PRP Records

Probable Primes Top 10000

(218736 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 ?
95015003^14217-15052592Enzo Doria07/2012
95022^174698-405552590Yves Minet02/2018
950319^41123+1052587Lelio R Paula01/2013
95042^174683+1290952585Lelio R Paula01/2011
95052^174643+5952573Lelio R Paula01/2011
9506(1017*2^174640-1)/77352572Lelio R Paula03/2015
950713529^7662+7662^1352952552Hans Havermann06/2016
9508121421#+18876752548Makoto Morimoto02/2016
950920^40375-592352530Enzo Doria03/2013
9510(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9511(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
95122^174462+34552519Lelio R Paula07/2009
9513t(178863)52509Robert Price10/2014
95142^174416+85552505Lelio R Paula07/2009
95156^67467-10352500Lelio R Paula10/2012
9516(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
95177888^13467-13467^788852481Norbert Schneider05/2018
95182^174329-1126552479Enzo Doria06/2014
95192^174314-124152474Yves Minet05/2009
952052^30577-5152471Norbert Schneider08/2014
95219403^13206-13206^940352471Norbert Schneider12/2017
952215692^2205+2205^1569252465Hans Havermann06/2016
9523(2^174281-7)/62881702961552453Lelio R Paula02/2012
9524(2^174240+5)/352451Lelio R Paula02/2012
9525(86*10^52450-221)/952451Robert Price06/2017
9526(62*10^52448-197)/952449Robert Price10/2017
9527(15*2^174221+1)/40352445Lelio R Paula07/2012
952826313!2-3252443Robert Price10/2015
9529(3*2^174214-1)/374872952438Lelio R Paula01/2014
95302*3^109900-552436Lelio R Paula03/2014
95324159^14488-15052432Enzo Doria07/2012
9531(89*10^52431-71)/952432Robert Price11/2015
95332^174170-394152431Yves Minet04/2017
9534(7*2^174171-1)/68552429Lelio R Paula01/2014
9535(260137^9679+1)/26013852409Faysal YAtim03/2008
95362^174098+7952409Lelio R Paula01/2011
953735^33940-221452406Enzo Doria03/2013
953815^44557+252404Ray Chandler07/2011
95392^174049-43952394Yves Minet01/2012
95406^67329+11552393Lelio R Paula10/2012
95422^174041+26214552392Lelio R Paula07/2009
9541141^24377+252392Lelio R Paula05/2013
9543lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
95442^174001-595552380Lelio R Paula07/2009
9545lucasV(-1,2,347969)52375Mike Oakes02/2017
95463^109764-14052371Lelio R Paula10/2012
95472*3^109761+752370Lelio R Paula03/2014
95489863^13112-13112^986352370Norbert Schneider10/2017
9550(145^24229+1)/14652366Richard Fischer02/2018
95498094^13399-13399^809452366Norbert Schneider03/2018
95512^173944-11225352363Enzo Doria06/2014
95532^173940+111152362Lelio R Paula01/2011
9552(3126^14983-1)/312552362Richard Fischer03/2015
955415214^2763+2763^1521452358Hans Havermann05/2016
955513200^9247+9247^1320052352Hans Havermann05/2016
9556(1017*2^173867-1)/717552339Lelio R Paula03/2015
955713732^6465+6465^1373252327Hans Havermann05/2016
9558(2^173867-1)/5253663750268952326Donovan Johnson06/2005
95592^173811-68487752323Paul Bourdelais11/2012
95602^173807-595552322Lelio R Paula06/2009
95612^173796-104468952318Paul Bourdelais11/2012
956210^52317+6449752318Patrick De Geest12/2012
956310^52317+6474352318Patrick De Geest12/2012
956510^52317-7152317Robert Price05/2011
