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 ?
9501(7*10^53287+17)/353288Erik Branger03/2014
950235^34506-1075853280Enzo Doria03/2013
9503(11*10^53274-17)/353275Erik Branger03/2014
9504(1017*2^176971-1)/33553275Lelio R Paula03/2015
95052^176961-283353271Yves Minet09/2014
95063^111642+11053267Lelio R Paula10/2012
950717^43290-9853267Lelio R Paula01/2013
95087^63028+3653265Lelio R Paula10/2012
9509(22*10^53264+71)/353265Robert Price05/2017
95107^63023-3653261Lelio R Paula10/2012
951119783^492+492^1978353256Anatoly F. Selevich02/2007
951213350^9739+9739^1335053247Hans Havermann10/2015
951314394^4993+4993^1439453235Hans Havermann10/2015
95142^176823-11280753230Enzo Doria06/2014
95151684^16495+16495^168453219Serge Batalov05/2014
951615277^3042+3042^1527753213Hans Havermann06/2016
9517(50322^11317-1)/5032153206Serge Batalov04/2015
95182^176742-159553205Lelio R Paula10/2009
9519(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
952072149!6-1253200Robert Price08/2018
9521(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9522(3*2^176696-1)/29953189Lelio R Paula01/2014
9523(7*10^53185-1)/353186Erik Branger03/2014
95242^176629+46553171Lelio R Paula07/2012
9525(3*2^176604-1)/35953162Lelio R Paula01/2014
952610955^13158-13158^1095553154Norbert Schneider11/2017
95275^76038-1436653149Enzo Doria02/2013
952815156^3209+3209^1515653143Hans Havermann06/2016
95292^176532-283753142Yves Minet09/2014
953052^30967-5153140Norbert Schneider08/2014
95319*5^76023-253139Lelio R Paula09/2014
9532(14283!+1)/46421617753135Michael Porter03/2016
95332^176461-16553121Lelio R Paula02/2011
9534(62*10^53111+1)/953112Serge Batalov05/2010
95352^176403-13953103Lelio R Paula02/2011
953655^30508-253095Lelio R Paula08/2013
9537(48591^11329-1)/4859053090Serge Batalov04/2015
95383^111254-8853082Lelio R Paula10/2012
953915^45129-5653076Lelio R Paula01/2013
9540(640^18913-1)/63953071Eric Chen09/2018
95412^176293-7353070Lelio R Paula01/2011
9543(67*10^53068+41)/953069Robert Price09/2015
954215271^2986+2986^1527153069Hans Havermann06/2016
95442^176255-66753059Yves Minet01/2012
954536471*2^176221+864753053Paul Vanderveen04/2016
9546(19*10^53049-1)/953050Serge Batalov03/2009
95479*2^176203-553044Lelio R Paula03/2014
95482^176205-9439553043Lelio R Paula08/2011
9549(19*2^176224-1)/21791691353042Lelio R Paula01/2014
95508600^13481-13481^860053041Norbert Schneider05/2018
955117^43103+1453037Lelio R Paula01/2013
9552(31*2^176188-1)/355553036Lelio R Paula01/2014
95532^176177+6094753035David Broadhurst05/2002
9554(22*10^53033-7)/353034Erik Branger09/2014
955513810^6909+6909^1381053023Hans Havermann06/2016
95572^176108+1609553014Lelio R Paula10/2009
95562^176107+1891553014Lelio R Paula07/2012
95583^111080-962852999Enzo Doria02/2013
95592^176047-155152996Yves Minet08/2012
95602^176042+7351952994Enzo Doria04/2016
9561lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
95622^175984-11225952977Enzo Doria06/2014
956311^50870+1052976Lelio R Paula01/2013
9564(11*10^52956+19)/352957Robert Price03/2016
9565gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9566(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9567(98*10^52931-89)/9952931Ray Chandler11/2010
956813774^6963+6963^1377452931Hans Havermann06/2016
95692^175812-136752925Yves Minet05/2013
95702^175801+1155*17580152922Henri Lifchitz01/2005
957111^50801-909052904Enzo Doria02/2013
95727803^13592-13592^780352904Norbert Schneider07/2018
957343^32374+1252882Robert Price11/2013
95742^175628+1352870Lelio R Paula01/2011
95752^175615-174752866Yves Minet09/2012
9576(13*10^52861+107)/352862Robert Price11/2017
95779*2^175586-752858Lelio R Paula03/2014
957812174^12937+12937^1217452854Norbert Schneider04/2016
9579(15*2^175565+1)/835952848Lelio R Paula07/2012
9580(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
958114256^5077+5077^1425652828Hans Havermann06/2016
95822^175467+8287552821Lelio R Paula07/2012
9583(7*10^52819+167)/352820Robert Kinser10/2017
