PRP Records

Probable Primes Top 10000

(193407 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 ?
92512^173064-182952098Yves Minet09/2012
92522^173062-136152097Yves Minet08/2012
92533^109190-7052097Lelio R Paula10/2012
92542^173059+9019552096Lelio R Paula07/2012
92552^173048-11262552093Enzo Doria06/2014
925692^26524+9152088Norbert Schneider04/2013
925741^32295-4052085Theodore Burton02/2007
92582^173002+17752079Lelio R Paula02/2011
9259p(11334)#/2+852075Robert Price01/2017
92602^172965-11236352068Enzo Doria06/2014
92619*2^172935+752060Lelio R Paula03/2014
926211^49978-819052047Enzo Doria02/2013
926310^52041+63352042Patrick De Geest11/2012
926410^52041-9352041Robert Price05/2011
9265(21*2^172815-1)/86952021Lelio R Paula01/2014
9266(182*10^52018+1)/352020Robert Price02/2017
92674*6^66843-552015Lelio R Paula09/2014
926819^40670-5452007Lelio R Paula01/2013
92692^172756-11288352005Enzo Doria06/2014
927011832^12763-12763^1183251985Norbert Schneider02/2017
92717^61511-3651983Lelio R Paula10/2012
927210591^12914-12914^1059151979Norbert Schneider05/2017
92732^172640-7551970Lelio R Paula01/2011
9274gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
927512240^12709-12709^1224051952Norbert Schneider01/2017
9276t(173589)51951Robert Price12/2014
92777^61469+3451948Lelio R Paula10/2012
92799*2^172553-751945Lelio R Paula03/2014
927811542^12787+12787^1154251945Norbert Schneider01/2016
928035^33640-708651943Enzo Doria03/2013
9281(7*2^172534+1)/247951936Lelio R Paula07/2012
9282(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9283(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9284((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9285((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9286((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9287((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
92892^172470+751919Lelio R Paula01/2011
9288((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9290((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9291((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9292((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9293((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
92962^172455+1551915Lelio R Paula01/2011
9294((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9295((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9297((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9298((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9299((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9300((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9301((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9302((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
93035^74263+5451908Lelio R Paula10/2012
930413804^5755+5755^1380451904Hans Havermann05/2016
93057*2^172403-351900Henri Lifchitz06/2003
9306t(196078)51892Robert Price02/2014
93072*3^108759-751892Lelio R Paula03/2014
9308(94*10^51889+11)/351891Robert Price02/2017
9309(73*10^51889+17)/951890Robert Price10/2015
931035^33603-402651886Enzo Doria03/2013
93112^172350-10751883Lelio R Paula02/2011
931214419^3960+3960^1441951876Hans Havermann05/2016
93132^172325-11318551875Enzo Doria07/2014
931410^51872+10068351873Patrick De Geest06/2016
931510^51872-100000000151872Robert Price05/2016
931610^51872-10014951872Patrick De Geest06/2016
93172147092^8192+6351871Jens K. Andersen04/2009
931813^46564-2451870Lelio R Paula01/2013
931910524^12893-12893^1052451858Norbert Schneider05/2017
932013981^5110+5110^1398151848Hans Havermann05/2016
93212^172228+7626151846Enzo Doria04/2016
932211^49772-126051833Enzo Doria11/2012
9323(11*2^172157-1)/35151823Lelio R Paula01/2014
9324(43*10^51816-403)/951817Robert Price04/2017
93259001^13102-11451810Enzo Doria07/2012
9326(80051^10567+1)/8005251809Faysal YAtim07/2007
93272^172101-6151808Lelio R Paula01/2011
9328(2^172125+3)/3112550551808Lelio R Paula02/2012
93299*7^61301+451807Lelio R Paula09/2014
9330(23*2^172090-1)/3650951802Lelio R Paula01/2014
