PRP Records

Probable Primes Top 10000

(202622 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 ?
9001(67607*2^178426+1)/353716Lelio R Paula05/2014
90029*10^53707+1153708Robert Kinser01/2017
900394601!8-253708Robert Price04/2017
900413214^11595+11595^1321453706Hans Havermann07/2016
9005Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
90062^178367-37953694Yves Minet03/2013
9007(2^178364-5)/1153692Lelio R Paula02/2012
90084339^14760-16853688Enzo Doria06/2012
900912^49746-1153685Lelio R Paula01/2013
901012950^13051-13051^1295053670Norbert Schneider08/2017
9012(9913*2^178266-1)/224753665Lelio R Paula03/2015
901113725^8128+8128^1372553665Hans Havermann07/2016
90132^178250-11326153659Enzo Doria07/2014
90142^178226+1171553652Lelio R Paula10/2009
901535^34742-197653645Enzo Doria03/2013
901620^41228-56353639Enzo Doria03/2013
9017359^20992+20992^35953637Norbert Schneider08/2014
9018(27*2^178183-1)/2906553636Lelio R Paula01/2014
9019(3^112414+7)/3738169653628Lelio R Paula03/2012
902017994^955+955^1799453623Anatoly F. Selevich10/2006
90212^178117-155153619Yves Minet08/2012
90222^178099-1128753614Enzo Doria06/2014
902310751^13298-13298^1075153611Norbert Schneider01/2018
9024(15*2^178080-1)/30907153604Lelio R Paula01/2014
90255^76672-1376653592Enzo Doria02/2013
90266^68868-13753590Lelio R Paula10/2012
9027(5*2^178021+1)/817353587Lelio R Paula07/2012
90285^76654-2653579Lelio R Paula10/2012
9029(3^112297-2)/762753576Lelio R Paula03/2012
90303*2^177948-753569Lelio R Paula03/2014
903110^53558+1854353559Patrick De Geest12/2012
903210^53558-2153558Robert Price03/2011
90332^177792-9553521Lelio R Paula02/2011
903413392^9919+9919^1339253521Hans Havermann07/2016
903513105^12132+12132^1310553520Hans Havermann07/2016
903613^48042+8253517Lelio R Paula01/2013
90372^177768+3912153514Yves Minet10/2010
903813835^7366+7366^1383553504Hans Havermann07/2016
903917^43477+8453497Lelio R Paula01/2013
90405*10^53492+953493Dmitry Domanov11/2010
90412^177683+9553488Lelio R Paula01/2011
904211057^13226-13226^1105753482Norbert Schneider12/2017
9043(2^177678+3)/51462753481Lelio R Paula02/2012
90442^177641-25546353476Gary Barnes08/2009
9045p(11608)#/2+1653469Robert Price12/2016
9046(14*10^53465+211)/953466Robert Price11/2017
904737302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
904812001^13104-13104^1200153455Norbert Schneider10/2017
90491829^16384+1828^1638453449Henri Lifchitz01/2007
905035^34608-960253438Enzo Doria03/2013
9051(3^111992+8)/1486753430Lelio R Paula03/2012
90532^177480+186966153427Enzo Doria05/2016
905211791^13122-13122^1179153427Norbert Schneider10/2017
9054(8*10^53411+1)/953411Serge Batalov12/2008
90554*5^76410-353409Lelio R Paula09/2014
90562^177380-11304553397Enzo Doria07/2014
90575^76362-2*3^7636253375Mike Oakes11/2009
90584159^14747-14053370Enzo Doria07/2012
9059(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9060p(11586)#/2+3253357Robert Price12/2016
906115^45362-4653350Lelio R Paula01/2013
906214147^5892+5892^1414753338Hans Havermann07/2016
90637^63109+4653334Lelio R Paula10/2012
906420^40986-134353325Enzo Doria03/2013
90654*10^53324-8953325Robert Price08/2017
906620^40977-888353313Enzo Doria03/2013
90673^111711+266053300Lelio R Paula10/2012
90682^177040-1186553295Enzo Doria10/2012
9069(7*10^53287+17)/353288Erik Branger03/2014
907035^34506-1075853280Enzo Doria03/2013
9071(11*10^53274-17)/353275Erik Branger03/2014
9072(1017*2^176971-1)/33553275Lelio R Paula03/2015
90732^176961-283353271Yves Minet09/2014
90743^111642+11053267Lelio R Paula10/2012
907517^43290-9853267Lelio R Paula01/2013
90767^63028+3653265Lelio R Paula10/2012
9077(22*10^53264+71)/353265Robert Price05/2017
90787^63023-3653261Lelio R Paula10/2012
907919783^492+492^1978353256Anatoly F. Selevich02/2007
908013350^9739+9739^1335053247Hans Havermann10/2015
908114394^4993+4993^1439453235Hans Havermann10/2015
90822^176823-11280753230Enzo Doria06/2014
90831684^16495+16495^168453219Serge Batalov05/2014
