PRP Records

Probable Primes Top 10000

(211563 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 ?
92514159^14747-14053370Enzo Doria07/2012
9252(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9253p(11586)#/2+3253357Robert Price12/2016
925415^45362-4653350Lelio R Paula01/2013
925514147^5892+5892^1414753338Hans Havermann07/2016
92567^63109+4653334Lelio R Paula10/2012
925720^40986-134353325Enzo Doria03/2013
92584*10^53324-8953325Robert Price08/2017
925920^40977-888353313Enzo Doria03/2013
92603^111711+266053300Lelio R Paula10/2012
92612^177040-1186553295Enzo Doria10/2012
9262(7*10^53287+17)/353288Erik Branger03/2014
926335^34506-1075853280Enzo Doria03/2013
9264(11*10^53274-17)/353275Erik Branger03/2014
9265(1017*2^176971-1)/33553275Lelio R Paula03/2015
92662^176961-283353271Yves Minet09/2014
92673^111642+11053267Lelio R Paula10/2012
926817^43290-9853267Lelio R Paula01/2013
92697^63028+3653265Lelio R Paula10/2012
9270(22*10^53264+71)/353265Robert Price05/2017
92717^63023-3653261Lelio R Paula10/2012
927219783^492+492^1978353256Anatoly F. Selevich02/2007
927313350^9739+9739^1335053247Hans Havermann10/2015
927414394^4993+4993^1439453235Hans Havermann10/2015
92752^176823-11280753230Enzo Doria06/2014
92761684^16495+16495^168453219Serge Batalov05/2014
927715277^3042+3042^1527753213Hans Havermann06/2016
9278(50322^11317-1)/5032153206Serge Batalov04/2015
92792^176742-159553205Lelio R Paula10/2009
9280(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
9281(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9282(3*2^176696-1)/29953189Lelio R Paula01/2014
9283(7*10^53185-1)/353186Erik Branger03/2014
92842^176629+46553171Lelio R Paula07/2012
9285(3*2^176604-1)/35953162Lelio R Paula01/2014
928610955^13158-13158^1095553154Norbert Schneider11/2017
92875^76038-1436653149Enzo Doria02/2013
928815156^3209+3209^1515653143Hans Havermann06/2016
92892^176532-283753142Yves Minet09/2014
929052^30967-5153140Norbert Schneider08/2014
92919*5^76023-253139Lelio R Paula09/2014
9292(14283!+1)/46421617753135Michael Porter03/2016
92932^176461-16553121Lelio R Paula02/2011
9294(62*10^53111+1)/953112Serge Batalov05/2010
92952^176403-13953103Lelio R Paula02/2011
929655^30508-253095Lelio R Paula08/2013
9297(48591^11329-1)/4859053090Serge Batalov04/2015
92983^111254-8853082Lelio R Paula10/2012
929915^45129-5653076Lelio R Paula01/2013
93002^176293-7353070Lelio R Paula01/2011
9301(67*10^53068+41)/953069Robert Price09/2015
930215271^2986+2986^1527153069Hans Havermann06/2016
93032^176255-66753059Yves Minet01/2012
930436471*2^176221+864753053Paul Vanderveen04/2016
9305(19*10^53049-1)/953050Serge Batalov03/2009
93069*2^176203-553044Lelio R Paula03/2014
93072^176205-9439553043Lelio R Paula08/2011
9308(19*2^176224-1)/21791691353042Lelio R Paula01/2014
93098600^13481-13481^860053041Norbert Schneider05/2018
931017^43103+1453037Lelio R Paula01/2013
9311(31*2^176188-1)/355553036Lelio R Paula01/2014
93122^176177+6094753035David Broadhurst05/2002
9313(22*10^53033-7)/353034Erik Branger09/2014
931413810^6909+6909^1381053023Hans Havermann06/2016
93162^176108+1609553014Lelio R Paula10/2009
93152^176107+1891553014Lelio R Paula07/2012
93173^111080-962852999Enzo Doria02/2013
93182^176047-155152996Yves Minet08/2012
93192^176042+7351952994Enzo Doria04/2016
9320lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
93212^175984-11225952977Enzo Doria06/2014
932211^50870+1052976Lelio R Paula01/2013
9323(11*10^52956+19)/352957Robert Price03/2016
9324gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9325(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9326(98*10^52931-89)/9952931Ray Chandler11/2010
932713774^6963+6963^1377452931Hans Havermann06/2016
93282^175812-136752925Yves Minet05/2013
93292^175801+1155*17580152922Henri Lifchitz01/2005
933011^50801-909052904Enzo Doria02/2013
933143^32374+1252882Robert Price11/2013
93322^175628+1352870Lelio R Paula01/2011
93332^175615-174752866Yves Minet09/2012
