PRP Records

Probable Primes Top 10000

(202622 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 ?
925113732^6465+6465^1373252327Hans Havermann05/2016
9252(2^173867-1)/5253663750268952326Donovan Johnson06/2005
92532^173811-68487752323Paul Bourdelais11/2012
92542^173807-595552322Lelio R Paula06/2009
92552^173796-104468952318Paul Bourdelais11/2012
925610^52317+6449752318Patrick De Geest12/2012
925710^52317+6474352318Patrick De Geest12/2012
925810^52317-7152317Robert Price05/2011
925910821^12968+12968^1082152317Norbert Schneider04/2016
9260(298*10^52308-7)/352310Robert Price06/2017
9261(2^173778-3)/5795952308Lelio R Paula02/2012
926210232^13043-13043^1023252302Norbert Schneider08/2017
92632^173727+952298Lelio R Paula01/2011
9264(14^45631+13^45631)/2752298Robert Price04/2013
926537856!3+656152293Robert Price11/2015
92664*3^109596+552292Lelio R Paula03/2014
926715436^2441+2441^1543652291Hans Havermann05/2016
926843^32005+2452280Robert Price11/2013
92692^173650-16552274Lelio R Paula02/2011
92704*10^52272+9352273Robert Price01/2017
927119^40873+8452267Lelio R Paula01/2013
92722^173621+424242952266Jason Earls09/2008
92739999^13064-13064^999952256Norbert Schneider09/2017
9274numbpart(46909^2-1)52247Serge Batalov04/2017
927514^45579-3152240Lelio R Paula01/2013
9276(10223*2^173518+1)/90352236Lelio R Paula05/2014
927720^40147-612352233Enzo Doria03/2013
92784^86754-3^(86754+1)52232Robert Price04/2016
92792^173477-343352222Yves Minet04/2009
9280(22*10^52217-73)/352218Robert Price09/2017
9281(25*2^173446+1)/6152213Lelio R Paula07/2012
92823^109431-3852212Lelio R Paula10/2012
92832^173424-395952206Yves Minet04/2017
928413^46861-7252201Lelio R Paula01/2013
92852^173373-136352191Yves Minet03/2009
928611^50114-174052189Enzo Doria11/2012
928713735^6304+6304^1373552188Hans Havermann05/2016
928811^50111-111052186Enzo Doria11/2012
9289lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
929020^40105-858352178Enzo Doria03/2013
9291(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
92922^173314-394152173Yves Minet04/2017
92932^173294+115552167Lelio R Paula07/2012
9295(19*2^173301-1)/2348952166Lelio R Paula01/2014
929415146^2781+2781^1514652166Hans Havermann06/2016
929611^50088-3252162Lelio R Paula01/2013
92973^109320+23652159Lelio R Paula10/2012
92982^173246-2863552153Lelio R Paula06/2009
92992*10^52147+1152148Robert Price01/2015
93002^173208-11262552141Enzo Doria06/2014
9301(9179*2^173206-1)/203552141Lelio R Paula03/2015
930215^44333-7652140Lelio R Paula01/2013
93032^173187-318952135Yves Minet10/2014
93042^173167+7557952129Enzo Doria04/2016
9305(2^173169+7)/9279352125Lelio R Paula02/2012
9306(25*10^52119+23)/352120Robert Price06/2017
93079*7^61671+452119Lelio R Paula09/2014
93092^173130-922152118Lelio R Paula07/2008
9308(17*2^173129-1)/352118Lelio R Paula01/2014
93102^173100-11255952109Enzo Doria06/2014
93112^173091-11233952106Enzo Doria06/2014
931211^50030+2852101Lelio R Paula01/2013
9313(59*10^52099+13)/952100Robert Price09/2015
93142^173064-182952098Yves Minet09/2012
93152^173062-136152097Yves Minet08/2012
93163^109190-7052097Lelio R Paula10/2012
93172^173059+9019552096Lelio R Paula07/2012
93182^173048-11262552093Enzo Doria06/2014
931992^26524+9152088Norbert Schneider04/2013
932041^32295-4052085Theodore Burton02/2007
93212^173002+17752079Lelio R Paula02/2011
9322p(11334)#/2+852075Robert Price01/2017
93232^172965-11236352068Enzo Doria06/2014
93249*2^172935+752060Lelio R Paula03/2014
932511^49978-819052047Enzo Doria02/2013
932610^52041+63352042Patrick De Geest11/2012
93278494^13245-13245^849452042Norbert Schneider01/2018
932810^52041-9352041Robert Price05/2011
9329(21*2^172815-1)/86952021Lelio R Paula01/2014
9330(182*10^52018+1)/352020Robert Price02/2017
93314*6^66843-552015Lelio R Paula09/2014
933219^40670-5452007Lelio R Paula01/2013
93332^172756-11288352005Enzo Doria06/2014
933411832^12763-12763^1183251985Norbert Schneider02/2017
93357^61511-3651983Lelio R Paula10/2012
933610591^12914-12914^1059151979Norbert Schneider05/2017