93312^172074+145951800Lelio R Paula07/2008
93322^172063+16551797Lelio R Paula02/2011
9333(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9334(56*10^51793+367)/951794Robert Price10/2017
933528^35785-2751787Norbert Schneider01/2014
9336(65*10^51778+43)/951779Ray Chandler09/2010
9337(15185*2^171975-1)/351774Lelio R Paula03/2015
93382^171978-11329751771Enzo Doria07/2014
933911^49708+7851766Lelio R Paula01/2013
9340(26*10^51764-107)/951765Robert Price07/2016
934112^47956-9751754Lelio R Paula12/2012
93422^171907-351151750Yves Minet03/2017
93438*10^51721+8751722Robert Price10/2017
934410306^12885-12885^1030651709Norbert Schneider05/2017
9345(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
9346(3*2^171761+1)/2951705Lelio R Paula07/2012
9347t(195346)51699Robert Price07/2014
934813^46409+4651697Lelio R Paula01/2013
93492^171663+1155*17166351676Henri Lifchitz01/2005
935015^43937+2651674Lelio R Paula01/2013
9351(3^108312-7)/12452651673Lelio R Paula03/2012
9352(12601^12601+465)/2/13151667Makoto Morimoto07/2016
9353(79*10^51663-97)/9951663Ray Chandler11/2010
935448589!4+102451656Robert Price08/2017
9356(10^51652-31)/351652Serge Batalov12/2014
93572^171583+7379351652Enzo Doria04/2016
9355(28*10^51651-31)/351652Robert Price10/2017
935812^47861-3551651Lelio R Paula12/2012
93596^66369-2681351646Enzo Doria03/2013
9360Phi(83967,10)/227248288951639Maksym Voznyy01/2010
93612^171524+15351634Lelio R Paula02/2011
9362(2^171516-509203)/486951628Lelio R Paula05/2012
9363(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
93645*10^51608-8151609Robert Price04/2017
9365(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
9366(2*10^51597-23)/351597Robert Price09/2017
936710171^12872-12872^1017151583Norbert Schneider04/2017
93682^171351-11267751582Enzo Doria06/2014
9369(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
93709818^12919-12919^981851573Norbert Schneider05/2017
9371(3^108091+7)/38251570Lelio R Paula03/2012
93732^171287-318751563Yves Minet04/2009
9372-lucasV(-1,2,342569)51563Mike Oakes02/2017
93742^171280-103070951561Paul Bourdelais11/2012
937513300^7527+7527^1330051560Hans Havermann05/2016
93762^171268+7371151557Enzo Doria04/2016
9377(17*2^171266+1)/696351554Lelio R Paula01/2012
9378(1964814^8192+1)/6553751551Lelio R Paula06/2013
9379(26*10^51537-503)/951538Robert Price12/2017
93804*10^51530-6351531Robert Price12/2016
93813*6^66216-551527Lelio R Paula09/2014
938212569^12569+54051525Makoto Morimoto07/2016
93832^171152-245951522Yves Minet07/2014
9384(13*10^51511-1)/351512Robert Price12/2014
93855*10^51508+351509Dmitry Domanov11/2010
93863^107919-4651491Lelio R Paula07/2012
93874*10^51489+8751490Robert Price05/2016
9388(22699*2^171030+1)/302951487Lelio R Paula05/2014
93892^171028-323951485Yves Minet12/2014
93902^170992-95420951474Paul Bourdelais11/2012
939176^27367+7551473Norbert Schneider11/2012
93926007^13620-10251466Enzo Doria07/2012
9393gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9394t(194442)51459Robert Price08/2014
9395(22*10^51457+161)/351458Robert Price02/2017
93969^53921+8^(53921+1)51454Robert Price06/2016
93982^170921-1699551453Lelio R Paula08/2011
93972^170922-213551453Yves Minet06/2013
93994357^14138-12051451Enzo Doria06/2012
9400153^23550+251450Lelio R Paula05/2013
9401(3^107833+2)/2551449Lelio R Paula03/2012
94027*10^51440-4751441Robert Price02/2017
9403(10^51431-3^51431)/751431Robert Price06/2011
9405U(250849)51425Michael Porter08/2007
9404(86*10^51424-41)/951425Robert Price11/2015
940712^47649+751422Lelio R Paula12/2012
9406(25*10^51421+11)/951422Robert Price03/2015
94083^107768+266051419Lelio R Paula07/2012
94102^170784-655551412Lelio R Paula05/2009
9409(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
941151^30106+251409Lelio R Paula05/2013
94125^73546-1280651407Enzo Doria02/2013
9413(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9414(3^107735-4)/43151401Lelio R Paula03/2012
941520^39505-648351398Enzo Doria03/2013
94162^170736-1519751397Enzo Doria04/2013
