PRP Records

Probable Primes Top 10000

(224660 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 ?
9751(25*10^52119+23)/352120Robert Price06/2017
97529*7^61671+452119Lelio R Paula09/2014
97542^173130-922152118Lelio R Paula07/2008
9753(17*2^173129-1)/352118Lelio R Paula01/2014
97556482^13673-13673^648252118Norbert Schneider08/2018
9756215^22342-21652112Karsten Bonath04/2018
97572^173100-11255952109Enzo Doria06/2014
97582^173091-11233952106Enzo Doria06/2014
975970797!6-3252106Robert Price08/2018
976011^50030+2852101Lelio R Paula01/2013
9761(59*10^52099+13)/952100Robert Price09/2015
97622^173064-182952098Yves Minet09/2012
97632^173062-136152097Yves Minet08/2012
97643^109190-7052097Lelio R Paula10/2012
97652^173059+9019552096Lelio R Paula07/2012
97662^173048-11262552093Enzo Doria06/2014
976792^26524+9152088Norbert Schneider04/2013
976841^32295-4052085Theodore Burton02/2007
97692^173002+17752079Lelio R Paula02/2011
9770p(11334)#/2+852075Robert Price01/2017
97712^172965-11236352068Enzo Doria06/2014
97729*2^172935+752060Lelio R Paula03/2014
977311^49978-819052047Enzo Doria02/2013
977410^52041+63352042Patrick De Geest11/2012
97758494^13245-13245^849452042Norbert Schneider01/2018
977610^52041-9352041Robert Price05/2011
9777(21*2^172815-1)/86952021Lelio R Paula01/2014
9778(182*10^52018+1)/352020Robert Price02/2017
97794*6^66843-552015Lelio R Paula09/2014
97807732^13377-13377^773252014Norbert Schneider03/2018
978119^40670-5452007Lelio R Paula01/2013
97822^172756-11288352005Enzo Doria06/2014
978311832^12763-12763^1183251985Norbert Schneider02/2017
97847^61511-3651983Lelio R Paula10/2012
978510591^12914-12914^1059151979Norbert Schneider05/2017
97862^172640-7551970Lelio R Paula01/2011
97876792^13559-13559^679251959Norbert Schneider07/2018
97887750^13359-13359^775051958Norbert Schneider03/2018
9789gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
979012240^12709-12709^1224051952Norbert Schneider01/2017
9791t(173589)51951Robert Price12/2014
97927^61469+3451948Lelio R Paula10/2012
97939*2^172553-751945Lelio R Paula03/2014
979411542^12787+12787^1154251945Norbert Schneider01/2016
979535^33640-708651943Enzo Doria03/2013
9796(7*2^172534+1)/247951936Lelio R Paula07/2012
97977353^13430-13430^735351927Norbert Schneider04/2018
9798(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9799(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9800((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9801((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9802((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9803((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
98052^172470+751919Lelio R Paula01/2011
9804((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9806((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9807((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9808((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9809((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
98122^172455+1551915Lelio R Paula01/2011
9810((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9811((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9813((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9814((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9815((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9816((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9817((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9818((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
98195^74263+5451908Lelio R Paula10/2012
982013804^5755+5755^1380451904Hans Havermann05/2016
98217*2^172403-351900Henri Lifchitz06/2003
9822t(196078)51892Robert Price02/2014
98232*3^108759-751892Lelio R Paula03/2014
9824(94*10^51889+11)/351891Robert Price02/2017
9825(73*10^51889+17)/951890Robert Price10/2015
982635^33603-402651886Enzo Doria03/2013
98272^172350-10751883Lelio R Paula02/2011
982814419^3960+3960^1441951876Hans Havermann05/2016
98292^172325-11318551875Enzo Doria07/2014
983010^51872+10068351873Patrick De Geest06/2016
