PRP Records

Probable Primes Top 10000

(172213 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 ?
850115^44333-7652140Lelio R Paula01/2013
85022^173187-318952135Yves Minet10/2014
85032^173167+7557952129Enzo Doria04/2016
8504(2^173169+7)/9279352125Lelio R Paula02/2012
85059*7^61671+452119Lelio R Paula09/2014
85072^173130-922152118Lelio R Paula07/2008
8506(17*2^173129-1)/352118Lelio R Paula01/2014
85082^173100-11255952109Enzo Doria06/2014
85092^173091-11233952106Enzo Doria06/2014
851011^50030+2852101Lelio R Paula01/2013
8511(59*10^52099+13)/952100Robert Price09/2015
85122^173064-182952098Yves Minet09/2012
85132^173062-136152097Yves Minet08/2012
85143^109190-7052097Lelio R Paula10/2012
85152^173059+9019552096Lelio R Paula07/2012
85162^173048-11262552093Enzo Doria06/2014
851792^26524+9152088Norbert Schneider04/2013
851841^32295-4052085Theodore Burton02/2007
85192^173002+17752079Lelio R Paula02/2011
8520p(11334)#/2+852075Robert Price01/2017
85212^172965-11236352068Enzo Doria06/2014
85229*2^172935+752060Lelio R Paula03/2014
852311^49978-819052047Enzo Doria02/2013
852410^52041+63352042Patrick De Geest11/2012
852510^52041-9352041Robert Price05/2011
8526(21*2^172815-1)/86952021Lelio R Paula01/2014
8527(182*10^52018+1)/352020Robert Price02/2017
85284*6^66843-552015Lelio R Paula09/2014
852919^40670-5452007Lelio R Paula01/2013
85302^172756-11288352005Enzo Doria06/2014
853111832^12763-12763^1183251985Norbert Schneider02/2017
85327^61511-3651983Lelio R Paula10/2012
85332^172640-7551970Lelio R Paula01/2011
8534gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
853512240^12709-12709^1224051952Norbert Schneider01/2017
8536t(173589)51951Robert Price12/2014
85377^61469+3451948Lelio R Paula10/2012
85389*2^172553-751945Lelio R Paula03/2014
853911542^12787+12787^1154251945Norbert Schneider01/2016
854035^33640-708651943Enzo Doria03/2013
8541(7*2^172534+1)/247951936Lelio R Paula07/2012
8542(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
8543(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
8544((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
8545((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
8546((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
8547((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
85492^172470+751919Lelio R Paula01/2011
8548((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
8550((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
8551((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
8552((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
8553((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
85562^172455+1551915Lelio R Paula01/2011
8554((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
8555((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
8557((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
8558((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
8559((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
8560((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
8561((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
8562((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
85635^74263+5451908Lelio R Paula10/2012
856413804^5755+5755^1380451904Hans Havermann05/2016
85657*2^172403-351900Henri Lifchitz06/2003
8566t(196078)51892Robert Price02/2014
85672*3^108759-751892Lelio R Paula03/2014
8568(94*10^51889+11)/351891Robert Price02/2017
8569(73*10^51889+17)/951890Robert Price10/2015
857035^33603-402651886Enzo Doria03/2013
85712^172350-10751883Lelio R Paula02/2011
857214419^3960+3960^1441951876Hans Havermann05/2016
85732^172325-11318551875Enzo Doria07/2014
857410^51872+10068351873Patrick De Geest06/2016
857510^51872-100000000151872Robert Price05/2016
857610^51872-10014951872Patrick De Geest06/2016
85772147092^8192+6351871Jens K. Andersen04/2009
857813^46564-2451870Lelio R Paula01/2013
857913981^5110+5110^1398151848Hans Havermann05/2016
85802^172228+7626151846Enzo Doria04/2016
