PRP Records

Probable Primes Top 10000

(225451 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 ?
950114147^5892+5892^1414753338Hans Havermann07/2016
95027^63109+4653334Lelio R Paula10/2012
950320^40986-134353325Enzo Doria03/2013
95044*10^53324-8953325Robert Price08/2017
950520^40977-888353313Enzo Doria03/2013
95063^111711+266053300Lelio R Paula10/2012
95072^177040-1186553295Enzo Doria10/2012
9508(7*10^53287+17)/353288Erik Branger03/2014
950935^34506-1075853280Enzo Doria03/2013
9510(11*10^53274-17)/353275Erik Branger03/2014
9511(1017*2^176971-1)/33553275Lelio R Paula03/2015
95122^176961-283353271Yves Minet09/2014
95133^111642+11053267Lelio R Paula10/2012
951417^43290-9853267Lelio R Paula01/2013
95157^63028+3653265Lelio R Paula10/2012
9516(22*10^53264+71)/353265Robert Price05/2017
95177^63023-3653261Lelio R Paula10/2012
951819783^492+492^1978353256Anatoly F. Selevich02/2007
951913350^9739+9739^1335053247Hans Havermann10/2015
952014394^4993+4993^1439453235Hans Havermann10/2015
95212^176823-11280753230Enzo Doria06/2014
95221684^16495+16495^168453219Serge Batalov05/2014
952315277^3042+3042^1527753213Hans Havermann06/2016
9524(50322^11317-1)/5032153206Serge Batalov04/2015
95252^176742-159553205Lelio R Paula10/2009
9526(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
952772149!6-1253200Robert Price08/2018
9528(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9529(3*2^176696-1)/29953189Lelio R Paula01/2014
9530(7*10^53185-1)/353186Erik Branger03/2014
95312^176629+46553171Lelio R Paula07/2012
9532(3*2^176604-1)/35953162Lelio R Paula01/2014
953310955^13158-13158^1095553154Norbert Schneider11/2017
95345^76038-1436653149Enzo Doria02/2013
953515156^3209+3209^1515653143Hans Havermann06/2016
95362^176532-283753142Yves Minet09/2014
953752^30967-5153140Norbert Schneider08/2014
95389*5^76023-253139Lelio R Paula09/2014
9539(14283!+1)/46421617753135Michael Porter03/2016
95402^176461-16553121Lelio R Paula02/2011
9541(62*10^53111+1)/953112Serge Batalov05/2010
95422^176403-13953103Lelio R Paula02/2011
954355^30508-253095Lelio R Paula08/2013
9544(48591^11329-1)/4859053090Serge Batalov04/2015
95453^111254-8853082Lelio R Paula10/2012
954615^45129-5653076Lelio R Paula01/2013
9547(640^18913-1)/63953071Eric Chen09/2018
95482^176293-7353070Lelio R Paula01/2011
9549(67*10^53068+41)/953069Robert Price09/2015
955015271^2986+2986^1527153069Hans Havermann06/2016
95512^176255-66753059Yves Minet01/2012
955236471*2^176221+864753053Paul Vanderveen04/2016
9553(19*10^53049-1)/953050Serge Batalov03/2009
95549*2^176203-553044Lelio R Paula03/2014
95552^176205-9439553043Lelio R Paula08/2011
9556(19*2^176224-1)/21791691353042Lelio R Paula01/2014
95578600^13481-13481^860053041Norbert Schneider05/2018
955817^43103+1453037Lelio R Paula01/2013
9559(31*2^176188-1)/355553036Lelio R Paula01/2014
95602^176177+6094753035David Broadhurst05/2002
9561(22*10^53033-7)/353034Erik Branger09/2014
956213810^6909+6909^1381053023Hans Havermann06/2016
95632^176108+1609553014Lelio R Paula10/2009
95642^176107+1891553014Lelio R Paula07/2012
95653^111080-962852999Enzo Doria02/2013
95662^176047-155152996Yves Minet08/2012
95672^176042+7351952994Enzo Doria04/2016
9568lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
95692^175984-11225952977Enzo Doria06/2014
957011^50870+1052976Lelio R Paula01/2013
9571(11*10^52956+19)/352957Robert Price03/2016
9572gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9573(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9575(98*10^52931-89)/9952931Ray Chandler11/2010
957413774^6963+6963^1377452931Hans Havermann06/2016
95762^175812-136752925Yves Minet05/2013
95772^175801+1155*17580152922Henri Lifchitz01/2005
957811^50801-909052904Enzo Doria02/2013
95797803^13592-13592^780352904Norbert Schneider07/2018
958043^32374+1252882Robert Price11/2013
95812^175628+1352870Lelio R Paula01/2011
95822^175615-174752866Yves Minet09/2012
9583(13*10^52861+107)/352862Robert Price11/2017