908415277^3042+3042^1527753213Hans Havermann06/2016
9085(50322^11317-1)/5032153206Serge Batalov04/2015
90862^176742-159553205Lelio R Paula10/2009
9087(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
9088(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9089(3*2^176696-1)/29953189Lelio R Paula01/2014
9090(7*10^53185-1)/353186Erik Branger03/2014
90912^176629+46553171Lelio R Paula07/2012
9092(3*2^176604-1)/35953162Lelio R Paula01/2014
909310955^13158-13158^1095553154Norbert Schneider11/2017
90945^76038-1436653149Enzo Doria02/2013
909515156^3209+3209^1515653143Hans Havermann06/2016
90962^176532-283753142Yves Minet09/2014
909752^30967-5153140Norbert Schneider08/2014
90989*5^76023-253139Lelio R Paula09/2014
9099(14283!+1)/46421617753135Michael Porter03/2016
91002^176461-16553121Lelio R Paula02/2011
9101(62*10^53111+1)/953112Serge Batalov05/2010
91022^176403-13953103Lelio R Paula02/2011
910355^30508-253095Lelio R Paula08/2013
9104(48591^11329-1)/4859053090Serge Batalov04/2015
91053^111254-8853082Lelio R Paula10/2012
910615^45129-5653076Lelio R Paula01/2013
91072^176293-7353070Lelio R Paula01/2011
9108(67*10^53068+41)/953069Robert Price09/2015
910915271^2986+2986^1527153069Hans Havermann06/2016
91102^176255-66753059Yves Minet01/2012
911136471*2^176221+864753053Paul Vanderveen04/2016
9112(19*10^53049-1)/953050Serge Batalov03/2009
91139*2^176203-553044Lelio R Paula03/2014
91142^176205-9439553043Lelio R Paula08/2011
9115(19*2^176224-1)/21791691353042Lelio R Paula01/2014
911617^43103+1453037Lelio R Paula01/2013
9117(31*2^176188-1)/355553036Lelio R Paula01/2014
91182^176177+6094753035David Broadhurst05/2002
9119(22*10^53033-7)/353034Erik Branger09/2014
912013810^6909+6909^1381053023Hans Havermann06/2016
91222^176108+1609553014Lelio R Paula10/2009
91212^176107+1891553014Lelio R Paula07/2012
91233^111080-962852999Enzo Doria02/2013
91242^176047-155152996Yves Minet08/2012
91252^176042+7351952994Enzo Doria04/2016
9126lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
91272^175984-11225952977Enzo Doria06/2014
912811^50870+1052976Lelio R Paula01/2013
9129(11*10^52956+19)/352957Robert Price03/2016
9130gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9131(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9133(98*10^52931-89)/9952931Ray Chandler11/2010
913213774^6963+6963^1377452931Hans Havermann06/2016
91342^175812-136752925Yves Minet05/2013
91352^175801+1155*17580152922Henri Lifchitz01/2005
913611^50801-909052904Enzo Doria02/2013
913743^32374+1252882Robert Price11/2013
91382^175628+1352870Lelio R Paula01/2011
91392^175615-174752866Yves Minet09/2012
9140(13*10^52861+107)/352862Robert Price11/2017
91419*2^175586-752858Lelio R Paula03/2014
914212174^12937+12937^1217452854Norbert Schneider04/2016
9143(15*2^175565+1)/835952848Lelio R Paula07/2012
9144(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
914514256^5077+5077^1425652828Hans Havermann06/2016
91462^175467+8287552821Lelio R Paula07/2012
9147(7*10^52819+167)/352820Robert Kinser10/2017
9148(67607*2^175426+1)/352813Lelio R Paula05/2014
914913^47400-6052801Lelio R Paula01/2013
91504*10^52792+6352793Robert Price06/2016
9152(78557*2^175360+1)/308752791Lelio R Paula06/2014
915118^42055-292952791Enzo Doria03/2013
91539*5^75521+252788Lelio R Paula09/2014
91546^67814+3152770Lelio R Paula10/2012
915570^28600+6952770Norbert Schneider10/2012
915614^46038+9752766Lelio R Paula01/2013
9157(61*10^52763-7)/952764Serge Batalov02/2009
91582*5^75474+952755Lelio R Paula09/2014
915910^52753+282643060952754Robert Price05/2015
916010^52753+18399752754Patrick De Geest01/2016
916110^52753-5015352753Patrick De Geest03/2016
916219846^455+455^1984652751Anatoly F. Selevich02/2007
91632^175217+7297752746Enzo Doria04/2016
9164p(11466)#/2-25652746Robert Price05/2017
9165(4*10^52740+41)/952740Robert Price11/2014
91662^175189+538552738Lelio R Paula08/2009
91672^175160+938552729Lelio R Paula07/2008
916812356^12885+12885^1235652724Norbert Schneider03/2016