858111^49772-126051833Enzo Doria11/2012
8582(11*2^172157-1)/35151823Lelio R Paula01/2014
85839001^13102-11451810Enzo Doria07/2012
8584(80051^10567+1)/8005251809Faysal YAtim07/2007
85862^172101-6151808Lelio R Paula01/2011
8585(2^172125+3)/3112550551808Lelio R Paula02/2012
85879*7^61301+451807Lelio R Paula09/2014
8588(23*2^172090-1)/3650951802Lelio R Paula01/2014
85892^172074+145951800Lelio R Paula07/2008
85902^172063+16551797Lelio R Paula02/2011
8591(21181*2^172061+1)/1814751796Lelio R Paula05/2014
859228^35785-2751787Norbert Schneider01/2014
8593(65*10^51778+43)/951779Ray Chandler09/2010
8594(15185*2^171975-1)/351774Lelio R Paula03/2015
85952^171978-11329751771Enzo Doria07/2014
859611^49708+7851766Lelio R Paula01/2013
8597(26*10^51764-107)/951765Robert Price07/2016
859812^47956-9751754Lelio R Paula12/2012
85992^171907-351151750Yves Minet03/2017
8600(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
8601(3*2^171761+1)/2951705Lelio R Paula07/2012
8602t(195346)51699Robert Price07/2014
860313^46409+4651697Lelio R Paula01/2013
86042^171663+1155*17166351676Henri Lifchitz01/2005
860515^43937+2651674Lelio R Paula01/2013
8606(3^108312-7)/12452651673Lelio R Paula03/2012
8607(12601^12601+465)/2/13151667Makoto Morimoto07/2016
8608(79*10^51663-97)/9951663Ray Chandler11/2010
8610(10^51652-31)/351652Serge Batalov12/2014
86092^171583+7379351652Enzo Doria04/2016
861112^47861-3551651Lelio R Paula12/2012
86126^66369-2681351646Enzo Doria03/2013
8613Phi(83967,10)/227248288951639Maksym Voznyy01/2010
86142^171524+15351634Lelio R Paula02/2011
8615(2^171516-509203)/486951628Lelio R Paula05/2012
8616(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
8617(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
86182^171351-11267751582Enzo Doria06/2014
8619(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
8620(3^108091+7)/38251570Lelio R Paula03/2012
86222^171287-318751563Yves Minet04/2009
8621-lucasV(-1,2,342569)51563Mike Oakes02/2017
86232^171280-103070951561Paul Bourdelais11/2012
862413300^7527+7527^1330051560Hans Havermann05/2016
86252^171268+7371151557Enzo Doria04/2016
8626(17*2^171266+1)/696351554Lelio R Paula01/2012
8627(1964814^8192+1)/6553751551Lelio R Paula06/2013
86284*10^51530-6351531Robert Price12/2016
86293*6^66216-551527Lelio R Paula09/2014
863012569^12569+54051525Makoto Morimoto07/2016
86312^171152-245951522Yves Minet07/2014
8632(13*10^51511-1)/351512Robert Price12/2014
86335*10^51508+351509Dmitry Domanov11/2010
86343^107919-4651491Lelio R Paula07/2012
86354*10^51489+8751490Robert Price05/2016
8636(22699*2^171030+1)/302951487Lelio R Paula05/2014
86372^171028-323951485Yves Minet12/2014
86382^170992-95420951474Paul Bourdelais11/2012
863976^27367+7551473Norbert Schneider11/2012
86406007^13620-10251466Enzo Doria07/2012
8641gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
8642t(194442)51459Robert Price08/2014
8643(22*10^51457+161)/351458Robert Price02/2017
86449^53921+8^(53921+1)51454Robert Price06/2016
86452^170921-1699551453Lelio R Paula08/2011
86462^170922-213551453Yves Minet06/2013
86474357^14138-12051451Enzo Doria06/2012
8648153^23550+251450Lelio R Paula05/2013
8649(3^107833+2)/2551449Lelio R Paula03/2012
86507*10^51440-4751441Robert Price02/2017
8651(10^51431-3^51431)/751431Robert Price06/2011
8653U(250849)51425Michael Porter08/2007
8652(86*10^51424-41)/951425Robert Price11/2015
865512^47649+751422Lelio R Paula12/2012
8654(25*10^51421+11)/951422Robert Price03/2015
86563^107768+266051419Lelio R Paula07/2012
86572^170784-655551412Lelio R Paula05/2009
8658(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
865951^30106+251409Lelio R Paula05/2013
86605^73546-1280651407Enzo Doria02/2013
8661(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
8662(3^107735-4)/43151401Lelio R Paula03/2012
866320^39505-648351398Enzo Doria03/2013
86642^170736-1519751397Enzo Doria04/2013
8665(12541^12541+393)/2/56351395Makoto Morimoto07/2016
86669^53857-8^5385751393Jean-Louis Charton11/2004
