PRP Records

Probable Primes Top 10000

(173006 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 ?
27512^339168+21102100Lelio R Paula07/2011
27522^339167-108807102100Enzo Doria03/2014
27532^339156+163102097Lelio R Paula08/2011
2754(2^338982-7)/1754517102038Lelio R Paula12/2013
27552^338891-18885102017Enzo Doria05/2013
27562^338829-113239101998Enzo Doria07/2014
27572^338828-113297101998Enzo Doria07/2014
27582^338796+93101988Donovan Johnson06/2008
2759lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
27602^338682-19865101954Enzo Doria06/2013
2761(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
27622^338568+37101920Lelio R Paula07/2011
27632^338559-1858777101917Enzo Doria04/2016
2764(9*2^338520+1)/365101904Lelio R Paula12/2013
27652^338497-17041101898Enzo Doria05/2013
27662^338475+54615101892Lelio R Paula10/2016
27672^338426-19797101877Enzo Doria06/2013
27682^338368-20369101859Enzo Doria06/2013
27692^338366+74179101859Enzo Doria04/2016
27702^338280-19745101833Enzo Doria06/2013
2771(3*2^338236-1)/347101818Lelio R Paula03/2014
27726^130841+103101815Lelio R Paula10/2016
27732^338122-20117101785Enzo Doria06/2013
2774(2^338139+5)/905333101785Lelio R Paula12/2013
277535^65917-7092101781Enzo Doria03/2013
27762^338010-19833101752Enzo Doria06/2013
27773^213215-76101730Lelio R Paula09/2016
27782^337930+63101728Lelio R Paula07/2011
27792^337920+1869661101725Enzo Doria05/2016
27802^337859-19645101706Enzo Doria05/2013
27812^337754+1869169101675Enzo Doria05/2016
2782(31*2^337677-1)/593101650Lelio R Paula03/2014
278311^97605-24101646Lelio R Paula10/2016
27848^112539-112539101633Robert Price01/2014
27852^337515-19869101603Enzo Doria06/2013
27862^337473+719101590Lelio R Paula08/2011
2787(2^337485-509203)/656647157101585Lelio R Paula12/2013
27882^337452-108815101584Enzo Doria03/2014
27892^337453+1185101584Lelio R Paula09/2016
27902^337410-113561101571Enzo Doria08/2014
27912^337387+855101564Lelio R Paula09/2016
27922^337367-17295101558Lelio R Paula09/2016
27932^337342-109035101551Enzo Doria04/2014
27942^337267-19101528Lelio R Paula07/2011
27952^337183-19989101503Enzo Doria06/2013
27962^337149+72425101492Enzo Doria04/2016
27972^337101-20241101478Enzo Doria06/2013
27982^337035-20001101458Enzo Doria06/2013
27992^337017-16995101453Lelio R Paula09/2016
28002^336979-115315101441Enzo Doria06/2015
28012^336970-20885101439Enzo Doria06/2013
28022^336958+79101435Lelio R Paula10/2009
28032^336942+169101430Lelio R Paula10/2009
2804(15185*2^336894-1)/7939101416Lelio R Paula05/2015
28052^336871+257463101409Tony Prest / Never Odd Or Even04/2016
28062^336871+318105101409Tony Prest / Never Odd Or Even04/2016
28072^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
28082^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
28092^336871+389273101409Tony Prest / Never Odd Or Even04/2016
28102^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
28112^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
28122^336871+586905101409Tony Prest / Never Odd Or Even04/2016
28132^336871+674571101409Tony Prest / Never Odd Or Even04/2016
28142^336871+707009101409Tony Prest / Never Odd Or Even04/2016
28152^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
28162^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
28172^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
28182^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
28192^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
28202^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
28212^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
28222^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
2823(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
2824(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
2825(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
2826(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
28272^336842+94065101400Lelio R Paula09/2016
2828(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
2829(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