93372^172640-7551970Lelio R Paula01/2011
9338gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
933912240^12709-12709^1224051952Norbert Schneider01/2017
9340t(173589)51951Robert Price12/2014
93417^61469+3451948Lelio R Paula10/2012
93439*2^172553-751945Lelio R Paula03/2014
934211542^12787+12787^1154251945Norbert Schneider01/2016
934435^33640-708651943Enzo Doria03/2013
9345(7*2^172534+1)/247951936Lelio R Paula07/2012
9346(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9347(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9348((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9349((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9350((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9351((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
93532^172470+751919Lelio R Paula01/2011
9352((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9354((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9355((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9356((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9357((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
93602^172455+1551915Lelio R Paula01/2011
9358((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9359((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9361((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9362((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9363((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9364((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9365((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9366((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
93675^74263+5451908Lelio R Paula10/2012
936813804^5755+5755^1380451904Hans Havermann05/2016
93697*2^172403-351900Henri Lifchitz06/2003
9370t(196078)51892Robert Price02/2014
93712*3^108759-751892Lelio R Paula03/2014
9372(94*10^51889+11)/351891Robert Price02/2017
9373(73*10^51889+17)/951890Robert Price10/2015
937435^33603-402651886Enzo Doria03/2013
93752^172350-10751883Lelio R Paula02/2011
937614419^3960+3960^1441951876Hans Havermann05/2016
93772^172325-11318551875Enzo Doria07/2014
937810^51872+10068351873Patrick De Geest06/2016
937910^51872-100000000151872Robert Price05/2016
938010^51872-10014951872Patrick De Geest06/2016
93812147092^8192+6351871Jens K. Andersen04/2009
938213^46564-2451870Lelio R Paula01/2013
938310524^12893-12893^1052451858Norbert Schneider05/2017
938413981^5110+5110^1398151848Hans Havermann05/2016
93852^172228+7626151846Enzo Doria04/2016
938611^49772-126051833Enzo Doria11/2012
9387(11*2^172157-1)/35151823Lelio R Paula01/2014
9388(43*10^51816-403)/951817Robert Price04/2017
93899001^13102-11451810Enzo Doria07/2012
9390(80051^10567+1)/8005251809Faysal YAtim07/2007
93912^172101-6151808Lelio R Paula01/2011
9392(2^172125+3)/3112550551808Lelio R Paula02/2012
93939*7^61301+451807Lelio R Paula09/2014
9394(23*2^172090-1)/3650951802Lelio R Paula01/2014
93952^172074+145951800Lelio R Paula07/2008
93962^172063+16551797Lelio R Paula02/2011
9397(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9398(56*10^51793+367)/951794Robert Price10/2017
939928^35785-2751787Norbert Schneider01/2014
9400(65*10^51778+43)/951779Ray Chandler09/2010
9401(15185*2^171975-1)/351774Lelio R Paula03/2015
94022^171978-11329751771Enzo Doria07/2014
940311^49708+7851766Lelio R Paula01/2013
9404(26*10^51764-107)/951765Robert Price07/2016
940512^47956-9751754Lelio R Paula12/2012
94062^171907-351151750Yves Minet03/2017
94078203^13220-13220^820351743Norbert Schneider12/2017
94088*10^51721+8751722Robert Price10/2017
940910306^12885-12885^1030651709Norbert Schneider05/2017
9410(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
9411(3*2^171761+1)/2951705Lelio R Paula07/2012
9412t(195346)51699Robert Price07/2014
941313^46409+4651697Lelio R Paula01/2013
94142^171663+1155*17166351676Henri Lifchitz01/2005
941515^43937+2651674Lelio R Paula01/2013
9416(3^108312-7)/12452651673Lelio R Paula03/2012
