PRP Records

Probable Primes Top 10000

(177649 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 ?
27512^340115-21181102385Enzo Doria06/2013
2752(55459*2^340090+1)/1591102379Lelio R Paula07/2014
275389^52511-88^52511102365Robert Price06/2015
27543^214539-112756102362Enzo Doria07/2014
27552^340000-19877102351Enzo Doria06/2013
27562^339990-114845102348Enzo Doria05/2015
2757(3^214516-2)/51383102346Lelio R Paula12/2013
275820^78661-99102341Lelio R Paula09/2016
27592^339951-19585102336Enzo Doria05/2013
2760(13*2^339943+1)/45102333Lelio R Paula12/2013
27612^339889+29327102317Yves Minet06/2010
27622^339834-109493102301Enzo Doria04/2014
2763(11^98221-5^98221)/6102286Robert Price01/2013
27643^214365+1820102279Lelio R Paula10/2016
2765(11*2^339705-1)/183102261Lelio R Paula03/2014
27662^339694-16995102259Lelio R Paula09/2016
27677^120985-38102245Lelio R Paula10/2016
276810^102244+122961102245Patrick De Geest12/2016
276910^102244-27102244Lelio R Paula09/2016
27707^120982-62102242Lelio R Paula10/2016
27714*6^131382-5102236Lelio R Paula11/2014
27722^339586-1091102226Yves Minet11/2012
277311^98161-3072000102225Enzo Doria12/2012
27749*7^120961-4102225Lelio R Paula11/2014
27755*3^214250+2102224Serge Batalov10/2010
277612^94713-59102213Lelio R Paula10/2016
277712^94705+89102204Lelio R Paula10/2016
27782^339407-177102172Lelio R Paula08/2011
27792^339355+65102157Lelio R Paula07/2011
2780(2^339323+47)/880715102141Lelio R Paula12/2013
27812^339168+21102100Lelio R Paula07/2011
27822^339167-108807102100Enzo Doria03/2014
27832^339156+163102097Lelio R Paula08/2011
2784(2^338982-7)/1754517102038Lelio R Paula12/2013
27852^338891-18885102017Enzo Doria05/2013
27862^338829-113239101998Enzo Doria07/2014
27872^338828-113297101998Enzo Doria07/2014
27882^338796+93101988Donovan Johnson06/2008
2789lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
27912^338682-19865101954Enzo Doria06/2013
2790(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
27922^338568+37101920Lelio R Paula07/2011
27932^338559-1858777101917Enzo Doria04/2016
2794(9*2^338520+1)/365101904Lelio R Paula12/2013
27952^338497-17041101898Enzo Doria05/2013
27962^338475+54615101892Lelio R Paula10/2016
27972^338426-19797101877Enzo Doria06/2013
27982^338368-20369101859Enzo Doria06/2013
27992^338366+74179101859Enzo Doria04/2016
28002^338280-19745101833Enzo Doria06/2013
2801(3*2^338236-1)/347101818Lelio R Paula03/2014
28026^130841+103101815Lelio R Paula10/2016
28032^338122-20117101785Enzo Doria06/2013
2804(2^338139+5)/905333101785Lelio R Paula12/2013
280535^65917-7092101781Enzo Doria03/2013
28062^338010-19833101752Enzo Doria06/2013
28073^213215-76101730Lelio R Paula09/2016
28082^337930+63101728Lelio R Paula07/2011
28092^337920+1869661101725Enzo Doria05/2016
28102^337859-19645101706Enzo Doria05/2013
28112^337754+1869169101675Enzo Doria05/2016
2812(31*2^337677-1)/593101650Lelio R Paula03/2014
281311^97605-24101646Lelio R Paula10/2016
28148^112539-112539101633Robert Price01/2014
28152^337515-19869101603Enzo Doria06/2013
28162^337473+719101590Lelio R Paula08/2011
2817(2^337485-509203)/656647157101585Lelio R Paula12/2013
28182^337452-108815101584Enzo Doria03/2014
28192^337453+1185101584Lelio R Paula09/2016
28202^337410-113561101571Enzo Doria08/2014
28212^337387+855101564Lelio R Paula09/2016
28222^337367-17295101558Lelio R Paula09/2016
28232^337342-109035101551Enzo Doria04/2014
28242^337267-19101528Lelio R Paula07/2011
28252^337183-19989101503Enzo Doria06/2013
28262^337149+72425101492Enzo Doria04/2016
28272^337101-20241101478Enzo Doria06/2013
28282^337035-20001101458Enzo Doria06/2013
28292^337017-16995101453Lelio R Paula09/2016
28302^336979-115315101441Enzo Doria06/2015
28312^336970-20885101439Enzo Doria06/2013
28322^336958+79101435Lelio R Paula10/2009
28332^336942+169101430Lelio R Paula10/2009
2834(15185*2^336894-1)/7939101416Lelio R Paula05/2015
28352^336871+257463101409Tony Prest / Never Odd Or Even04/2016
28362^336871+318105101409Tony Prest / Never Odd Or Even04/2016