2830(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
2831(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
2832(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
2833(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
2834(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
283510^101369+203811101370Patrick De Geest11/2016
283610^101369-99101369Lelio R Paula09/2016
2837(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
28382^336701-113563101358Enzo Doria08/2014
28392^336644-109023101340Enzo Doria04/2014
28402^336601-21081101327Enzo Doria06/2013
284120^77869+63101310Lelio R Paula09/2016
2842(13*2^336523-1)/19101304Lelio R Paula03/2014
28446^130179-137101299Lelio R Paula10/2016
2843(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
2845(24737*2^336485+1)/7285101293Lelio R Paula07/2014
2846(2^336448+9)/497405101276Lelio R Paula12/2013
28472^336369-19753101258Enzo Doria05/2013
28482^336350-344291101252Enzo Doria07/2015
28492^336243-108777101220Enzo Doria03/2014
2850(31*2^336189-1)/19101204Lelio R Paula03/2014
2851(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
28522^336150-20393101192Enzo Doria06/2013
28532^336112-1865249101180Enzo Doria03/2016
28542^336103-109015101178Enzo Doria04/2014
285513^90809-96101157Lelio R Paula10/2016
285619^79098-30101147Lelio R Paula10/2016
285719^79095+88101144Lelio R Paula10/2016
285815^85976+32101116Lelio R Paula10/2016
2859(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
2860(4^167933+17)/3101106Robert Price02/2017
28612^335858+153101104Lelio R Paula10/2009
28626^129918-35101096Lelio R Paula10/2016
28633^211885-70101095Lelio R Paula09/2016
2864(29*2^335835-1)/550599101093Lelio R Paula03/2014
28652^335818-20033101092Enzo Doria06/2013
28662^335813-110083101090Enzo Doria04/2014
28672^335804+2155101088Lelio R Paula09/2016
28682^335784-16145101082Enzo Doria04/2013
286911^97051+62101069Lelio R Paula10/2016
2870(2^335691-3)/26515101049Lelio R Paula12/2013
28712^335658-94395101044Lelio R Paula09/2016
28722^335586+169101022Lelio R Paula10/2009
287347599!2+1024100991Robert Price02/2015
28742^335468-18629100986Enzo Doria05/2013
28752^335454-20961100982Enzo Doria06/2013
287610^100978+61100979Lelio R Paula09/2016
287710^100978-156437100978Patrick De Geest11/2016
2878(15*2^335417+1)/481100970Lelio R Paula12/2013
28792^335403-1859167100967Enzo Doria03/2016
28809*2^335364-5100956Lelio R Paula08/2014
28812^335349+72287100951Enzo Doria04/2016
28822^335329+16095100945Lelio R Paula09/2016
28832^335237-20893100917Enzo Doria06/2013
28842^335222-19337100912Enzo Doria05/2013
28852^335222-109985100912Enzo Doria04/2014
28862^335182-17237100900Enzo Doria05/2013
28872^335043-16737100858Enzo Doria05/2013
2888(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
28892^335038-20633100857Enzo Doria06/2013
28902^335031+1873373100855Enzo Doria06/2016
28913^211354-8816100842Enzo Doria05/2014
28922^334984-112757100841Enzo Doria06/2014
28942^334857+48527100803Lelio R Paula08/2011
289312^93406+29100803Lelio R Paula10/2016
2895(5*2^334825+1)/47100792Lelio R Paula12/2013
28962^334809-13100788Lelio R Paula04/2011
2897(82*10^100780-1)/9100781Robert Price12/2014
2898(2^334779+47)/5100778Lelio R Paula12/2013
28992^334751+2049100771Lelio R Paula09/2016
290013^90443-98100749Lelio R Paula10/2016
2901(24737*2^334628+1)/3100737Lelio R Paula07/2014
290215^85639-28100720Lelio R Paula10/2016
29032^334562+577294575100711Lelio R Paula09/2016
29044*3^211077-5100710Lelio R Paula08/2014
29052^334524+145100702Lelio R Paula07/2009
2906(1017*2^334391-1)/3535100662Lelio R Paula05/2015
29072^334294-113111100633Enzo Doria07/2014
29086^129308-17723100622Enzo Doria03/2013
29096^129305+95100619Lelio R Paula10/2016
29102^334244-1167100618Lelio R Paula09/2016
2911(21*2^334050+1)/935100558Lelio R Paula12/2013
2912(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
2913(35*10^100542+1)/9100543Serge Batalov11/2010
291413^90251+24100535Lelio R Paula10/2016
29152^333963+789100533Lelio R Paula08/2011
