PRP Records

Probable Primes Top 10000

(177649 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
87513^109320+23652159Lelio R Paula10/2012
87522^173246-2863552153Lelio R Paula06/2009
87532*10^52147+1152148Robert Price01/2015
87542^173208-11262552141Enzo Doria06/2014
8755(9179*2^173206-1)/203552141Lelio R Paula03/2015
875615^44333-7652140Lelio R Paula01/2013
87572^173187-318952135Yves Minet10/2014
87582^173167+7557952129Enzo Doria04/2016
8759(2^173169+7)/9279352125Lelio R Paula02/2012
8760(25*10^52119+23)/352120Robert Price06/2017
87619*7^61671+452119Lelio R Paula09/2014
87632^173130-922152118Lelio R Paula07/2008
8762(17*2^173129-1)/352118Lelio R Paula01/2014
87642^173100-11255952109Enzo Doria06/2014
87652^173091-11233952106Enzo Doria06/2014
876611^50030+2852101Lelio R Paula01/2013
8767(59*10^52099+13)/952100Robert Price09/2015
87682^173064-182952098Yves Minet09/2012
87692^173062-136152097Yves Minet08/2012
87703^109190-7052097Lelio R Paula10/2012
87712^173059+9019552096Lelio R Paula07/2012
87722^173048-11262552093Enzo Doria06/2014
877392^26524+9152088Norbert Schneider04/2013
877441^32295-4052085Theodore Burton02/2007
87752^173002+17752079Lelio R Paula02/2011
8776p(11334)#/2+852075Robert Price01/2017
87772^172965-11236352068Enzo Doria06/2014
87789*2^172935+752060Lelio R Paula03/2014
877911^49978-819052047Enzo Doria02/2013
878010^52041+63352042Patrick De Geest11/2012
878110^52041-9352041Robert Price05/2011
8782(21*2^172815-1)/86952021Lelio R Paula01/2014
8783(182*10^52018+1)/352020Robert Price02/2017
87844*6^66843-552015Lelio R Paula09/2014
878519^40670-5452007Lelio R Paula01/2013
87862^172756-11288352005Enzo Doria06/2014
878711832^12763-12763^1183251985Norbert Schneider02/2017
87887^61511-3651983Lelio R Paula10/2012
878910591^12914-12914^1059151979Norbert Schneider05/2017
87902^172640-7551970Lelio R Paula01/2011
8791gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
879212240^12709-12709^1224051952Norbert Schneider01/2017
8793t(173589)51951Robert Price12/2014
87947^61469+3451948Lelio R Paula10/2012
87959*2^172553-751945Lelio R Paula03/2014
879611542^12787+12787^1154251945Norbert Schneider01/2016
879735^33640-708651943Enzo Doria03/2013
8798(7*2^172534+1)/247951936Lelio R Paula07/2012
8799(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
8800(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
8801((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
8802((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
8803((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
8804((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
88062^172470+751919Lelio R Paula01/2011
8805((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
8807((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
8808((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
8809((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
8810((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
88132^172455+1551915Lelio R Paula01/2011
8811((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
8812((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
8814((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
8815((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
8816((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
8817((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
8818((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
8819((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
88205^74263+5451908Lelio R Paula10/2012
882113804^5755+5755^1380451904Hans Havermann05/2016
88227*2^172403-351900Henri Lifchitz06/2003
8823t(196078)51892Robert Price02/2014
88242*3^108759-751892Lelio R Paula03/2014
8825(94*10^51889+11)/351891Robert Price02/2017
8826(73*10^51889+17)/951890Robert Price10/2015
882735^33603-402651886Enzo Doria03/2013
88282^172350-10751883Lelio R Paula02/2011
882914419^3960+3960^1441951876Hans Havermann05/2016
88302^172325-11318551875Enzo Doria07/2014
