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 ?
9251(15*2^175565+1)/835952848Lelio R Paula07/2012
9252(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
925314256^5077+5077^1425652828Hans Havermann06/2016
92542^175467+8287552821Lelio R Paula07/2012
9255(7*10^52819+167)/352820Robert Kinser10/2017
9256(67607*2^175426+1)/352813Lelio R Paula05/2014
925713^47400-6052801Lelio R Paula01/2013
92584*10^52792+6352793Robert Price06/2016
9260(78557*2^175360+1)/308752791Lelio R Paula06/2014
925918^42055-292952791Enzo Doria03/2013
92619*5^75521+252788Lelio R Paula09/2014
92626^67814+3152770Lelio R Paula10/2012
926370^28600+6952770Norbert Schneider10/2012
926414^46038+9752766Lelio R Paula01/2013
9265(61*10^52763-7)/952764Serge Batalov02/2009
92662*5^75474+952755Lelio R Paula09/2014
926710^52753+282643060952754Robert Price05/2015
926810^52753+18399752754Patrick De Geest01/2016
926910^52753-5015352753Patrick De Geest03/2016
927019846^455+455^1984652751Anatoly F. Selevich02/2007
92712^175217+7297752746Enzo Doria04/2016
9272p(11466)#/2-25652746Robert Price05/2017
9273(4*10^52740+41)/952740Robert Price11/2014
92742^175189+538552738Lelio R Paula08/2009
92752^175160+938552729Lelio R Paula07/2008
927612356^12885+12885^1235652724Norbert Schneider03/2016
92772^175137+1152722Lelio R Paula01/2011
927865^29077-64^2907752715Robert Price08/2013
92792*10^52713-8752714Robert Price06/2016
92802^175106-46552713Lelio R Paula08/2009
92812^175089-5869552708Lelio R Paula08/2009
92822^175045+19552694Lelio R Paula02/2011
9283195^23010-252694Lelio R Paula10/2017
92842^175025+14952688Lelio R Paula02/2011
9286(19^41201+1)/2052685Paul Bourdelais03/2010
9285(436*10^52683-13)/952685Robert Price10/2017
92872*12^48815-5^4881552681Mike Oakes10/2010
9288335^20862-20862^33552678Norbert Schneider09/2015
92892^174983-760552676Lelio R Paula07/2009
92904*10^52667+1952668Robert Price04/2016
9291(10^52667+77)/352667Robert Price01/2017
929211434^12977+12977^1143452664Norbert Schneider04/2016
92932^174941-120352663Lelio R Paula07/2009
92948501^13400-13400^850152655Norbert Schneider03/2018
92952^174910+1270552654Lelio R Paula07/2012
92963^110338+7452645Lelio R Paula10/2012
92975^75303+1252635Lelio R Paula10/2012
92982^174836+25525552631Lelio R Paula07/2009
9299(66^28921+1)/6752622Paul Bourdelais08/2017
930020^40443+952618Lelio R Paula01/2013
9301(11*2^174788+1)/952617Lelio R Paula01/2012
9302(11*2^174786-1)/70352615Lelio R Paula01/2014
930311^50520-129052612Enzo Doria11/2012
9304(10^52608-19)/952608Robert Price10/2017
9305(9913*2^174736-1)/33352603Lelio R Paula03/2015
930613145^10024+10024^1314552594Hans Havermann05/2016
93075003^14217-15052592Enzo Doria07/2012
93082^174698-405552590Yves Minet02/2018
930919^41123+1052587Lelio R Paula01/2013
93102^174683+1290952585Lelio R Paula01/2011
93112^174643+5952573Lelio R Paula01/2011
9312(1017*2^174640-1)/77352572Lelio R Paula03/2015
931313529^7662+7662^1352952552Hans Havermann06/2016
9314121421#+18876752548Makoto Morimoto02/2016
931520^40375-592352530Enzo Doria03/2013
9316(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9317(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
93182^174462+34552519Lelio R Paula07/2009
9319t(178863)52509Robert Price10/2014
93202^174416+85552505Lelio R Paula07/2009
93216^67467-10352500Lelio R Paula10/2012
9322(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
93232^174329-1126552479Enzo Doria06/2014
93242^174314-124152474Yves Minet05/2009
932552^30577-5152471Norbert Schneider08/2014
93269403^13206-13206^940352471Norbert Schneider12/2017
932715692^2205+2205^1569252465Hans Havermann06/2016
9328(2^174281-7)/62881702961552453Lelio R Paula02/2012
9329(2^174240+5)/352451Lelio R Paula02/2012
9330(86*10^52450-221)/952451Robert Price06/2017
9331(62*10^52448-197)/952449Robert Price10/2017
9332(15*2^174221+1)/40352445Lelio R Paula07/2012
933326313!2-3252443Robert Price10/2015
9334(3*2^174214-1)/374872952438Lelio R Paula01/2014
93352*3^109900-552436Lelio R Paula03/2014