29162^333919-1840087100520Enzo Doria06/2015
29172^333911+72623100518Enzo Doria04/2016
291818^80064-67100503Lelio R Paula10/2016
29195^143742-48100472Lelio R Paula10/2016
29202^333757-112123100471Enzo Doria06/2014
29212^333603-108861100425Enzo Doria03/2014
29229*7^118818-2100414Lelio R Paula11/2014
29232^333546-17097100408Enzo Doria05/2013
292417^81597+72100401Lelio R Paula10/2016
2925p(20559)#/2+8100384Robert Price01/2017
292611^96390-24100380Lelio R Paula10/2016
29274832563059*2^333333+30029100353Donovan Johnson01/2008
29282^333354+763100350Lelio R Paula08/2011
29292^333289-109483100330Enzo Doria04/2014
29302^333240-2790209100316Enzo Doria03/2016
2932(2^333227-2^166614+1)/510031111/2006
29312^333225+719100311Lelio R Paula08/2011
29332^333221-2785333100310Enzo Doria10/2015
293476^53332-75100308Norbert Schneider02/2015
29356^128892-17573100298Enzo Doria03/2013
29362^333105-113215100275Enzo Doria07/2014
2937(31*2^333102+1)/2375100272Lelio R Paula11/2013
293817^81476-74100253Lelio R Paula10/2016
293917^81417-16100180Theodore Burton11/2005
29402^332739-113215100165Enzo Doria07/2014
29412^332730-1865621100162Enzo Doria03/2016
294291^51127-2100160Lelio R Paula09/2013
294315^85159-32100155Lelio R Paula10/2016
29446^128661+97100118Lelio R Paula10/2016
294519^78285+40100108Lelio R Paula07/2016
29466^128640+5100102Lelio R Paula11/2014
29476^128565-127100044Lelio R Paula08/2016
29482^332309-133100035Lelio R Paula02/2011
29492^332307+731100035Lelio R Paula07/2011
29502^332301+12927100033Lelio R Paula04/2013
295112^92684-13100023Lelio R Paula07/2016
296725206!+p(4114)100001Henri Lifchitz09/2005
296825206!-p(5447)100001Henri Lifchitz10/2005
296925206!-p(12402)100001Henri Lifchitz04/2006
297025206!-p(16290)100001Henri Lifchitz09/2006
297125206!-p(19647)100001Henri Lifchitz02/2007
29722^332194+11473100001Henri Lifchitz03/2007
297610^100000+342909100001Milton L. Brown12/2007
296310^100000+346579100001Robert Price04/2012
296410^100000+829767100001Robert Price05/2012
296510^100000+871899100001Robert Price05/2012
296610^100000+1475997100001Robert Price07/2012
297710^100000+1751769100001Robert Price08/2012
297810^100000+2155489100001Robert Price10/2012
297910^100000+2483527100001Robert Price12/2012
298010^100000+2503087100001Robert Price12/2012
298110^100000+2686179100001Robert Price12/2012
298210^100000+2688933100001Robert Price12/2012
298310^100000+3667159100001Robert Price08/2013
296010^100000+3938473100001Robert Price05/2015
296110^100000+3979761100001Robert Price05/2015
296210^100000+4293973100001Robert Price09/2015
297310^100000+4858267100001Robert Price12/2015
297410^100000+5113299100001Robert Price02/2016
297510^100000+5169411100001Robert Price02/2016
295210^100000+5354043100001Robert Price05/2016
295310^100000+5717979100001Robert Price05/2016
295410^100000+6080631100001Robert Price07/2016
295510^100000+6308469100001Robert Price07/2016
295610^100000+6512023100001Robert Price08/2016
295710^100000+6596557100001Robert Price08/2016
295810^100000+7115409100001Robert Price10/2016
295910^100000+7235803100001Robert Price10/2016
298410^100000+7867333100001Robert Price12/2016
298510^100000+8743093100001Robert Price02/2017
298610^100000+8955391100001Robert Price03/2017
298710^100000+9180019100001Robert Price03/2017
298810^100000+9225987100001Robert Price04/2017
298910^100000+9265587100001Robert Price04/2017
299010^100000+9287049100001Robert Price04/2017
299110^100000+9425053100001Robert Price05/2017
299210^100000+9450769100001Robert Price05/2017
299310^99999+309403100000Daniel Heuer01/2004
299410^100000-260199100000Patrick De Geest01/2010
299510^99999-5951199999Patrick De Geest07/2009
29962^332141-11307399985Enzo Doria07/2014
2997(3^209561+2)/72810125599978Lelio R Paula09/2013
29982^332085+186589799968Enzo Doria03/2016
2999(9787*2^332070-1)/93640236999959Lelio R Paula05/2015
30002^332023+19199949Lelio R Paula02/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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