883110^51872+10068351873Patrick De Geest06/2016
883210^51872-100000000151872Robert Price05/2016
883310^51872-10014951872Patrick De Geest06/2016
88342147092^8192+6351871Jens K. Andersen04/2009
883513^46564-2451870Lelio R Paula01/2013
883610524^12893-12893^1052451858Norbert Schneider05/2017
883713981^5110+5110^1398151848Hans Havermann05/2016
88382^172228+7626151846Enzo Doria04/2016
883911^49772-126051833Enzo Doria11/2012
8840(11*2^172157-1)/35151823Lelio R Paula01/2014
8841(43*10^51816-403)/951817Robert Price04/2017
88429001^13102-11451810Enzo Doria07/2012
8843(80051^10567+1)/8005251809Faysal YAtim07/2007
88452^172101-6151808Lelio R Paula01/2011
8844(2^172125+3)/3112550551808Lelio R Paula02/2012
88469*7^61301+451807Lelio R Paula09/2014
8847(23*2^172090-1)/3650951802Lelio R Paula01/2014
88482^172074+145951800Lelio R Paula07/2008
88492^172063+16551797Lelio R Paula02/2011
8850(21181*2^172061+1)/1814751796Lelio R Paula05/2014
885128^35785-2751787Norbert Schneider01/2014
8852(65*10^51778+43)/951779Ray Chandler09/2010
8853(15185*2^171975-1)/351774Lelio R Paula03/2015
88542^171978-11329751771Enzo Doria07/2014
885511^49708+7851766Lelio R Paula01/2013
8856(26*10^51764-107)/951765Robert Price07/2016
885712^47956-9751754Lelio R Paula12/2012
88582^171907-351151750Yves Minet03/2017
885910306^12885-12885^1030651709Norbert Schneider05/2017
8860(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
8861(3*2^171761+1)/2951705Lelio R Paula07/2012
8862t(195346)51699Robert Price07/2014
886313^46409+4651697Lelio R Paula01/2013
88642^171663+1155*17166351676Henri Lifchitz01/2005
886515^43937+2651674Lelio R Paula01/2013
8866(3^108312-7)/12452651673Lelio R Paula03/2012
8867(12601^12601+465)/2/13151667Makoto Morimoto07/2016
8868(79*10^51663-97)/9951663Ray Chandler11/2010
8869(10^51652-31)/351652Serge Batalov12/2014
88702^171583+7379351652Enzo Doria04/2016
887112^47861-3551651Lelio R Paula12/2012
88726^66369-2681351646Enzo Doria03/2013
8873Phi(83967,10)/227248288951639Maksym Voznyy01/2010
88742^171524+15351634Lelio R Paula02/2011
8875(2^171516-509203)/486951628Lelio R Paula05/2012
8876(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
88775*10^51608-8151609Robert Price04/2017
8878(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
887910171^12872-12872^1017151583Norbert Schneider04/2017
88802^171351-11267751582Enzo Doria06/2014
8881(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016
88829818^12919-12919^981851573Norbert Schneider05/2017
8883(3^108091+7)/38251570Lelio R Paula03/2012
88852^171287-318751563Yves Minet04/2009
8884-lucasV(-1,2,342569)51563Mike Oakes02/2017
88862^171280-103070951561Paul Bourdelais11/2012
888713300^7527+7527^1330051560Hans Havermann05/2016
88882^171268+7371151557Enzo Doria04/2016
8889(17*2^171266+1)/696351554Lelio R Paula01/2012
8890(1964814^8192+1)/6553751551Lelio R Paula06/2013
88914*10^51530-6351531Robert Price12/2016
88923*6^66216-551527Lelio R Paula09/2014
889312569^12569+54051525Makoto Morimoto07/2016
88942^171152-245951522Yves Minet07/2014
8895(13*10^51511-1)/351512Robert Price12/2014
88965*10^51508+351509Dmitry Domanov11/2010
88973^107919-4651491Lelio R Paula07/2012
88984*10^51489+8751490Robert Price05/2016
8899(22699*2^171030+1)/302951487Lelio R Paula05/2014
89002^171028-323951485Yves Minet12/2014
89012^170992-95420951474Paul Bourdelais11/2012
890276^27367+7551473Norbert Schneider11/2012
89036007^13620-10251466Enzo Doria07/2012
8904gcd(V(923445),5*F(184689)*(F(184689)-1)+1)51462Serge Batalov04/2015
8905t(194442)51459Robert Price08/2014
8906(22*10^51457+161)/351458Robert Price02/2017
89079^53921+8^(53921+1)51454Robert Price06/2016
89092^170921-1699551453Lelio R Paula08/2011
89082^170922-213551453Yves Minet06/2013
89104357^14138-12051451Enzo Doria06/2012
8911153^23550+251450Lelio R Paula05/2013
8912(3^107833+2)/2551449Lelio R Paula03/2012
89137*10^51440-4751441Robert Price02/2017
8914(10^51431-3^51431)/751431Robert Price06/2011
8916U(250849)51425Michael Porter08/2007