9334(13*10^52861+107)/352862Robert Price11/2017
93359*2^175586-752858Lelio R Paula03/2014
933612174^12937+12937^1217452854Norbert Schneider04/2016
9337(15*2^175565+1)/835952848Lelio R Paula07/2012
9338(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
933914256^5077+5077^1425652828Hans Havermann06/2016
93402^175467+8287552821Lelio R Paula07/2012
9341(7*10^52819+167)/352820Robert Kinser10/2017
9342(67607*2^175426+1)/352813Lelio R Paula05/2014
934313^47400-6052801Lelio R Paula01/2013
93444*10^52792+6352793Robert Price06/2016
9346(78557*2^175360+1)/308752791Lelio R Paula06/2014
934518^42055-292952791Enzo Doria03/2013
93479*5^75521+252788Lelio R Paula09/2014
93486^67814+3152770Lelio R Paula10/2012
934970^28600+6952770Norbert Schneider10/2012
935014^46038+9752766Lelio R Paula01/2013
9351(61*10^52763-7)/952764Serge Batalov02/2009
93522*5^75474+952755Lelio R Paula09/2014
935310^52753+282643060952754Robert Price05/2015
935410^52753+18399752754Patrick De Geest01/2016
935510^52753-5015352753Patrick De Geest03/2016
935619846^455+455^1984652751Anatoly F. Selevich02/2007
93572^175217+7297752746Enzo Doria04/2016
9358p(11466)#/2-25652746Robert Price05/2017
9359(4*10^52740+41)/952740Robert Price11/2014
93602^175189+538552738Lelio R Paula08/2009
93612^175160+938552729Lelio R Paula07/2008
936212356^12885+12885^1235652724Norbert Schneider03/2016
93632^175137+1152722Lelio R Paula01/2011
936465^29077-64^2907752715Robert Price08/2013
93652*10^52713-8752714Robert Price06/2016
93662^175106-46552713Lelio R Paula08/2009
93672^175089-5869552708Lelio R Paula08/2009
93692^175045+19552694Lelio R Paula02/2011
9368195^23010-252694Lelio R Paula10/2017
93702^175025+14952688Lelio R Paula02/2011
9372(19^41201+1)/2052685Paul Bourdelais03/2010
9371(436*10^52683-13)/952685Robert Price10/2017
93732*12^48815-5^4881552681Mike Oakes10/2010
9374335^20862-20862^33552678Norbert Schneider09/2015
93752^174983-760552676Lelio R Paula07/2009
93764*10^52667+1952668Robert Price04/2016
9377(10^52667+77)/352667Robert Price01/2017
937811434^12977+12977^1143452664Norbert Schneider04/2016
93792^174941-120352663Lelio R Paula07/2009
93808501^13400-13400^850152655Norbert Schneider03/2018
93812^174910+1270552654Lelio R Paula07/2012
93823^110338+7452645Lelio R Paula10/2012
93835^75303+1252635Lelio R Paula10/2012
93842^174836+25525552631Lelio R Paula07/2009
9385(66^28921+1)/6752622Paul Bourdelais08/2017
938620^40443+952618Lelio R Paula01/2013
9387(11*2^174788+1)/952617Lelio R Paula01/2012
9388(11*2^174786-1)/70352615Lelio R Paula01/2014
938911^50520-129052612Enzo Doria11/2012
9390(10^52608-19)/952608Robert Price10/2017
9391(9913*2^174736-1)/33352603Lelio R Paula03/2015
939213145^10024+10024^1314552594Hans Havermann05/2016
93935003^14217-15052592Enzo Doria07/2012
93942^174698-405552590Yves Minet02/2018
939519^41123+1052587Lelio R Paula01/2013
93962^174683+1290952585Lelio R Paula01/2011
93972^174643+5952573Lelio R Paula01/2011
9398(1017*2^174640-1)/77352572Lelio R Paula03/2015
939913529^7662+7662^1352952552Hans Havermann06/2016
9400121421#+18876752548Makoto Morimoto02/2016
940120^40375-592352530Enzo Doria03/2013
9402(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9403(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
94042^174462+34552519Lelio R Paula07/2009
9405t(178863)52509Robert Price10/2014
94062^174416+85552505Lelio R Paula07/2009
94076^67467-10352500Lelio R Paula10/2012
9408(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
94097888^13467-13467^788852481Norbert Schneider05/2018
94102^174329-1126552479Enzo Doria06/2014
94112^174314-124152474Yves Minet05/2009
941252^30577-5152471Norbert Schneider08/2014
94139403^13206-13206^940352471Norbert Schneider12/2017
941415692^2205+2205^1569252465Hans Havermann06/2016
9415(2^174281-7)/62881702961552453Lelio R Paula02/2012
9416(2^174240+5)/352451Lelio R Paula02/2012
9417(86*10^52450-221)/952451Robert Price06/2017
9418(62*10^52448-197)/952449Robert Price10/2017