93374159^14488-15052432Enzo Doria07/2012
9336(89*10^52431-71)/952432Robert Price11/2015
93382^174170-394152431Yves Minet04/2017
9339(7*2^174171-1)/68552429Lelio R Paula01/2014
9340(260137^9679+1)/26013852409Faysal YAtim03/2008
93412^174098+7952409Lelio R Paula01/2011
934235^33940-221452406Enzo Doria03/2013
934315^44557+252404Ray Chandler07/2011
93442^174049-43952394Yves Minet01/2012
93456^67329+11552393Lelio R Paula10/2012
93472^174041+26214552392Lelio R Paula07/2009
9346141^24377+252392Lelio R Paula05/2013
9348lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
93492^174001-595552380Lelio R Paula07/2009
9350lucasV(-1,2,347969)52375Mike Oakes02/2017
93513^109764-14052371Lelio R Paula10/2012
93532*3^109761+752370Lelio R Paula03/2014
93529863^13112-13112^986352370Norbert Schneider10/2017
9355(145^24229+1)/14652366Richard Fischer02/2018
93548094^13399-13399^809452366Norbert Schneider03/2018
93562^173944-11225352363Enzo Doria06/2014
93582^173940+111152362Lelio R Paula01/2011
9357(3126^14983-1)/312552362Richard Fischer03/2015
935915214^2763+2763^1521452358Hans Havermann05/2016
936013200^9247+9247^1320052352Hans Havermann05/2016
9361(1017*2^173867-1)/717552339Lelio R Paula03/2015
936213732^6465+6465^1373252327Hans Havermann05/2016
9363(2^173867-1)/5253663750268952326Donovan Johnson06/2005
93642^173811-68487752323Paul Bourdelais11/2012
93652^173807-595552322Lelio R Paula06/2009
93662^173796-104468952318Paul Bourdelais11/2012
936710^52317+6449752318Patrick De Geest12/2012
936810^52317+6474352318Patrick De Geest12/2012
937010^52317-7152317Robert Price05/2011
936910821^12968+12968^1082152317Norbert Schneider04/2016
9371(298*10^52308-7)/352310Robert Price06/2017
9372(2^173778-3)/5795952308Lelio R Paula02/2012
937310232^13043-13043^1023252302Norbert Schneider08/2017
93742^173727+952298Lelio R Paula01/2011
9375(14^45631+13^45631)/2752298Robert Price04/2013
937637856!3+656152293Robert Price11/2015
93774*3^109596+552292Lelio R Paula03/2014
937815436^2441+2441^1543652291Hans Havermann05/2016
937943^32005+2452280Robert Price11/2013
93802^173650-16552274Lelio R Paula02/2011
93814*10^52272+9352273Robert Price01/2017
938219^40873+8452267Lelio R Paula01/2013
93832^173621+424242952266Jason Earls09/2008
93849999^13064-13064^999952256Norbert Schneider09/2017
9385numbpart(46909^2-1)52247Serge Batalov04/2017
938614^45579-3152240Lelio R Paula01/2013
9387(10223*2^173518+1)/90352236Lelio R Paula05/2014
938820^40147-612352233Enzo Doria03/2013
93894^86754-3^(86754+1)52232Robert Price04/2016
93902^173477-343352222Yves Minet04/2009
9391(22*10^52217-73)/352218Robert Price09/2017
9392(25*2^173446+1)/6152213Lelio R Paula07/2012
93933^109431-3852212Lelio R Paula10/2012
93942^173424-395952206Yves Minet04/2017
939513^46861-7252201Lelio R Paula01/2013
93962^173373-136352191Yves Minet03/2009
939711^50114-174052189Enzo Doria11/2012
939813735^6304+6304^1373552188Hans Havermann05/2016
939911^50111-111052186Enzo Doria11/2012
9400lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
940120^40105-858352178Enzo Doria03/2013
9402(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
94032^173314-394152173Yves Minet04/2017
94042^173294+115552167Lelio R Paula07/2012
9406(19*2^173301-1)/2348952166Lelio R Paula01/2014
940515146^2781+2781^1514652166Hans Havermann06/2016
940711^50088-3252162Lelio R Paula01/2013
94083^109320+23652159Lelio R Paula10/2012
94092^173246-2863552153Lelio R Paula06/2009
94102*10^52147+1152148Robert Price01/2015
94112^173208-11262552141Enzo Doria06/2014
9412(9179*2^173206-1)/203552141Lelio R Paula03/2015
941315^44333-7652140Lelio R Paula01/2013
94142^173187-318952135Yves Minet10/2014
94152^173167+7557952129Enzo Doria04/2016
9416(2^173169+7)/9279352125Lelio R Paula02/2012
9417(25*10^52119+23)/352120Robert Price06/2017
94189*7^61671+452119Lelio R Paula09/2014
94202^173130-922152118Lelio R Paula07/2008
9419(17*2^173129-1)/352118Lelio R Paula01/2014
9421215^22342-21652112Karsten Bonath04/2018
94222^173100-11255952109Enzo Doria06/2014