956410821^12968+12968^1082152317Norbert Schneider04/2016
9566(298*10^52308-7)/352310Robert Price06/2017
9567(2^173778-3)/5795952308Lelio R Paula02/2012
956810232^13043-13043^1023252302Norbert Schneider08/2017
95692^173727+952298Lelio R Paula01/2011
9570(14^45631+13^45631)/2752298Robert Price04/2013
957137856!3+656152293Robert Price11/2015
95724*3^109596+552292Lelio R Paula03/2014
957315436^2441+2441^1543652291Hans Havermann05/2016
957443^32005+2452280Robert Price11/2013
95752^173650-16552274Lelio R Paula02/2011
95764*10^52272+9352273Robert Price01/2017
957719^40873+8452267Lelio R Paula01/2013
95782^173621+424242952266Jason Earls09/2008
95799999^13064-13064^999952256Norbert Schneider09/2017
9580numbpart(46909^2-1)52247Serge Batalov04/2017
958114^45579-3152240Lelio R Paula01/2013
95827395^13502-13502^739552239Norbert Schneider05/2018
9583(10223*2^173518+1)/90352236Lelio R Paula05/2014
958420^40147-612352233Enzo Doria03/2013
95854^86754-3^(86754+1)52232Robert Price04/2016
95867452^13487-13487^745252226Norbert Schneider05/2018
95872^173477-343352222Yves Minet04/2009
9588(22*10^52217-73)/352218Robert Price09/2017
9589(25*2^173446+1)/6152213Lelio R Paula07/2012
95903^109431-3852212Lelio R Paula10/2012
95912^173424-395952206Yves Minet04/2017
959213^46861-7252201Lelio R Paula01/2013
95932^173373-136352191Yves Minet03/2009
959411^50114-174052189Enzo Doria11/2012
959513735^6304+6304^1373552188Hans Havermann05/2016
959611^50111-111052186Enzo Doria11/2012
9597lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
959820^40105-858352178Enzo Doria03/2013
9599(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
96002^173314-394152173Yves Minet04/2017
96012^173294+115552167Lelio R Paula07/2012
9603(19*2^173301-1)/2348952166Lelio R Paula01/2014
960215146^2781+2781^1514652166Hans Havermann06/2016
960411^50088-3252162Lelio R Paula01/2013
96053^109320+23652159Lelio R Paula10/2012
96062^173246-2863552153Lelio R Paula06/2009
96072*10^52147+1152148Robert Price01/2015
96087605^13436-13436^760552147Norbert Schneider04/2018
96092^173208-11262552141Enzo Doria06/2014
9610(9179*2^173206-1)/203552141Lelio R Paula03/2015
961115^44333-7652140Lelio R Paula01/2013
96122^173187-318952135Yves Minet10/2014
96132^173167+7557952129Enzo Doria04/2016
9614(2^173169+7)/9279352125Lelio R Paula02/2012
9615(25*10^52119+23)/352120Robert Price06/2017
96169*7^61671+452119Lelio R Paula09/2014
96182^173130-922152118Lelio R Paula07/2008
9617(17*2^173129-1)/352118Lelio R Paula01/2014
9619215^22342-21652112Karsten Bonath04/2018
96202^173100-11255952109Enzo Doria06/2014
96212^173091-11233952106Enzo Doria06/2014
962270797!6-3252106Robert Price08/2018
962311^50030+2852101Lelio R Paula01/2013
9624(59*10^52099+13)/952100Robert Price09/2015
96252^173064-182952098Yves Minet09/2012
96262^173062-136152097Yves Minet08/2012
96273^109190-7052097Lelio R Paula10/2012
96282^173059+9019552096Lelio R Paula07/2012
96292^173048-11262552093Enzo Doria06/2014
963092^26524+9152088Norbert Schneider04/2013
963141^32295-4052085Theodore Burton02/2007
96322^173002+17752079Lelio R Paula02/2011
9633p(11334)#/2+852075Robert Price01/2017