95849*2^175586-752858Lelio R Paula03/2014
958512174^12937+12937^1217452854Norbert Schneider04/2016
9586(15*2^175565+1)/835952848Lelio R Paula07/2012
9587(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
958814256^5077+5077^1425652828Hans Havermann06/2016
95892^175467+8287552821Lelio R Paula07/2012
9590(7*10^52819+167)/352820Robert Kinser10/2017
9592(67607*2^175426+1)/352813Lelio R Paula05/2014
959171671!6-3252813Robert Price08/2018
959313^47400-6052801Lelio R Paula01/2013
95944*10^52792+6352793Robert Price06/2016
9596(78557*2^175360+1)/308752791Lelio R Paula06/2014
959518^42055-292952791Enzo Doria03/2013
95979*5^75521+252788Lelio R Paula09/2014
95986^67814+3152770Lelio R Paula10/2012
959970^28600+6952770Norbert Schneider10/2012
960014^46038+9752766Lelio R Paula01/2013
9601(61*10^52763-7)/952764Serge Batalov02/2009
96022*5^75474+952755Lelio R Paula09/2014
960310^52753+282643060952754Robert Price05/2015
960410^52753+18399752754Patrick De Geest01/2016
960510^52753-5015352753Patrick De Geest03/2016
960619846^455+455^1984652751Anatoly F. Selevich02/2007
96072^175217+7297752746Enzo Doria04/2016
9608p(11466)#/2-25652746Robert Price05/2017
9609(4*10^52740+41)/952740Robert Price11/2014
96102^175189+538552738Lelio R Paula08/2009
96112^175160+938552729Lelio R Paula07/2008
961212356^12885+12885^1235652724Norbert Schneider03/2016
96132^175137+1152722Lelio R Paula01/2011
961465^29077-64^2907752715Robert Price08/2013
96152*10^52713-8752714Robert Price06/2016
96162^175106-46552713Lelio R Paula08/2009
96172^175089-5869552708Lelio R Paula08/2009
96192^175045+19552694Lelio R Paula02/2011
9618195^23010-252694Lelio R Paula10/2017
96202^175025+14952688Lelio R Paula02/2011
9621(19^41201+1)/2052685Paul Bourdelais03/2010
9622(436*10^52683-13)/952685Robert Price10/2017
96232*12^48815-5^4881552681Mike Oakes10/2010
9624335^20862-20862^33552678Norbert Schneider09/2015
96252^174983-760552676Lelio R Paula07/2009
96264*10^52667+1952668Robert Price04/2016
9627(10^52667+77)/352667Robert Price01/2017
962811434^12977+12977^1143452664Norbert Schneider04/2016
96292^174941-120352663Lelio R Paula07/2009
96308501^13400-13400^850152655Norbert Schneider03/2018
96312^174910+1270552654Lelio R Paula07/2012
96323^110338+7452645Lelio R Paula10/2012
96335^75303+1252635Lelio R Paula10/2012
96342^174836+25525552631Lelio R Paula07/2009
9635(66^28921+1)/6752622Paul Bourdelais08/2017
963620^40443+952618Lelio R Paula01/2013
9637(11*2^174788+1)/952617Lelio R Paula01/2012
9638(11*2^174786-1)/70352615Lelio R Paula01/2014
963911^50520-129052612Enzo Doria11/2012
9640(670^18617-1)/66952611Eric Chen09/2018
9641(10^52608-19)/952608Robert Price10/2017
9642(9913*2^174736-1)/33352603Lelio R Paula03/2015
964313145^10024+10024^1314552594Hans Havermann05/2016
96445003^14217-15052592Enzo Doria07/2012
96452^174698-405552590Yves Minet02/2018
964619^41123+1052587Lelio R Paula01/2013
96472^174683+1290952585Lelio R Paula01/2011
96482^174643+5952573Lelio R Paula01/2011
9649(1017*2^174640-1)/77352572Lelio R Paula03/2015
965013529^7662+7662^1352952552Hans Havermann06/2016
9651121421#+18876752548Makoto Morimoto02/2016
965220^40375-592352530Enzo Doria03/2013
9653(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9654(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
96552^174462+34552519Lelio R Paula07/2009
9656t(178863)52509Robert Price10/2014
96572^174416+85552505Lelio R Paula07/2009
96586^67467-10352500Lelio R Paula10/2012
9659(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
96607888^13467-13467^788852481Norbert Schneider05/2018
96612^174329-1126552479Enzo Doria06/2014
96622^174314-124152474Yves Minet05/2009
966352^30577-5152471Norbert Schneider08/2014
96649403^13206-13206^940352471Norbert Schneider12/2017
966515692^2205+2205^1569252465Hans Havermann06/2016
9666(2^174281-7)/62881702961552453Lelio R Paula02/2012
9667(2^174240+5)/352451Lelio R Paula02/2012
9668(86*10^52450-221)/952451Robert Price06/2017