983110^51872-100000000151872Robert Price05/2016
983210^51872-10014951872Patrick De Geest06/2016
98332147092^8192+6351871Jens K. Andersen04/2009
983413^46564-2451870Lelio R Paula01/2013
983510524^12893-12893^1052451858Norbert Schneider05/2017
983613981^5110+5110^1398151848Hans Havermann05/2016
98372^172228+7626151846Enzo Doria04/2016
983811^49772-126051833Enzo Doria11/2012
9839(11*2^172157-1)/35151823Lelio R Paula01/2014
9840(43*10^51816-403)/951817Robert Price04/2017
98419001^13102-11451810Enzo Doria07/2012
9842(80051^10567+1)/8005251809Faysal YAtim07/2007
98442^172101-6151808Lelio R Paula01/2011
9843(2^172125+3)/3112550551808Lelio R Paula02/2012
98459*7^61301+451807Lelio R Paula09/2014
9846(23*2^172090-1)/3650951802Lelio R Paula01/2014
98472^172074+145951800Lelio R Paula07/2008
98482^172063+16551797Lelio R Paula02/2011
9849(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9850(56*10^51793+367)/951794Robert Price10/2017
985128^35785-2751787Norbert Schneider01/2014
9852(65*10^51778+43)/951779Ray Chandler09/2010
9853(15185*2^171975-1)/351774Lelio R Paula03/2015
98542^171978-11329751771Enzo Doria07/2014
985511^49708+7851766Lelio R Paula01/2013
9856(26*10^51764-107)/951765Robert Price07/2016
985712^47956-9751754Lelio R Paula12/2012
98582^171907-351151750Yves Minet03/2017
98598203^13220-13220^820351743Norbert Schneider12/2017
98607706^13307-13307^770651723Norbert Schneider02/2018
98618*10^51721+8751722Robert Price10/2017
986210306^12885-12885^1030651709Norbert Schneider05/2017
9863(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
9864(3*2^171761+1)/2951705Lelio R Paula07/2012
9865t(195346)51699Robert Price07/2014
986613^46409+4651697Lelio R Paula01/2013
98672^171663+1155*17166351676Henri Lifchitz01/2005
986815^43937+2651674Lelio R Paula01/2013
9869(3^108312-7)/12452651673Lelio R Paula03/2012
9870(12601^12601+465)/2/13151667Makoto Morimoto07/2016
9871(79*10^51663-97)/9951663Ray Chandler11/2010
987248589!4+102451656Robert Price08/2017
9875(10^51652-31)/351652Serge Batalov12/2014
98742^171583+7379351652Enzo Doria04/2016
9873(28*10^51651-31)/351652Robert Price10/2017
987612^47861-3551651Lelio R Paula12/2012
98776^66369-2681351646Enzo Doria03/2013
9878Phi(83967,10)/227248288951639Maksym Voznyy01/2010
98792^171524+15351634Lelio R Paula02/2011
9880(2^171516-509203)/486951628Lelio R Paula05/2012
9881(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
98825*10^51608-8151609Robert Price04/2017
9883(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
9884(2*10^51597-23)/351597Robert Price09/2017
988510171^12872-12872^1017151583Norbert Schneider04/2017
98862^171351-11267751582Enzo Doria06/2014
9887(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
98889818^12919-12919^981851573Norbert Schneider05/2017
9889(3^108091+7)/38251570Lelio R Paula03/2012
98912^171287-318751563Yves Minet04/2009
9890-lucasV(-1,2,342569)51563Mike Oakes02/2017
98922^171280-103070951561Paul Bourdelais11/2012
989313300^7527+7527^1330051560Hans Havermann05/2016
98942^171268+7371151557Enzo Doria04/2016
9895(17*2^171266+1)/696351554Lelio R Paula01/2012
9896(1964814^8192+1)/6553751551Lelio R Paula06/2013
9897(26*10^51537-503)/951538Robert Price12/2017
98984*10^51530-6351531Robert Price12/2016
98993*6^66216-551527Lelio R Paula09/2014
990012569^12569+54051525Makoto Morimoto07/2016
99012^171152-245951522Yves Minet07/2014
9902(13*10^51511-1)/351512Robert Price12/2014
99035*10^51508+351509Dmitry Domanov11/2010
99043^107919-4651491Lelio R Paula07/2012
99054*10^51489+8751490Robert Price05/2016
9906(22699*2^171030+1)/302951487Lelio R Paula05/2014
99072^171028-323951485Yves Minet12/2014
99082^170992-95420951474Paul Bourdelais11/2012
990976^27367+7551473Norbert Schneider11/2012
99106007^13620-10251466Enzo Doria07/2012
9911gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
9912t(194442)51459Robert Price08/2014
99136470^13503-13503^647051459Norbert Schneider05/2018
9914(22*10^51457+161)/351458Robert Price02/2017
99159^53921+8^(53921+1)51454Robert Price06/2016