28372^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
28382^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
28392^336871+389273101409Tony Prest / Never Odd Or Even04/2016
28402^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
28412^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
28422^336871+586905101409Tony Prest / Never Odd Or Even04/2016
28432^336871+674571101409Tony Prest / Never Odd Or Even04/2016
28442^336871+707009101409Tony Prest / Never Odd Or Even04/2016
28452^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
28462^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
28472^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
28482^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
28492^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
28502^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
28512^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
28522^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
2853(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
2854(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
2855(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
2856(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
28572^336842+94065101400Lelio R Paula09/2016
2858(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
2859(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
2860(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
2861(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
2862(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
2863(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
2864(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
286510^101369+203811101370Patrick De Geest11/2016
286610^101369-99101369Lelio R Paula09/2016
2867(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
28682^336701-113563101358Enzo Doria08/2014
28692^336644-109023101340Enzo Doria04/2014
28702^336601-21081101327Enzo Doria06/2013
287120^77869+63101310Lelio R Paula09/2016
2872(13*2^336523-1)/19101304Lelio R Paula03/2014
28746^130179-137101299Lelio R Paula10/2016
2873(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
2875(24737*2^336485+1)/7285101293Lelio R Paula07/2014
2876(2^336448+9)/497405101276Lelio R Paula12/2013
28772^336369-19753101258Enzo Doria05/2013
28782^336350-344291101252Enzo Doria07/2015
28792^336243-108777101220Enzo Doria03/2014
2880(31*2^336189-1)/19101204Lelio R Paula03/2014
2881(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
28822^336150-20393101192Enzo Doria06/2013
28832^336112-1865249101180Enzo Doria03/2016
28842^336103-109015101178Enzo Doria04/2014
288513^90809-96101157Lelio R Paula10/2016
288619^79098-30101147Lelio R Paula10/2016
288719^79095+88101144Lelio R Paula10/2016
288815^85976+32101116Lelio R Paula10/2016
2889(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
2890(4^167933+17)/3101106Robert Price02/2017
28912^335858+153101104Lelio R Paula10/2009
28926^129918-35101096Lelio R Paula10/2016
28933^211885-70101095Lelio R Paula09/2016
2894(29*2^335835-1)/550599101093Lelio R Paula03/2014
28952^335818-20033101092Enzo Doria06/2013
28962^335813-110083101090Enzo Doria04/2014
28972^335804+2155101088Lelio R Paula09/2016
28982^335784-16145101082Enzo Doria04/2013
289911^97051+62101069Lelio R Paula10/2016
2900(2^335691-3)/26515101049Lelio R Paula12/2013
29012^335658-94395101044Lelio R Paula09/2016
29022^335586+169101022Lelio R Paula10/2009
290347599!2+1024100991Robert Price02/2015
29042^335468-18629100986Enzo Doria05/2013
29052^335454-20961100982Enzo Doria06/2013
290610^100978+61100979Lelio R Paula09/2016
290710^100978-156437100978Patrick De Geest11/2016
2908(15*2^335417+1)/481100970Lelio R Paula12/2013
29092^335403-1859167100967Enzo Doria03/2016
29109*2^335364-5100956Lelio R Paula08/2014
29112^335349+72287100951Enzo Doria04/2016
29122^335329+16095100945Lelio R Paula09/2016
29132^335237-20893100917Enzo Doria06/2013
29142^335222-19337100912Enzo Doria05/2013
