539-112539101633Robert Price01/2014
30652^337515-19869101603Enzo Doria06/2013
30662^337473+719101590Lelio R Paula08/2011
3067(2^337485-509203)/656647157101585Lelio R Paula12/2013
30682^337452-108815101584Enzo Doria03/2014
30692^337453+1185101584Lelio R Paula09/2016
30702^337410-113561101571Enzo Doria08/2014
30712^337387+855101564Lelio R Paula09/2016
30722^337367-17295101558Lelio R Paula09/2016
30732^337342-109035101551Enzo Doria04/2014
30742^337267-19101528Lelio R Paula07/2011
30752^337183-19989101503Enzo Doria06/2013
30762^337149+72425101492Enzo Doria04/2016
30772^337101-20241101478Enzo Doria06/2013
30782^337035-20001101458Enzo Doria06/2013
30792^337017-16995101453Lelio R Paula09/2016
30802^336979-115315101441Enzo Doria06/2015
30812^336970-20885101439Enzo Doria06/2013
30822^336958+79101435Lelio R Paula10/2009
30832^336942+169101430Lelio R Paula10/2009
3084(15185*2^336894-1)/7939101416Lelio R Paula05/2015
30852^336871+257463101409Tony Prest / Never Odd Or Even04/2016
30862^336871+318105101409Tony Prest / Never Odd Or Even04/2016
30872^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
30882^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
30892^336871+389273101409Tony Prest / Never Odd Or Even04/2016
30902^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
30912^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
30922^336871+586905101409Tony Prest / Never Odd Or Even04/2016
30932^336871+674571101409Tony Prest / Never Odd Or Even04/2016
30942^336871+707009101409Tony Prest / Never Odd Or Even04/2016
30952^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
30962^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
30972^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
30982^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
30992^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
31002^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
31012^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
31022^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3103(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3104(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3105(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3106(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
31072^336842+94065101400Lelio R Paula09/2016
3108(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3109(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3110(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3111(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3112(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3113(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3114(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
311510^101369+203811101370Patrick De Geest11/2016
311610^101369-99101369Lelio R Paula09/2016
3117(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
31182^336701-113563101358Enzo Doria08/2014
31192^336644-109023101340Enzo Doria04/2014
31202^336601-21081101327Enzo Doria06/2013
312120^77869+63101310Lelio R Paula09/2016
3122(13*2^336523-1)/19101304Lelio R Paula03/2014
31236^130179-137101299Lelio R Paula10/2016
3124(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3125(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3126(2^336448+9)/497405101276Lelio R Paula12/2013
31272^336369-19753101258Enzo Doria05/2013
31282^336350-344291101252Enzo Doria07/2015
31292^336243-108777101220Enzo Doria03/2014
3130(31*2^336189-1)/19101204Lelio R Paula03/2014
3131(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
31322^336150-20393101192Enzo Doria06/2013
31332^336112-1865249101180Enzo Doria03/2016
31342^336103-109015101178Enzo Doria04/2014
313513^90809-96101157Lelio R Paula10/2016
313619^79098-30101147Lelio R Paula10/2016
313719^79095+88101144Lelio R Paula10/2016
313815^85976+32101116Lelio R Paula10/2016
3139(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3140(4^167933+17)/3101106Robert Price02/2017
31412^335858+153101104Lelio R Paula10/2009
31426^129918-35101096Lelio R Paula10/2016
31433^211885-70101095Lelio R Paula09/2016
3144(29*2^335835-1)/550599101093Lelio R Paula03/2014
31452^335818-20033101092Enzo Doria06/2013
31462^335813-110083101090Enzo Doria04/2014
31472^335804+2155101088Lelio R Paula09/2016
31482^335784-16145101082Enzo Doria04/2013
314911^97051+62101069Lelio R Paula10/2016
3150(2^335691-3)/26515101049Lelio R Paula12/2013
31512^335658-94395101044Lelio R Paula09/2016
31522^335586+169101022Lelio R Paula10/2009
3153(56^57787-1)/55101021Paul Bourdelais08/2017