91692^175137+1152722Lelio R Paula01/2011
917065^29077-64^2907752715Robert Price08/2013
91712*10^52713-8752714Robert Price06/2016
91722^175106-46552713Lelio R Paula08/2009
91732^175089-5869552708Lelio R Paula08/2009
91742^175045+19552694Lelio R Paula02/2011
9175195^23010-252694Lelio R Paula10/2017
91762^175025+14952688Lelio R Paula02/2011
9178(19^41201+1)/2052685Paul Bourdelais03/2010
9177(436*10^52683-13)/952685Robert Price10/2017
91792*12^48815-5^4881552681Mike Oakes10/2010
9180335^20862-20862^33552678Norbert Schneider09/2015
91812^174983-760552676Lelio R Paula07/2009
91824*10^52667+1952668Robert Price04/2016
9183(10^52667+77)/352667Robert Price01/2017
918411434^12977+12977^1143452664Norbert Schneider04/2016
91852^174941-120352663Lelio R Paula07/2009
91862^174910+1270552654Lelio R Paula07/2012
91873^110338+7452645Lelio R Paula10/2012
91885^75303+1252635Lelio R Paula10/2012
91892^174836+25525552631Lelio R Paula07/2009
9190(66^28921+1)/6752622Paul Bourdelais08/2017
919120^40443+952618Lelio R Paula01/2013
9192(11*2^174788+1)/952617Lelio R Paula01/2012
9193(11*2^174786-1)/70352615Lelio R Paula01/2014
919411^50520-129052612Enzo Doria11/2012
9195(10^52608-19)/952608Robert Price10/2017
9196(9913*2^174736-1)/33352603Lelio R Paula03/2015
919713145^10024+10024^1314552594Hans Havermann05/2016
91985003^14217-15052592Enzo Doria07/2012
919919^41123+1052587Lelio R Paula01/2013
92002^174683+1290952585Lelio R Paula01/2011
92012^174643+5952573Lelio R Paula01/2011
9202(1017*2^174640-1)/77352572Lelio R Paula03/2015
920313529^7662+7662^1352952552Hans Havermann06/2016
9204121421#+18876752548Makoto Morimoto02/2016
920520^40375-592352530Enzo Doria03/2013
9206(67607*2^174503+1)/9094807952528Lelio R Paula05/2014
9207(-lucasV(1,2,349014)+2)/(7*50873*1047043)52521Mike Oakes03/2017
92082^174462+34552519Lelio R Paula07/2009
9209t(178863)52509Robert Price10/2014
92102^174416+85552505Lelio R Paula07/2009
92116^67467-10352500Lelio R Paula10/2012
9212(2^174533-1)/(193594572654550537*91917886778031629891960890057)52494Dario Alpern06/2017
92132^174329-1126552479Enzo Doria06/2014
92142^174314-124152474Yves Minet05/2009
921552^30577-5152471Norbert Schneider08/2014
92169403^13206-13206^940352471Norbert Schneider12/2017
921715692^2205+2205^1569252465Hans Havermann06/2016
9218(2^174281-7)/62881702961552453Lelio R Paula02/2012
9219(2^174240+5)/352451Lelio R Paula02/2012
9220(86*10^52450-221)/952451Robert Price06/2017
9221(62*10^52448-197)/952449Robert Price10/2017
9222(15*2^174221+1)/40352445Lelio R Paula07/2012
922326313!2-3252443Robert Price10/2015
9224(3*2^174214-1)/374872952438Lelio R Paula01/2014
92252*3^109900-552436Lelio R Paula03/2014
92274159^14488-15052432Enzo Doria07/2012
9226(89*10^52431-71)/952432Robert Price11/2015
92282^174170-394152431Yves Minet04/2017
9229(7*2^174171-1)/68552429Lelio R Paula01/2014
9230(260137^9679+1)/26013852409Faysal YAtim03/2008
92312^174098+7952409Lelio R Paula01/2011
923235^33940-221452406Enzo Doria03/2013
923315^44557+252404Ray Chandler07/2011
92342^174049-43952394Yves Minet01/2012
92356^67329+11552393Lelio R Paula10/2012
92372^174041+26214552392Lelio R Paula07/2009
9236141^24377+252392Lelio R Paula05/2013
9238lucasU(285,1,21339)-lucasU(285,1,21338)52382Mike Oakes05/2009
92392^174001-595552380Lelio R Paula07/2009
9240lucasV(-1,2,347969)52375Mike Oakes02/2017
92413^109764-14052371Lelio R Paula10/2012
92432*3^109761+752370Lelio R Paula03/2014
92429863^13112-13112^986352370Norbert Schneider10/2017
9244(145^24229+1)/14652366Richard Fischer02/2018
92452^173944-11225352363Enzo Doria06/2014
92472^173940+111152362Lelio R Paula01/2011
9246(3126^14983-1)/312552362Richard Fischer03/2015
924815214^2763+2763^1521452358Hans Havermann05/2016
924913200^9247+9247^1320052352Hans Havermann05/2016
9250(1017*2^173867-1)/717552339Lelio R Paula03/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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