29152^335222-109985100912Enzo Doria04/2014
29162^335182-17237100900Enzo Doria05/2013
29172^335043-16737100858Enzo Doria05/2013
2918(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
29192^335038-20633100857Enzo Doria06/2013
29202^335031+1873373100855Enzo Doria06/2016
29213^211354-8816100842Enzo Doria05/2014
29222^334984-112757100841Enzo Doria06/2014
29242^334857+48527100803Lelio R Paula08/2011
292312^93406+29100803Lelio R Paula10/2016
2925(5*2^334825+1)/47100792Lelio R Paula12/2013
29262^334809-13100788Lelio R Paula04/2011
2927(82*10^100780-1)/9100781Robert Price12/2014
2928(2^334779+47)/5100778Lelio R Paula12/2013
29292^334751+2049100771Lelio R Paula09/2016
293013^90443-98100749Lelio R Paula10/2016
2931(24737*2^334628+1)/3100737Lelio R Paula07/2014
293215^85639-28100720Lelio R Paula10/2016
29332^334562+577294575100711Lelio R Paula09/2016
29344*3^211077-5100710Lelio R Paula08/2014
29352^334524+145100702Lelio R Paula07/2009
2936(1017*2^334391-1)/3535100662Lelio R Paula05/2015
29372^334294-113111100633Enzo Doria07/2014
29386^129308-17723100622Enzo Doria03/2013
29396^129305+95100619Lelio R Paula10/2016
29402^334244-1167100618Lelio R Paula09/2016
2941(21*2^334050+1)/935100558Lelio R Paula12/2013
2942(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
2943(35*10^100542+1)/9100543Serge Batalov11/2010
294413^90251+24100535Lelio R Paula10/2016
29452^333963+789100533Lelio R Paula08/2011
29462^333919-1840087100520Enzo Doria06/2015
29472^333911+72623100518Enzo Doria04/2016
294818^80064-67100503Lelio R Paula10/2016
29495^143742-48100472Lelio R Paula10/2016
29502^333757-112123100471Enzo Doria06/2014
29512^333603-108861100425Enzo Doria03/2014
29529*7^118818-2100414Lelio R Paula11/2014
29532^333546-17097100408Enzo Doria05/2013
295417^81597+72100401Lelio R Paula10/2016
2955p(20559)#/2+8100384Robert Price01/2017
295611^96390-24100380Lelio R Paula10/2016
29574832563059*2^333333+30029100353Donovan Johnson01/2008
29582^333354+763100350Lelio R Paula08/2011
29592^333289-109483100330Enzo Doria04/2014
29602^333240-2790209100316Enzo Doria03/2016
2961(2^333227-2^166614+1)/510031111/2006
29622^333225+719100311Lelio R Paula08/2011
29632^333221-2785333100310Enzo Doria10/2015
296476^53332-75100308Norbert Schneider02/2015
29656^128892-17573100298Enzo Doria03/2013
29662^333105-113215100275Enzo Doria07/2014
2967(31*2^333102+1)/2375100272Lelio R Paula11/2013
296817^81476-74100253Lelio R Paula10/2016
296917^81417-16100180Theodore Burton11/2005
29702^332739-113215100165Enzo Doria07/2014
29712^332730-1865621100162Enzo Doria03/2016
297291^51127-2100160Lelio R Paula09/2013
297315^85159-32100155Lelio R Paula10/2016
29746^128661+97100118Lelio R Paula10/2016
297519^78285+40100108Lelio R Paula07/2016
29766^128640+5100102Lelio R Paula11/2014
29776^128565-127100044Lelio R Paula08/2016
29782^332309-133100035Lelio R Paula02/2011
29792^332307+731100035Lelio R Paula07/2011
29802^332301+12927100033Lelio R Paula04/2013
298112^92684-13100023Lelio R Paula07/2016
299710^100000+342909100001Milton L. Brown12/2007
299010^100000+1751769100001Robert Price08/2012
299110^100000+2155489100001Robert Price10/2012
299210^100000+2483527100001Robert Price12/2012
299310^100000+2503087100001Robert Price12/2012
299410^100000+2686179100001Robert Price12/2012
299510^100000+2688933100001Robert Price12/2012
299610^100000+3667159100001Robert Price08/2013
299810^100000+3938473100001Robert Price05/2015
299910^100000+3979761100001Robert Price05/2015
300010^100000+4293973100001Robert Price09/2015
298210^100000+5354043100001Robert Price05/2016
298310^100000+5717979100001Robert Price05/2016
298410^100000+6080631100001Robert Price07/2016
298510^100000+6308469100001Robert Price07/2016
298610^100000+6512023100001Robert Price08/2016
298710^100000+6596557100001Robert Price08/2016
298810^100000+7115409100001Robert Price10/2016
298910^100000+7235803100001Robert Price10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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