315447599!2+1024100991Robert Price02/2015
31552^335468-18629100986Enzo Doria05/2013
31562^335454-20961100982Enzo Doria06/2013
315710^100978+61100979Lelio R Paula09/2016
315810^100978-156437100978Patrick De Geest11/2016
3159(15*2^335417+1)/481100970Lelio R Paula12/2013
31602^335403-1859167100967Enzo Doria03/2016
31619*2^335364-5100956Lelio R Paula08/2014
31622^335349+72287100951Enzo Doria04/2016
31632^335329+16095100945Lelio R Paula09/2016
3164232823#+233663100937Makoto Morimoto10/2017
31652^335237-20893100917Enzo Doria06/2013
31662^335222-19337100912Enzo Doria05/2013
31672^335222-109985100912Enzo Doria04/2014
31682^335182-17237100900Enzo Doria05/2013
31692^335043-16737100858Enzo Doria05/2013
3170(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
31712^335038-20633100857Enzo Doria06/2013
31722^335031+1873373100855Enzo Doria06/2016
31733^211354-8816100842Enzo Doria05/2014
31742^334984-112757100841Enzo Doria06/2014
31762^334857+48527100803Lelio R Paula08/2011
317512^93406+29100803Lelio R Paula10/2016
3177(5*2^334825+1)/47100792Lelio R Paula12/2013
31782^334809-13100788Lelio R Paula04/2011
3179(82*10^100780-1)/9100781Robert Price12/2014
3180(2^334779+47)/5100778Lelio R Paula12/2013
31812^334751+2049100771Lelio R Paula09/2016
318213^90443-98100749Lelio R Paula10/2016
3183(24737*2^334628+1)/3100737Lelio R Paula07/2014
318415^85639-28100720Lelio R Paula10/2016
31852^334562+577294575100711Lelio R Paula09/2016
31864*3^211077-5100710Lelio R Paula08/2014
31872^334524+145100702Lelio R Paula07/2009
3188(1017*2^334391-1)/3535100662Lelio R Paula05/2015
31892^334294-113111100633Enzo Doria07/2014
31906^129308-17723100622Enzo Doria03/2013
31916^129305+95100619Lelio R Paula10/2016
31922^334244-1167100618Lelio R Paula09/2016
3193(21*2^334050+1)/935100558Lelio R Paula12/2013
3194(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3195(35*10^100542+1)/9100543Serge Batalov11/2010
319613^90251+24100535Lelio R Paula10/2016
31972^333963+789100533Lelio R Paula08/2011
31982^333919-1840087100520Enzo Doria06/2015
31992^333911+72623100518Enzo Doria04/2016
320018^80064-67100503Lelio R Paula10/2016
32015^143742-48100472Lelio R Paula10/2016
32022^333757-112123100471Enzo Doria06/2014
32032^333603-108861100425Enzo Doria03/2014
32049*7^118818-2100414Lelio R Paula11/2014
32052^333546-17097100408Enzo Doria05/2013
320617^81597+72100401Lelio R Paula10/2016
3207p(20559)#/2+8100384Robert Price01/2017
320811^96390-24100380Lelio R Paula10/2016
32094832563059*2^333333+30029100353Donovan Johnson01/2008
32102^333354+763100350Lelio R Paula08/2011
32112^333289-109483100330Enzo Doria04/2014
32122^333240-2790209100316Enzo Doria03/2016
3214(2^333227-2^166614+1)/510031111/2006
32132^333225+719100311Lelio R Paula08/2011
32152^333221-2785333100310Enzo Doria10/2015
321676^53332-75100308Norbert Schneider02/2015
32176^128892-17573100298Enzo Doria03/2013
32182^333105-113215100275Enzo Doria07/2014
3219(31*2^333102+1)/2375100272Lelio R Paula11/2013
322017^81476-74100253Lelio R Paula10/2016
322117^81417-16100180Theodore Burton11/2005
32222^332739-113215100165Enzo Doria07/2014
32232^332730-1865621100162Enzo Doria03/2016
322491^51127-2100160Lelio R Paula09/2013
322515^85159-32100155Lelio R Paula10/2016
32266^128661+97100118Lelio R Paula10/2016
322719^78285+40100108Lelio R Paula07/2016
32286^128640+5100102Lelio R Paula11/2014
32296^128565-127100044Lelio R Paula08/2016
32302^332309-133100035Lelio R Paula02/2011
32312^332307+731100035Lelio R Paula07/2011
32322^332301+12927100033Lelio R Paula04/2013
323323406^18781+18781^23406100031Hans Havermann04/2018
323412^92684-13100023Lelio R Paula07/2016
3235(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
3236(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
324225206!+p(4114)100001Henri Lifchitz09/2005
324325206!-p(5447)100001Henri Lifchitz10/2005
324425206!-p(12402)100001Henri Lifchitz04/2006
324525206!-p(16290)100001Henri Lifchitz09/2006
324625206!-p(19647)100001Henri Lifchitz02/2007
32472^332194+11473100001Henri Lifchitz03/2007
323910^100000+3938473100001Robert Price05/2015
324010^100000+3979761100001Robert Price05/2015
324110^100000+4293973100001Robert Price09/2015
324810^100000+4858267100001Robert Price12/2015
324910^100000+5113299100001Robert Price02/2016
325010^100000+5169411100001Robert Price02/2016
323710^100000+11187931100001Robert Price03/2018
323810^100000+11264721100001Robert Price04/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 22 2018 09:48 (Time in France)

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