99172^170921-1699551453Lelio R Paula08/2011
99162^170922-213551453Yves Minet06/2013
99184357^14138-12051451Enzo Doria06/2012
9919153^23550+251450Lelio R Paula05/2013
9920(3^107833+2)/2551449Lelio R Paula03/2012
9921(159^23369+1)/16051443Eric Chen12/2017
99227*10^51440-4751441Robert Price02/2017
9923(10^51431-3^51431)/751431Robert Price06/2011
9925U(250849)51425Michael Porter08/2007
9924(86*10^51424-41)/951425Robert Price11/2015
992712^47649+751422Lelio R Paula12/2012
9926(25*10^51421+11)/951422Robert Price03/2015
99283^107768+266051419Lelio R Paula07/2012
99302^170784-655551412Lelio R Paula05/2009
9929(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
993251^30106+251409Lelio R Paula05/2013
99312^170777-415951409Yves Minet02/2018
99335^73546-1280651407Enzo Doria02/2013
9934(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
9935(3^107735-4)/43151401Lelio R Paula03/2012
993620^39505-648351398Enzo Doria03/2013
99372^170736-1519751397Enzo Doria04/2013
99382^170737-382351397Yves Minet04/2017
9939(12541^12541+393)/2/56351395Makoto Morimoto07/2016
99409^53857-8^5385751393Jean-Louis Charton11/2004
99415^73524-1442651392Enzo Doria02/2013
99422^170712+24351390Lelio R Paula10/2011
9943(15*2^170713+1)/179351388Lelio R Paula07/2012
9944(2^170702+9)/126151384Lelio R Paula01/2012
9945283^20956+20956^28351380Norbert Schneider08/2014
99462^170665-3151376Lelio R Paula01/2011
994711^49330-1251372Lelio R Paula01/2013
9948(25*10^51366-73)/351367Robert Price09/2016
99495^73486-2^7348751365Mike Oakes10/2010
9950(10^51364+119)/351364Serge Batalov12/2014
995115^43672+6851363Lelio R Paula01/2013
99522^170609-11314351359Enzo Doria07/2014
9953760^17827-759^1782751357Jean-Louis Charton12/2010
9954(22699*2^170592+1)/443551355Lelio R Paula05/2014
99558*7^60767+351355Lelio R Paula09/2014
99567009^13352-13352^700951348Norbert Schneider03/2018
99575^73452-2064651341Enzo Doria03/2013
99582^170531-23040751335Gary Barnes08/2009
995935^33243-211251330Enzo Doria03/2013
9960(1845768^8192+1)/6553751328Lelio R Paula06/2013
996113^46072+4251322Lelio R Paula01/2013
996214^44778-9551322Lelio R Paula01/2013
996311008^12697+12697^1100851318Norbert Schneider01/2016
9964(11^49279+7^49279)/1851318Eric Chen05/2018
9965t(180039)51312Robert Price09/2014
99662^170444-44351309Yves Minet05/2013
9967(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
9968(2*10^51285-71)/351285Robert Price01/2017
9969(23*10^51283-47)/351284Robert Price10/2017
9970(1819288^8192+1)/6553751277Lelio R Paula06/2013
99714714^13959-13959^471451277Norbert Schneider09/2018
99728907^12982-12982^890751276Norbert Schneider06/2017
99735^73350+2851270Lelio R Paula10/2012
99743^107450+251267Mike Oakes11/2009
99752^170296+253351265Henri Lifchitz07/2004
99762^170293+7648151264Enzo Doria05/2016
997711835^12584+12584^1183551257Norbert Schneider11/2015
9978(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
998012^47489+47489^1251250Serge Batalov02/2012
997914637^3172+3172^1463751250Hans Havermann04/2016
9981(2^170245+7)/951248Lelio R Paula02/2012
99825^73308-1992651241Enzo Doria03/2013
99838966^12963-12963^896651238Norbert Schneider06/2017
99843*2^170203+551237Lelio R Paula02/2014
99855^73300+4651235Lelio R Paula10/2012
99862^170167+7151226Lelio R Paula01/2011
9987((2^42543+1)^4+1)/251226Harsh Aggarwal10/2018
99882^170140-1507751218Enzo Doria04/2013
998915^43542-4651210Lelio R Paula01/2013
99912^170111-101751209Lelio R Paula06/2008
99904*10^51208-8751209Robert Price03/2017
999314^44679+8351208Lelio R Paula01/2013
999210^51207+10014751208Patrick De Geest06/2016
999410^51207-80151207Robert Price04/2016
9996t(170300)51191Robert Price03/2015
999511966^12553-12553^1196651191Norbert Schneider11/2016
999714670^3083+3083^1467051184Hans Havermann04/2016
999899^25644-9851177Norbert Schneider07/2013
999913211^7468+7468^1321151169Hans Havermann04/2016
10000(2^169969-1017)/3551165Lelio R Paula01/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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