8915(86*10^51424-41)/951425Robert Price11/2015
891712^47649+751422Lelio R Paula12/2012
8918(25*10^51421+11)/951422Robert Price03/2015
89193^107768+266051419Lelio R Paula07/2012
89202^170784-655551412Lelio R Paula05/2009
8921(-lucasV(1,2,341584)-2)/7951412Mike Oakes03/2017
892251^30106+251409Lelio R Paula05/2013
89235^73546-1280651407Enzo Doria02/2013
8924(12545^12545+12546^12546)/(1584571*19137767639)51404Walter Nissen09/2014
8925(3^107735-4)/43151401Lelio R Paula03/2012
892620^39505-648351398Enzo Doria03/2013
89272^170736-1519751397Enzo Doria04/2013
89282^170737-382351397Yves Minet04/2017
8929(12541^12541+393)/2/56351395Makoto Morimoto07/2016
89309^53857-8^5385751393Jean-Louis Charton11/2004
89315^73524-1442651392Enzo Doria02/2013
89322^170712+24351390Lelio R Paula10/2011
8933(15*2^170713+1)/179351388Lelio R Paula07/2012
8934(2^170702+9)/126151384Lelio R Paula01/2012
8935283^20956+20956^28351380Norbert Schneider08/2014
89362^170665-3151376Lelio R Paula01/2011
893711^49330-1251372Lelio R Paula01/2013
8938(25*10^51366-73)/351367Robert Price09/2016
89395^73486-2^7348751365Mike Oakes10/2010
8940(10^51364+119)/351364Serge Batalov12/2014
894115^43672+6851363Lelio R Paula01/2013
89422^170609-11314351359Enzo Doria07/2014
8943760^17827-759^1782751357Jean-Louis Charton12/2010
8944(22699*2^170592+1)/443551355Lelio R Paula05/2014
89458*7^60767+351355Lelio R Paula09/2014
89465^73452-2064651341Enzo Doria03/2013
89472^170531-23040751335Gary Barnes08/2009
894835^33243-211251330Enzo Doria03/2013
8949(1845768^8192+1)/6553751328Lelio R Paula06/2013
895013^46072+4251322Lelio R Paula01/2013
895114^44778-9551322Lelio R Paula01/2013
895211008^12697+12697^1100851318Norbert Schneider01/2016
8953t(180039)51312Robert Price09/2014
89542^170444-44351309Yves Minet05/2013
8955(-lucasV(1,2,340915)+2)/(340913*4220189*8187163)51294Mike Oakes03/2017
8956(2*10^51285-71)/351285Robert Price01/2017
8957(1819288^8192+1)/6553751277Lelio R Paula06/2013
89588907^12982-12982^890751276Norbert Schneider06/2017
89595^73350+2851270Lelio R Paula10/2012
89603^107450+251267Mike Oakes11/2009
89612^170296+253351265Henri Lifchitz07/2004
89622^170293+7648151264Enzo Doria05/2016
896311835^12584+12584^1183551257Norbert Schneider11/2015
8964(12511^12511+193)/2^5/3937151256Makoto Morimoto07/2016
896612^47489+47489^1251250Serge Batalov02/2012
896514637^3172+3172^1463751250Hans Havermann04/2016
8967(2^170245+7)/951248Lelio R Paula02/2012
89685^73308-1992651241Enzo Doria03/2013
89698966^12963-12963^896651238Norbert Schneider06/2017
89703*2^170203+551237Lelio R Paula02/2014
89715^73300+4651235Lelio R Paula10/2012
89722^170167+7151226Lelio R Paula01/2011
89732^170140-1507751218Enzo Doria04/2013
897415^43542-4651210Lelio R Paula01/2013
89762^170111-101751209Lelio R Paula06/2008
89754*10^51208-8751209Robert Price03/2017
897714^44679+8351208Lelio R Paula01/2013
897810^51207+10014751208Patrick De Geest06/2016
897910^51207-80151207Robert Price04/2016
8980t(170300)51191Robert Price03/2015
898111966^12553-12553^1196651191Norbert Schneider11/2016
898214670^3083+3083^1467051184Hans Havermann04/2016
898399^25644-9851177Norbert Schneider07/2013
898413211^7468+7468^1321151169Hans Havermann04/2016
8985(2^169969-1017)/3551165Lelio R Paula01/2012
89865*10^51163-751164Dmitry Domanov11/2010
8987(73*10^51162-1)/951163Robert Price01/2015
89882^169899+6351145Lelio R Paula05/2009
89892^169898+51351145Lelio R Paula05/2009
89903^107186-1238851141Enzo Doria02/2013
8991(12487^12487+173)/2^2/3/2917/3463/4448351140Makoto Morimoto07/2016
89923*6^65715-751137Lelio R Paula09/2014
8993116^24768+11551133Norbert Schneider10/2013
899435^33113-402651129Enzo Doria03/2013
8995(13*2^169830-1)/8447751121Lelio R Paula01/2014
8996(46*10^51111-1)/951112Serge Batalov10/2014
899715^43452-3451104Lelio R Paula01/2013
89982^169750-13751100Lelio R Paula01/2011
89992^169739+9406551097Lelio R Paula10/2011
900015^43442-2651092Lelio R Paula01/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!