9585(67607*2^175426+1)/352813Lelio R Paula05/2014
958471671!6-3252813Robert Price08/2018
958613^47400-6052801Lelio R Paula01/2013
95874*10^52792+6352793Robert Price06/2016
9589(78557*2^175360+1)/308752791Lelio R Paula06/2014
958818^42055-292952791Enzo Doria03/2013
95909*5^75521+252788Lelio R Paula09/2014
95916^67814+3152770Lelio R Paula10/2012
959270^28600+6952770Norbert Schneider10/2012
959314^46038+9752766Lelio R Paula01/2013
9594(61*10^52763-7)/952764Serge Batalov02/2009
95952*5^75474+952755Lelio R Paula09/2014
959610^52753+282643060952754Robert Price05/2015
959710^52753+18399752754Patrick De Geest01/2016
959810^52753-5015352753Patrick De Geest03/2016
959919846^455+455^1984652751Anatoly F. Selevich02/2007
96012^175217+7297752746Enzo Doria04/2016
9600p(11466)#/2-25652746Robert Price05/2017
9602(4*10^52740+41)/952740Robert Price11/2014
96032^175189+538552738Lelio R Paula08/2009
96042^175160+938552729Lelio R Paula07/2008
960512356^12885+12885^1235652724Norbert Schneider03/2016
96062^175137+1152722Lelio R Paula01/2011
960765^29077-64^2907752715Robert Price08/2013
96082*10^52713-8752714Robert Price06/2016
96092^175106-46552713Lelio R Paula08/2009
96102^175089-5869552708Lelio R Paula08/2009
96112^175045+19552694Lelio R Paula02/2011
9612195^23010-252694Lelio R Paula10/2017
96132^175025+14952688Lelio R Paula02/2011
9614(19^41201+1)/2052685Paul Bourdelais03/2010
9615(436*10^52683-13)/952685Robert Price10/2017
96162*12^48815-5^4881552681Mike Oakes10/2010
9617335^20862-20862^33552678Norbert Schneider09/2015
96182^174983-760552676Lelio R Paula07/2009
96194*10^52667+1952668Robert Price04/2016
9620(10^52667+77)/352667Robert Price01/2017
962111434^12977+12977^1143452664Norbert Schneider04/2016
96222^174941-120352663Lelio R Paula07/2009
96238501^13400-13400^850152655Norbert Schneider03/2018
96242^174910+1270552654Lelio R Paula07/2012
96253^110338+7452645Lelio R Paula10/2012
96265^75303+1252635Lelio R Paula10/2012
96272^174836+25525552631Lelio R Paula07/2009
9628(66^28921+1)/6752622Paul Bourdelais08/2017
962920^40443+952618Lelio R Paula01/2013
9630(11*2^174788+1)/952617Lelio R Paula01/2012
9631(11*2^174786-1)/70352615Lelio R Paula01/2014
963211^50520-129052612Enzo Doria11/2012
9633(670^18617-1)/66952611Eric Chen09/2018
9634(10^52608-19)/952608Robert Price10/2017
9635(9913*2^174736-1)/33352603Lelio R Paula03/2015
963613145^10024+10024^1314552594Hans Havermann05/2016
96375003^14217-15052592Enzo Doria07/2012
96382^174698-405552590Yves Minet02/2018
963919^41123+1052587Lelio R Paula01/2013
96402^174683+1290952585Lelio R Paula01/2011
96412^174643+5952573Lelio R Paula01/2011
9642(1017*2^174640-1)/77352572Lelio R Paula03/2015
964313529^7662+7662^1352952552Hans Havermann06/2016
9644121421#+18876752548Makoto Morimoto02/2016
964520^40375-592352530Enzo Doria03/2013
9646(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9647(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
96482^174462+34552519Lelio R Paula07/2009
9649t(178863)52509Robert Price10/2014
96502^174416+85552505Lelio R Paula07/2009
96516^67467-10352500Lelio R Paula10/2012
9652(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
96537888^13467-13467^788852481Norbert Schneider05/2018
96542^174329-1126552479Enzo Doria06/2014
96552^174314-124152474Yves Minet05/2009
965652^30577-5152471Norbert Schneider08/2014
96579403^13206-13206^940352471Norbert Schneider12/2017
965815692^2205+2205^1569252465Hans Havermann06/2016
9659(2^174281-7)/62881702961552453Lelio R Paula02/2012
9660(2^174240+5)/352451Lelio R Paula02/2012
9661(86*10^52450-221)/952451Robert Price06/2017
9662(62*10^52448-197)/952449Robert Price10/2017
9663(15*2^174221+1)/40352445Lelio R Paula07/2012
966426313!2-3252443Robert Price10/2015
9665(3*2^174214-1)/374872952438Lelio R Paula01/2014
96662*3^109900-552436Lelio R Paula03/2014
96684159^14488-15052432Enzo Doria07/2012
9667(89*10^52431-71)/952432Robert Price11/2015
96692^174170-394152431Yves Minet04/2017