94172^170737-382351397Yves Minet04/2017
9418(12541^12541+393)/2/56351395Makoto Morimoto07/2016
94199^53857-8^5385751393Jean-Louis Charton11/2004
94205^73524-1442651392Enzo Doria02/2013
94212^170712+24351390Lelio R Paula10/2011
9422(15*2^170713+1)/179351388Lelio R Paula07/2012
9423(2^170702+9)/126151384Lelio R Paula01/2012
9424283^20956+20956^28351380Norbert Schneider08/2014
94252^170665-3151376Lelio R Paula01/2011
942611^49330-1251372Lelio R Paula01/2013
9427(25*10^51366-73)/351367Robert Price09/2016
94285^73486-2^7348751365Mike Oakes10/2010
9429(10^51364+119)/351364Serge Batalov12/2014
943015^43672+6851363Lelio R Paula01/2013
94312^170609-11314351359Enzo Doria07/2014
9432760^17827-759^1782751357Jean-Louis Charton12/2010
9433(22699*2^170592+1)/443551355Lelio R Paula05/2014
94348*7^60767+351355Lelio R Paula09/2014
94355^73452-2064651341Enzo Doria03/2013
94362^170531-23040751335Gary Barnes08/2009
943735^33243-211251330Enzo Doria03/2013
9438(1845768^8192+1)/6553751328Lelio R Paula06/2013
943913^46072+4251322Lelio R Paula01/2013
944014^44778-9551322Lelio R Paula01/2013
944111008^12697+12697^1100851318Norbert Schneider01/2016
9442t(180039)51312Robert Price09/2014
94432^170444-44351309Yves Minet05/2013
9444(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
9445(2*10^51285-71)/351285Robert Price01/2017
9446(23*10^51283-47)/351284Robert Price10/2017
9447(1819288^8192+1)/6553751277Lelio R Paula06/2013
94488907^12982-12982^890751276Norbert Schneider06/2017
94495^73350+2851270Lelio R Paula10/2012
94503^107450+251267Mike Oakes11/2009
94512^170296+253351265Henri Lifchitz07/2004
94522^170293+7648151264Enzo Doria05/2016
945311835^12584+12584^1183551257Norbert Schneider11/2015
9454(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
945612^47489+47489^1251250Serge Batalov02/2012
945514637^3172+3172^1463751250Hans Havermann04/2016
9457(2^170245+7)/951248Lelio R Paula02/2012
94585^73308-1992651241Enzo Doria03/2013
94598966^12963-12963^896651238Norbert Schneider06/2017
94603*2^170203+551237Lelio R Paula02/2014
94615^73300+4651235Lelio R Paula10/2012
94622^170167+7151226Lelio R Paula01/2011
94632^170140-1507751218Enzo Doria04/2013
946415^43542-4651210Lelio R Paula01/2013
94662^170111-101751209Lelio R Paula06/2008
94654*10^51208-8751209Robert Price03/2017
946814^44679+8351208Lelio R Paula01/2013
946710^51207+10014751208Patrick De Geest06/2016
946910^51207-80151207Robert Price04/2016
9471t(170300)51191Robert Price03/2015
947011966^12553-12553^1196651191Norbert Schneider11/2016
947214670^3083+3083^1467051184Hans Havermann04/2016
947399^25644-9851177Norbert Schneider07/2013
947413211^7468+7468^1321151169Hans Havermann04/2016
9475(2^169969-1017)/3551165Lelio R Paula01/2012
94765*10^51163-751164Dmitry Domanov11/2010
9477(73*10^51162-1)/951163Robert Price01/2015
9478(22*10^51154+383)/951155Robert Price11/2017
94792^169899+6351145Lelio R Paula05/2009
94802^169898+51351145Lelio R Paula05/2009
94823^107186-1238851141Enzo Doria02/2013
9481(299*10^51139+1)/351141Robert Price11/2017
9483(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
94843*6^65715-751137Lelio R Paula09/2014
9485116^24768+11551133Norbert Schneider10/2013
948635^33113-402651129Enzo Doria03/2013
9487(13*2^169830-1)/8447751121Lelio R Paula01/2014
9488(46*10^51111-1)/951112Serge Batalov10/2014
948915^43452-3451104Lelio R Paula01/2013
94902^169750-13751100Lelio R Paula01/2011
94912^169739+9406551097Lelio R Paula10/2011
949215^43442-2651092Lelio R Paula01/2013
94935^73096-1700651092Enzo Doria02/2013
949410^51091+7160151092Patrick De Geest07/2017
949510^51091-70151091Robert Price06/2017
9496(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
94972^169706-27055151087Gary Barnes08/2009
9498(2^169696+5)/2151083Lelio R Paula01/2012
9499(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
950011^49051-876051082Enzo Doria02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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