9419(15*2^174221+1)/40352445Lelio R Paula07/2012
942026313!2-3252443Robert Price10/2015
9421(3*2^174214-1)/374872952438Lelio R Paula01/2014
94222*3^109900-552436Lelio R Paula03/2014
94244159^14488-15052432Enzo Doria07/2012
9423(89*10^52431-71)/952432Robert Price11/2015
94252^174170-394152431Yves Minet04/2017
9426(7*2^174171-1)/68552429Lelio R Paula01/2014
9428(260137^9679+1)/26013852409Faysal YAtim03/2008
94272^174098+7952409Lelio R Paula01/2011
942935^33940-221452406Enzo Doria03/2013
943015^44557+252404Ray Chandler07/2011
94312^174049-43952394Yves Minet01/2012
94326^67329+11552393Lelio R Paula10/2012
94342^174041+26214552392Lelio R Paula07/2009
9433141^24377+252392Lelio R Paula05/2013
9435lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
94362^174001-595552380Lelio R Paula07/2009
9437lucasV(-1,2,347969)52375Mike Oakes02/2017
94383^109764-14052371Lelio R Paula10/2012
94392*3^109761+752370Lelio R Paula03/2014
94409863^13112-13112^986352370Norbert Schneider10/2017
9442(145^24229+1)/14652366Richard Fischer02/2018
94418094^13399-13399^809452366Norbert Schneider03/2018
94432^173944-11225352363Enzo Doria06/2014
94452^173940+111152362Lelio R Paula01/2011
9444(3126^14983-1)/312552362Richard Fischer03/2015
944615214^2763+2763^1521452358Hans Havermann05/2016
944713200^9247+9247^1320052352Hans Havermann05/2016
9448(1017*2^173867-1)/717552339Lelio R Paula03/2015
944913732^6465+6465^1373252327Hans Havermann05/2016
9450(2^173867-1)/5253663750268952326Donovan Johnson06/2005
94512^173811-68487752323Paul Bourdelais11/2012
94522^173807-595552322Lelio R Paula06/2009
94532^173796-104468952318Paul Bourdelais11/2012
945410^52317+6449752318Patrick De Geest12/2012
945510^52317+6474352318Patrick De Geest12/2012
945610^52317-7152317Robert Price05/2011
945710821^12968+12968^1082152317Norbert Schneider04/2016
9458(298*10^52308-7)/352310Robert Price06/2017
9459(2^173778-3)/5795952308Lelio R Paula02/2012
946010232^13043-13043^1023252302Norbert Schneider08/2017
94612^173727+952298Lelio R Paula01/2011
9462(14^45631+13^45631)/2752298Robert Price04/2013
946337856!3+656152293Robert Price11/2015
94644*3^109596+552292Lelio R Paula03/2014
946515436^2441+2441^1543652291Hans Havermann05/2016
946643^32005+2452280Robert Price11/2013
94672^173650-16552274Lelio R Paula02/2011
94684*10^52272+9352273Robert Price01/2017
946919^40873+8452267Lelio R Paula01/2013
94702^173621+424242952266Jason Earls09/2008
94719999^13064-13064^999952256Norbert Schneider09/2017
9472numbpart(46909^2-1)52247Serge Batalov04/2017
947314^45579-3152240Lelio R Paula01/2013
94747395^13502-13502^739552239Norbert Schneider05/2018
9475(10223*2^173518+1)/90352236Lelio R Paula05/2014
947620^40147-612352233Enzo Doria03/2013
94774^86754-3^(86754+1)52232Robert Price04/2016
94787452^13487-13487^745252226Norbert Schneider05/2018
94792^173477-343352222Yves Minet04/2009
9480(22*10^52217-73)/352218Robert Price09/2017
9481(25*2^173446+1)/6152213Lelio R Paula07/2012
94823^109431-3852212Lelio R Paula10/2012
94832^173424-395952206Yves Minet04/2017
948413^46861-7252201Lelio R Paula01/2013
94852^173373-136352191Yves Minet03/2009
948611^50114-174052189Enzo Doria11/2012
948713735^6304+6304^1373552188Hans Havermann05/2016
948811^50111-111052186Enzo Doria11/2012
9489lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
949020^40105-858352178Enzo Doria03/2013
9491(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
94922^173314-394152173Yves Minet04/2017
94932^173294+115552167Lelio R Paula07/2012
9495(19*2^173301-1)/2348952166Lelio R Paula01/2014
949415146^2781+2781^1514652166Hans Havermann06/2016
949611^50088-3252162Lelio R Paula01/2013
94973^109320+23652159Lelio R Paula10/2012
94982^173246-2863552153Lelio R Paula06/2009
94992*10^52147+1152148Robert Price01/2015
95007605^13436-13436^760552147Norbert Schneider04/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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