94232^173091-11233952106Enzo Doria06/2014
942411^50030+2852101Lelio R Paula01/2013
9425(59*10^52099+13)/952100Robert Price09/2015
94262^173064-182952098Yves Minet09/2012
94272^173062-136152097Yves Minet08/2012
94283^109190-7052097Lelio R Paula10/2012
94292^173059+9019552096Lelio R Paula07/2012
94302^173048-11262552093Enzo Doria06/2014
943192^26524+9152088Norbert Schneider04/2013
943241^32295-4052085Theodore Burton02/2007
94332^173002+17752079Lelio R Paula02/2011
9434p(11334)#/2+852075Robert Price01/2017
94352^172965-11236352068Enzo Doria06/2014
94369*2^172935+752060Lelio R Paula03/2014
943711^49978-819052047Enzo Doria02/2013
943810^52041+63352042Patrick De Geest11/2012
94398494^13245-13245^849452042Norbert Schneider01/2018
944010^52041-9352041Robert Price05/2011
9441(21*2^172815-1)/86952021Lelio R Paula01/2014
9442(182*10^52018+1)/352020Robert Price02/2017
94434*6^66843-552015Lelio R Paula09/2014
94447732^13377-13377^773252014Norbert Schneider03/2018
944519^40670-5452007Lelio R Paula01/2013
94462^172756-11288352005Enzo Doria06/2014
944711832^12763-12763^1183251985Norbert Schneider02/2017
94487^61511-3651983Lelio R Paula10/2012
944910591^12914-12914^1059151979Norbert Schneider05/2017
94502^172640-7551970Lelio R Paula01/2011
94517750^13359-13359^775051958Norbert Schneider03/2018
9452gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
945312240^12709-12709^1224051952Norbert Schneider01/2017
9454t(173589)51951Robert Price12/2014
94557^61469+3451948Lelio R Paula10/2012
94569*2^172553-751945Lelio R Paula03/2014
945711542^12787+12787^1154251945Norbert Schneider01/2016
945835^33640-708651943Enzo Doria03/2013
9459(7*2^172534+1)/247951936Lelio R Paula07/2012
9460(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9461(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9462((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9463((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9464((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9465((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
94672^172470+751919Lelio R Paula01/2011
9466((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9468((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9469((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9470((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9471((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
94742^172455+1551915Lelio R Paula01/2011
9472((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9473((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9475((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9476((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9477((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9478((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9479((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9480((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
94815^74263+5451908Lelio R Paula10/2012
948213804^5755+5755^1380451904Hans Havermann05/2016
94837*2^172403-351900Henri Lifchitz06/2003
9484t(196078)51892Robert Price02/2014
94852*3^108759-751892Lelio R Paula03/2014
9486(94*10^51889+11)/351891Robert Price02/2017
9487(73*10^51889+17)/951890Robert Price10/2015
948835^33603-402651886Enzo Doria03/2013
94892^172350-10751883Lelio R Paula02/2011
949014419^3960+3960^1441951876Hans Havermann05/2016
94912^172325-11318551875Enzo Doria07/2014
949210^51872+10068351873Patrick De Geest06/2016
949310^51872-100000000151872Robert Price05/2016
949410^51872-10014951872Patrick De Geest06/2016
94952147092^8192+6351871Jens K. Andersen04/2009
949613^46564-2451870Lelio R Paula01/2013
949710524^12893-12893^1052451858Norbert Schneider05/2017
949813981^5110+5110^1398151848Hans Havermann05/2016
94992^172228+7626151846Enzo Doria04/2016
950011^49772-126051833Enzo Doria11/2012


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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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