86675^73524-1442651392Enzo Doria02/2013
86682^170712+24351390Lelio R Paula10/2011
8669(15*2^170713+1)/179351388Lelio R Paula07/2012
8670(2^170702+9)/126151384Lelio R Paula01/2012
8671283^20956+20956^28351380Norbert Schneider08/2014
86722^170665-3151376Lelio R Paula01/2011
867311^49330-1251372Lelio R Paula01/2013
8674(25*10^51366-73)/351367Robert Price09/2016
86755^73486-2^7348751365Mike Oakes10/2010
8676(10^51364+119)/351364Serge Batalov12/2014
867715^43672+6851363Lelio R Paula01/2013
86782^170609-11314351359Enzo Doria07/2014
8679760^17827-759^1782751357Jean-Louis Charton12/2010
8680(22699*2^170592+1)/443551355Lelio R Paula05/2014
86818*7^60767+351355Lelio R Paula09/2014
86825^73452-2064651341Enzo Doria03/2013
86832^170531-23040751335Gary Barnes08/2009
868435^33243-211251330Enzo Doria03/2013
8685(1845768^8192+1)/6553751328Lelio R Paula06/2013
868613^46072+4251322Lelio R Paula01/2013
868714^44778-9551322Lelio R Paula01/2013
868811008^12697+12697^1100851318Norbert Schneider01/2016
8689t(180039)51312Robert Price09/2014
86902^170444-44351309Yves Minet05/2013
8691(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
8692(2*10^51285-71)/351285Robert Price01/2017
8693(1819288^8192+1)/6553751277Lelio R Paula06/2013
86945^73350+2851270Lelio R Paula10/2012
86953^107450+251267Mike Oakes11/2009
86962^170296+253351265Henri Lifchitz07/2004
86972^170293+7648151264Enzo Doria05/2016
869811835^12584+12584^1183551257Norbert Schneider11/2015
8699(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
870112^47489+47489^1251250Serge Batalov02/2012
870014637^3172+3172^1463751250Hans Havermann04/2016
8702(2^170245+7)/951248Lelio R Paula02/2012
87035^73308-1992651241Enzo Doria03/2013
87043*2^170203+551237Lelio R Paula02/2014
87055^73300+4651235Lelio R Paula10/2012
87062^170167+7151226Lelio R Paula01/2011
87072^170140-1507751218Enzo Doria04/2013
870815^43542-4651210Lelio R Paula01/2013
87102^170111-101751209Lelio R Paula06/2008
87094*10^51208-8751209Robert Price03/2017
871214^44679+8351208Lelio R Paula01/2013
871110^51207+10014751208Patrick De Geest06/2016
871310^51207-80151207Robert Price04/2016
8714t(170300)51191Robert Price03/2015
871511966^12553-12553^1196651191Norbert Schneider11/2016
871614670^3083+3083^1467051184Hans Havermann04/2016
871799^25644-9851177Norbert Schneider07/2013
871813211^7468+7468^1321151169Hans Havermann04/2016
8719(2^169969-1017)/3551165Lelio R Paula01/2012
87205*10^51163-751164Dmitry Domanov11/2010
8721(73*10^51162-1)/951163Robert Price01/2015
87222^169899+6351145Lelio R Paula05/2009
87232^169898+51351145Lelio R Paula05/2009
87243^107186-1238851141Enzo Doria02/2013
8725(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
87263*6^65715-751137Lelio R Paula09/2014
8727116^24768+11551133Norbert Schneider10/2013
872835^33113-402651129Enzo Doria03/2013
8729(13*2^169830-1)/8447751121Lelio R Paula01/2014
8730(46*10^51111-1)/951112Serge Batalov10/2014
873115^43452-3451104Lelio R Paula01/2013
87322^169750-13751100Lelio R Paula01/2011
87332^169739+9406551097Lelio R Paula10/2011
873415^43442-2651092Lelio R Paula01/2013
87355^73096-1700651092Enzo Doria02/2013
8736(-lucasV(1,2,339439)-2)/(79*83)51088Mike Oakes03/2017
87372^169706-27055151087Gary Barnes08/2009
8738(2^169696+5)/2151083Lelio R Paula01/2012
8740(1722520^8192+1)/6553751082Syoichiro Yamada01/2009
873911^49051-876051082Enzo Doria02/2013
8741(24737*2^169672+1)/2751080Lelio R Paula05/2014
87422^169677+1609551078Lelio R Paula05/2009
87432^169659-13551073Lelio R Paula01/2011
87442^169638-11318351067Enzo Doria07/2014
8745(29*2^169622-1)/234653118551054Lelio R Paula01/2014
8746(10^51054+17)/951054Robert Price10/2014
8747(24737*2^169577+1)/551052Lelio R Paula05/2014
874811^49021-7851051Lelio R Paula01/2013
874918^40669+6151051Lelio R Paula01/2013
875014038^4327+4327^1403851045Hans Havermann02/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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