9670(7*2^174171-1)/68552429Lelio R Paula01/2014
9672(260137^9679+1)/26013852409Faysal YAtim03/2008
96712^174098+7952409Lelio R Paula01/2011
967335^33940-221452406Enzo Doria03/2013
967415^44557+252404Ray Chandler07/2011
96752^174049-43952394Yves Minet01/2012
96766^67329+11552393Lelio R Paula10/2012
96782^174041+26214552392Lelio R Paula07/2009
9677141^24377+252392Lelio R Paula05/2013
9679lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
96802^174001-595552380Lelio R Paula07/2009
9681lucasV(-1,2,347969)52375Mike Oakes02/2017
96823^109764-14052371Lelio R Paula10/2012
96842*3^109761+752370Lelio R Paula03/2014
96839863^13112-13112^986352370Norbert Schneider10/2017
9686(145^24229+1)/14652366Richard Fischer02/2018
96858094^13399-13399^809452366Norbert Schneider03/2018
96872^173944-11225352363Enzo Doria06/2014
96892^173940+111152362Lelio R Paula01/2011
9688(3126^14983-1)/312552362Richard Fischer03/2015
969015214^2763+2763^1521452358Hans Havermann05/2016
969113200^9247+9247^1320052352Hans Havermann05/2016
9692(1017*2^173867-1)/717552339Lelio R Paula03/2015
969313732^6465+6465^1373252327Hans Havermann05/2016
9694(2^173867-1)/5253663750268952326Donovan Johnson06/2005
96952^173811-68487752323Paul Bourdelais11/2012
96962^173807-595552322Lelio R Paula06/2009
96972^173796-104468952318Paul Bourdelais11/2012
969810^52317+6449752318Patrick De Geest12/2012
969910^52317+6474352318Patrick De Geest12/2012
970110^52317-7152317Robert Price05/2011
970010821^12968+12968^1082152317Norbert Schneider04/2016
9702(298*10^52308-7)/352310Robert Price06/2017
9703(2^173778-3)/5795952308Lelio R Paula02/2012
970410232^13043-13043^1023252302Norbert Schneider08/2017
97052^173727+952298Lelio R Paula01/2011
9706(14^45631+13^45631)/2752298Robert Price04/2013
970737856!3+656152293Robert Price11/2015
97084*3^109596+552292Lelio R Paula03/2014
970915436^2441+2441^1543652291Hans Havermann05/2016
971043^32005+2452280Robert Price11/2013
97112^173650-16552274Lelio R Paula02/2011
97124*10^52272+9352273Robert Price01/2017
971319^40873+8452267Lelio R Paula01/2013
97142^173621+424242952266Jason Earls09/2008
97159999^13064-13064^999952256Norbert Schneider09/2017
9716numbpart(46909^2-1)52247Serge Batalov04/2017
971714^45579-3152240Lelio R Paula01/2013
97187395^13502-13502^739552239Norbert Schneider05/2018
9719(10223*2^173518+1)/90352236Lelio R Paula05/2014
972020^40147-612352233Enzo Doria03/2013
97214^86754-3^(86754+1)52232Robert Price04/2016
97227452^13487-13487^745252226Norbert Schneider05/2018
97232^173477-343352222Yves Minet04/2009
9724(22*10^52217-73)/352218Robert Price09/2017
9725(25*2^173446+1)/6152213Lelio R Paula07/2012
97263^109431-3852212Lelio R Paula10/2012
97272^173424-395952206Yves Minet04/2017
972813^46861-7252201Lelio R Paula01/2013
97292^173373-136352191Yves Minet03/2009
973011^50114-174052189Enzo Doria11/2012
973113735^6304+6304^1373552188Hans Havermann05/2016
973211^50111-111052186Enzo Doria11/2012
9733lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
973420^40105-858352178Enzo Doria03/2013
9735(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
97362^173314-394152173Yves Minet04/2017
97372^173294+115552167Lelio R Paula07/2012
9739(19*2^173301-1)/2348952166Lelio R Paula01/2014
973815146^2781+2781^1514652166Hans Havermann06/2016
974011^50088-3252162Lelio R Paula01/2013
97413^109320+23652159Lelio R Paula10/2012
97422^173246-2863552153Lelio R Paula06/2009
97432*10^52147+1152148Robert Price01/2015
97447605^13436-13436^760552147Norbert Schneider04/2018
97452^173208-11262552141Enzo Doria06/2014
9746(9179*2^173206-1)/203552141Lelio R Paula03/2015
974715^44333-7652140Lelio R Paula01/2013
97482^173187-318952135Yves Minet10/2014
97492^173167+7557952129Enzo Doria04/2016
9750(2^173169+7)/9279352125Lelio R Paula02/2012


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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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