96342^172965-11236352068Enzo Doria06/2014
96359*2^172935+752060Lelio R Paula03/2014
963611^49978-819052047Enzo Doria02/2013
963710^52041+63352042Patrick De Geest11/2012
96388494^13245-13245^849452042Norbert Schneider01/2018
963910^52041-9352041Robert Price05/2011
9640(21*2^172815-1)/86952021Lelio R Paula01/2014
9641(182*10^52018+1)/352020Robert Price02/2017
96424*6^66843-552015Lelio R Paula09/2014
96437732^13377-13377^773252014Norbert Schneider03/2018
964419^40670-5452007Lelio R Paula01/2013
96452^172756-11288352005Enzo Doria06/2014
964611832^12763-12763^1183251985Norbert Schneider02/2017
96477^61511-3651983Lelio R Paula10/2012
964810591^12914-12914^1059151979Norbert Schneider05/2017
96492^172640-7551970Lelio R Paula01/2011
96506792^13559-13559^679251959Norbert Schneider07/2018
96517750^13359-13359^775051958Norbert Schneider03/2018
9652gcd(V(932265),5*F(186453)*(F(186453)-1)+1)51953Serge Batalov04/2015
965312240^12709-12709^1224051952Norbert Schneider01/2017
9654t(173589)51951Robert Price12/2014
96557^61469+3451948Lelio R Paula10/2012
96569*2^172553-751945Lelio R Paula03/2014
965711542^12787+12787^1154251945Norbert Schneider01/2016
965835^33640-708651943Enzo Doria03/2013
9659(7*2^172534+1)/247951936Lelio R Paula07/2012
96607353^13430-13430^735351927Norbert Schneider04/2018
9661(2^86243+43467)^2+(2^86243+43467)+4151924Makoto Morimoto05/2016
9662(2^86243+84085)^2+(2^86243+84085)+4151924Makoto Morimoto05/2016
9663((2^86243+75146)^2+(2^86243+75146)+41)/6151922Makoto Morimoto05/2016
9664((2^86243+8692)^2+(2^86243+8692)+41)/301151920Makoto Morimoto05/2016
9665((2^86243+30085)^2+(2^86243+30085)+41)/41/19951920Makoto Morimoto05/2016
9666((2^86243+36540)^2+(2^86243+36540)+41)/43/64751920Makoto Morimoto05/2016
96682^172470+751919Lelio R Paula01/2011
9667((2^86243+76136)^2+(2^86243+76136)+41)/6050951919Makoto Morimoto05/2016
9669((2^86243+50999)^2+(2^86243+50999)+41)/249686951918Makoto Morimoto05/2016
9670((2^86243+80760)^2+(2^86243+80760)+41)/93048151918Makoto Morimoto05/2016
9671((2^86243+26732)^2+(2^86243+26732)+41)/223/9651751917Makoto Morimoto05/2016
9672((2^86243+51479)^2+(2^86243+51479)+41)/1607/2202751916Makoto Morimoto05/2016
96752^172455+1551915Lelio R Paula01/2011
9673((2^86243+27637)^2+(2^86243+27637)+41)/2693/51843151915Makoto Morimoto05/2016
9674((2^86243+82275)^2+(2^86243+82275)+41)/71/930992951915Makoto Morimoto05/2016
9676((2^86243+57757)^2+(2^86243+57757)+41)/30871/62272951914Makoto Morimoto05/2016
9677((2^86243+18643)^2+(2^86243+18643)+41)/47/23071/6529351913Makoto Morimoto05/2016
9678((2^86243+8693)^2+(2^86243+8693)+41)/494107/293389151912Makoto Morimoto05/2016
9679((2^86243+8250)^2+(2^86243+8250)+41)/223/34877/147262351911Makoto Morimoto05/2016
9680((2^86243+51745)^2+(2^86243+51745)+41)/71/95891/217129351911Makoto Morimoto05/2016
9681((2^86243+29592)^2+(2^86243+29592)+41)/7717/11933/1256650951909Makoto Morimoto05/2016
96825^74263+5451908Lelio R Paula10/2012
968313804^5755+5755^1380451904Hans Havermann05/2016
96847*2^172403-351900Henri Lifchitz06/2003
9685t(196078)51892Robert Price02/2014
96862*3^108759-751892Lelio R Paula03/2014
9687(94*10^51889+11)/351891Robert Price02/2017