9669(62*10^52448-197)/952449Robert Price10/2017
9670(15*2^174221+1)/40352445Lelio R Paula07/2012
967126313!2-3252443Robert Price10/2015
9672(3*2^174214-1)/374872952438Lelio R Paula01/2014
96732*3^109900-552436Lelio R Paula03/2014
96754159^14488-15052432Enzo Doria07/2012
9674(89*10^52431-71)/952432Robert Price11/2015
96762^174170-394152431Yves Minet04/2017
9677(7*2^174171-1)/68552429Lelio R Paula01/2014
9678(260137^9679+1)/26013852409Faysal YAtim03/2008
96792^174098+7952409Lelio R Paula01/2011
968035^33940-221452406Enzo Doria03/2013
968115^44557+252404Ray Chandler07/2011
96822^174049-43952394Yves Minet01/2012
96836^67329+11552393Lelio R Paula10/2012
96852^174041+26214552392Lelio R Paula07/2009
9684141^24377+252392Lelio R Paula05/2013
9686lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
96872^174001-595552380Lelio R Paula07/2009
9688lucasV(-1,2,347969)52375Mike Oakes02/2017
96893^109764-14052371Lelio R Paula10/2012
96902*3^109761+752370Lelio R Paula03/2014
96919863^13112-13112^986352370Norbert Schneider10/2017
9692(145^24229+1)/14652366Richard Fischer02/2018
96938094^13399-13399^809452366Norbert Schneider03/2018
96942^173944-11225352363Enzo Doria06/2014
96962^173940+111152362Lelio R Paula01/2011
9695(3126^14983-1)/312552362Richard Fischer03/2015
969715214^2763+2763^1521452358Hans Havermann05/2016
969813200^9247+9247^1320052352Hans Havermann05/2016
9699(1017*2^173867-1)/717552339Lelio R Paula03/2015
970013732^6465+6465^1373252327Hans Havermann05/2016
9701(2^173867-1)/5253663750268952326Donovan Johnson06/2005
97022^173811-68487752323Paul Bourdelais11/2012
97032^173807-595552322Lelio R Paula06/2009
97042^173796-104468952318Paul Bourdelais11/2012
970510^52317+6449752318Patrick De Geest12/2012
970610^52317+6474352318Patrick De Geest12/2012
970810^52317-7152317Robert Price05/2011
970710821^12968+12968^1082152317Norbert Schneider04/2016
9709(298*10^52308-7)/352310Robert Price06/2017
9710(2^173778-3)/5795952308Lelio R Paula02/2012
971110232^13043-13043^1023252302Norbert Schneider08/2017
97122^173727+952298Lelio R Paula01/2011
9713(14^45631+13^45631)/2752298Robert Price04/2013
971437856!3+656152293Robert Price11/2015
97154*3^109596+552292Lelio R Paula03/2014
971615436^2441+2441^1543652291Hans Havermann05/2016
971743^32005+2452280Robert Price11/2013
97182^173650-16552274Lelio R Paula02/2011
97194*10^52272+9352273Robert Price01/2017
972019^40873+8452267Lelio R Paula01/2013
97212^173621+424242952266Jason Earls09/2008
97229999^13064-13064^999952256Norbert Schneider09/2017
9723numbpart(46909^2-1)52247Serge Batalov04/2017
972414^45579-3152240Lelio R Paula01/2013
97257395^13502-13502^739552239Norbert Schneider05/2018
9726(10223*2^173518+1)/90352236Lelio R Paula05/2014
972720^40147-612352233Enzo Doria03/2013
97284^86754-3^(86754+1)52232Robert Price04/2016
97297452^13487-13487^745252226Norbert Schneider05/2018
97302^173477-343352222Yves Minet04/2009
9731(22*10^52217-73)/352218Robert Price09/2017
9732(25*2^173446+1)/6152213Lelio R Paula07/2012
97333^109431-3852212Lelio R Paula10/2012
97342^173424-395952206Yves Minet04/2017
973513^46861-7252201Lelio R Paula01/2013
97362^173373-136352191Yves Minet03/2009
973711^50114-174052189Enzo Doria11/2012
973813735^6304+6304^1373552188Hans Havermann05/2016
973911^50111-111052186Enzo Doria11/2012
9740lucasU(46,1,31387)+lucasU(46,1,31386)52181Mike Oakes04/2009
974120^40105-858352178Enzo Doria03/2013
9742(10322^13001+2679^13001)/13001^252175Lelio R Paula08/2008
97432^173314-394152173Yves Minet04/2017
97442^173294+115552167Lelio R Paula07/2012
9746(19*2^173301-1)/2348952166Lelio R Paula01/2014
974515146^2781+2781^1514652166Hans Havermann06/2016
974711^50088-3252162Lelio R Paula01/2013
97483^109320+23652159Lelio R Paula10/2012
97492^173246-2863552153Lelio R Paula06/2009
97502*10^52147+1152148Robert Price01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 20 2018 23:15 (Time in France)

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