9417(12601^12601+465)/2/13151667Makoto Morimoto07/2016
9418(79*10^51663-97)/9951663Ray Chandler11/2010
941948589!4+102451656Robert Price08/2017
9421(10^51652-31)/351652Serge Batalov12/2014
94222^171583+7379351652Enzo Doria04/2016
9420(28*10^51651-31)/351652Robert Price10/2017
942312^47861-3551651Lelio R Paula12/2012
94246^66369-2681351646Enzo Doria03/2013
9425Phi(83967,10)/227248288951639Maksym Voznyy01/2010
94262^171524+15351634Lelio R Paula02/2011
9427(2^171516-509203)/486951628Lelio R Paula05/2012
9428(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
94295*10^51608-8151609Robert Price04/2017
9430(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
9431(2*10^51597-23)/351597Robert Price09/2017
943210171^12872-12872^1017151583Norbert Schneider04/2017
94332^171351-11267751582Enzo Doria06/2014
9434(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
94359818^12919-12919^981851573Norbert Schneider05/2017
9436(3^108091+7)/38251570Lelio R Paula03/2012
94382^171287-318751563Yves Minet04/2009
9437-lucasV(-1,2,342569)51563Mike Oakes02/2017
94392^171280-103070951561Paul Bourdelais11/2012
944013300^7527+7527^1330051560Hans Havermann05/2016
94412^171268+7371151557Enzo Doria04/2016
9442(17*2^171266+1)/696351554Lelio R Paula01/2012
9443(1964814^8192+1)/6553751551Lelio R Paula06/2013
9444(26*10^51537-503)/951538Robert Price12/2017
94454*10^51530-6351531Robert Price12/2016
94463*6^66216-551527Lelio R Paula09/2014
944712569^12569+54051525Makoto Morimoto07/2016
94482^171152-245951522Yves Minet07/2014
9449(13*10^51511-1)/351512Robert Price12/2014
94505*10^51508+351509Dmitry Domanov11/2010
94513^107919-4651491Lelio R Paula07/2012
94524*10^51489+8751490Robert Price05/2016
9453(22699*2^171030+1)/302951487Lelio R Paula05/2014
94542^171028-323951485Yves Minet12/2014
94552^170992-95420951474Paul Bourdelais11/2012
945676^27367+7551473Norbert Schneider11/2012
94576007^13620-10251466Enzo Doria07/2012
9458gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9459t(194442)51459Robert Price08/2014
9460(22*10^51457+161)/351458Robert Price02/2017
94619^53921+8^(53921+1)51454Robert Price06/2016
94632^170921-1699551453Lelio R Paula08/2011
94622^170922-213551453Yves Minet06/2013
94644357^14138-12051451Enzo Doria06/2012
9465153^23550+251450Lelio R Paula05/2013
9466(3^107833+2)/2551449Lelio R Paula03/2012
9467(159^23369+1)/16051443Eric Chen12/2017
94687*10^51440-4751441Robert Price02/2017
9469(10^51431-3^51431)/751431Robert Price06/2011
9471U(250849)51425Michael Porter08/2007
9470(86*10^51424-41)/951425Robert Price11/2015
947312^47649+751422Lelio R Paula12/2012
9472(25*10^51421+11)/951422Robert Price03/2015
94743^107768+266051419Lelio R Paula07/2012
94762^170784-655551412Lelio R Paula05/2009
9475(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
947751^30106+251409Lelio R Paula05/2013
94785^73546-1280651407Enzo Doria02/2013
9479(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9480(3^107735-4)/43151401Lelio R Paula03/2012
948120^39505-648351398Enzo Doria03/2013
94822^170736-1519751397Enzo Doria04/2013
94832^170737-382351397Yves Minet04/2017
9484(12541^12541+393)/2/56351395Makoto Morimoto07/2016
94859^53857-8^5385751393Jean-Louis Charton11/2004
94865^73524-1442651392Enzo Doria02/2013
94872^170712+24351390Lelio R Paula10/2011
9488(15*2^170713+1)/179351388Lelio R Paula07/2012
9489(2^170702+9)/126151384Lelio R Paula01/2012
9490283^20956+20956^28351380Norbert Schneider08/2014
94912^170665-3151376Lelio R Paula01/2011
949211^49330-1251372Lelio R Paula01/2013
9493(25*10^51366-73)/351367Robert Price09/2016
94945^73486-2^7348751365Mike Oakes10/2010
9495(10^51364+119)/351364Serge Batalov12/2014
949615^43672+6851363Lelio R Paula01/2013
94972^170609-11314351359Enzo Doria07/2014
9498760^17827-759^1782751357Jean-Louis Charton12/2010
9499(22699*2^170592+1)/443551355Lelio R Paula05/2014
95008*7^60767+351355Lelio R Paula09/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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