9688(73*10^51889+17)/951890Robert Price10/2015
968935^33603-402651886Enzo Doria03/2013
96902^172350-10751883Lelio R Paula02/2011
969114419^3960+3960^1441951876Hans Havermann05/2016
96922^172325-11318551875Enzo Doria07/2014
969310^51872+10068351873Patrick De Geest06/2016
969410^51872-100000000151872Robert Price05/2016
969510^51872-10014951872Patrick De Geest06/2016
96962147092^8192+6351871Jens K. Andersen04/2009
969713^46564-2451870Lelio R Paula01/2013
969810524^12893-12893^1052451858Norbert Schneider05/2017
969913981^5110+5110^1398151848Hans Havermann05/2016
97002^172228+7626151846Enzo Doria04/2016
970111^49772-126051833Enzo Doria11/2012
9702(11*2^172157-1)/35151823Lelio R Paula01/2014
9703(43*10^51816-403)/951817Robert Price04/2017
97049001^13102-11451810Enzo Doria07/2012
9705(80051^10567+1)/8005251809Faysal YAtim07/2007
97062^172101-6151808Lelio R Paula01/2011
9707(2^172125+3)/3112550551808Lelio R Paula02/2012
97089*7^61301+451807Lelio R Paula09/2014
9709(23*2^172090-1)/3650951802Lelio R Paula01/2014
97102^172074+145951800Lelio R Paula07/2008
97112^172063+16551797Lelio R Paula02/2011
9712(21181*2^172061+1)/1814751796Lelio R Paula05/2014
9713(56*10^51793+367)/951794Robert Price10/2017
971428^35785-2751787Norbert Schneider01/2014
9715(65*10^51778+43)/951779Ray Chandler09/2010
9716(15185*2^171975-1)/351774Lelio R Paula03/2015
97172^171978-11329751771Enzo Doria07/2014
971811^49708+7851766Lelio R Paula01/2013
9719(26*10^51764-107)/951765Robert Price07/2016
972012^47956-9751754Lelio R Paula12/2012
97212^171907-351151750Yves Minet03/2017
97228203^13220-13220^820351743Norbert Schneider12/2017
97237706^13307-13307^770651723Norbert Schneider02/2018
97248*10^51721+8751722Robert Price10/2017
972510306^12885-12885^1030651709Norbert Schneider05/2017
9726(12611^12611+311)/2/13/1357790351707Makoto Morimoto07/2016
9727(3*2^171761+1)/2951705Lelio R Paula07/2012
9728t(195346)51699Robert Price07/2014
972913^46409+4651697Lelio R Paula01/2013
97302^171663+1155*17166351676Henri Lifchitz01/2005
973115^43937+2651674Lelio R Paula01/2013
9732(3^108312-7)/12452651673Lelio R Paula03/2012
9733(12601^12601+465)/2/13151667Makoto Morimoto07/2016
9734(79*10^51663-97)/9951663Ray Chandler11/2010
973548589!4+102451656Robert Price08/2017
9738(10^51652-31)/351652Serge Batalov12/2014
97372^171583+7379351652Enzo Doria04/2016
9736(28*10^51651-31)/351652Robert Price10/2017
973912^47861-3551651Lelio R Paula12/2012
97406^66369-2681351646Enzo Doria03/2013
9741Phi(83967,10)/227248288951639Maksym Voznyy01/2010
97422^171524+15351634Lelio R Paula02/2011
9743(2^171516-509203)/486951628Lelio R Paula05/2012
9744(12589^12589+323)/2^5/351613Makoto Morimoto07/2016
97455*10^51608-8151609Robert Price04/2017
9746(lucasV(1,2,342870)+2)/(13*25933*242617)51597Mike Oakes03/2017
9747(2*10^51597-23)/351597Robert Price09/2017
974810171^12872-12872^1017151583Norbert Schneider04/2017
97492^171351-11267751582Enzo Doria06/2014
9750(12583^12583+1695)/2/11^2/753508951579Makoto Morimoto07/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 14 2018 21:45 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!