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) !!!


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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 ?
92512^179120+253353921Henri Lifchitz09/2004
9252(2^179126+78557)/464932118753913Lelio R Paula05/2012
925374^28842+7353913Norbert Schneider11/2012
92541271^17368+17368^127153913Serge Batalov05/2014
92552^179079+5353909Lelio R Paula02/2011
925617^43807+5453903Lelio R Paula01/2013
925717^43807+3053903Lelio R Paula01/2013
92583^112951-31053892Lelio R Paula10/2012
9259Phi(7,2957!)53888Robert Price05/2015
9260(10223*2^178975+1)/3398553877Lelio R Paula05/2014
92612^178944-21920953868Enzo Doria11/2012
9262(10^53859+149)/353859Serge Batalov12/2014
92632^178910-19153858Lelio R Paula02/2011
926416170^2141+2141^1617053857Hans Havermann07/2016
9265(5*10^53855-107)/353856Robert Price01/2017
9266(72*10^53847-27)/9953847Patrick De Geest08/2004
92672^178841-86968810553837Lelio R Paula06/2012
92682*10^53834-2753835Robert Price02/2017
92702^178821-101152353831Paul Bourdelais11/2012
926912601^13128-13128^1260153831Norbert Schneider10/2017
92712^178819-1553830Lelio R Paula02/2011
9272(14450!-1)/22529658153829Donovan Johnson04/2006
9273(124351#+125386)/(2^5*71*883*4489103*9820259)53826Makoto Morimoto10/2017
927410530^13381-13381^1053053825Norbert Schneider03/2018
92752^178761-46553813Lelio R Paula10/2009
927618900^703+703^1890053808Anatoly F. Selevich02/2007
927713918^7343+7343^1391853806Hans Havermann08/2016
927810^53804+3174953805Patrick De Geest12/2012
927910^53804-7153804Robert Price05/2011
9280t(178994)53804Robert Price03/2015
9281(2^178693-lucasV(1,2,178693)+1)/253792Mike Oakes11/2016
92822^178671-11321553786Enzo Doria07/2014
928315110^3621+3621^1511053774Hans Havermann07/2016
92842^178611+9553768Lelio R Paula02/2011
92852^178597+571153764Lelio R Paula10/2011
92862^178598+1291553764Lelio R Paula07/2012
9287(9179*2^178579-1)/30353760Lelio R Paula03/2015
928810671^13342-13342^1067153745Norbert Schneider02/2018
92895*7^63589+253740Lelio R Paula09/2014
92902^178516-11251553739Enzo Doria06/2014
929120^41302-2753736Lelio R Paula01/2013
92926^69054-3920953735Mike Oakes12/2010
929313086^12769+12769^1308653734Hans Havermann07/2016
92942^178455+7604353721Enzo Doria04/2016
9295(10^53718-7)/353718Makoto Kamada10/2004
9296(67607*2^178426+1)/353716Lelio R Paula05/2014
92979*10^53707+1153708Robert Kinser01/2017
929894601!8-253708Robert Price04/2017
929913214^11595+11595^1321453706Hans Havermann07/2016
9300Phi(134350,10)/537401/801196225153705Maksym Voznyy10/2011
93012^178367-37953694Yves Minet03/2013
9302(2^178364-5)/1153692Lelio R Paula02/2012
93034339^14760-16853688Enzo Doria06/2012
930412^49746-1153685Lelio R Paula01/2013
930512950^13051-13051^1295053670Norbert Schneider08/2017
9306(9913*2^178266-1)/224753665Lelio R Paula03/2015
930713725^8128+8128^1372553665Hans Havermann07/2016
93082^178250-11326153659Enzo Doria07/2014
93092^178226+1171553652Lelio R Paula10/2009
931035^34742-197653645Enzo Doria03/2013
931120^41228-56353639Enzo Doria03/2013
9312359^20992+20992^35953637Norbert Schneider08/2014
9313(27*2^178183-1)/2906553636Lelio R Paula01/2014
9314(3^112414+7)/3738169653628Lelio R Paula03/2012
931517994^955+955^1799453623Anatoly F. Selevich10/2006
93162^178117-155153619Yves Minet08/2012
93172^178099-1128753614Enzo Doria06/2014
931810751^13298-13298^1075153611Norbert Schneider01/2018
9319(15*2^178080-1)/30907153604Lelio R Paula01/2014
93205^76672-1376653592Enzo Doria02/2013
93216^68868-13753590Lelio R Paula10/2012
9322(5*2^178021+1)/817353587Lelio R Paula07/2012
93235^76654-2653579Lelio R Paula10/2012
9324(3^112297-2)/762753576Lelio R Paula03/2012
93253*2^177948-753569Lelio R Paula03/2014
932610^53558+1854353559Patrick De Geest12/2012
932710^53558-2153558Robert Price03/2011
93282^177792-9553521Lelio R Paula02/2011
932913392^9919+9919^1339253521Hans Havermann07/2016
933013105^12132+12132^1310553520Hans Havermann07/2016
933113^48042+8253517Lelio R Paula01/2013
93322^177768+3912153514Yves Minet10/2010
933313835^7366+7366^1383553504Hans Havermann07/2016
933417^43477+8453497Lelio R Paula01/2013
93355*10^53492+953493Dmitry Domanov11/2010
93362^177683+9553488Lelio R Paula01/2011
933711057^13226-13226^1105753482Norbert Schneider12/2017
9338(2^177678+3)/51462753481Lelio R Paula02/2012
93392^177641-25546353476Gary Barnes08/2009
9340p(11608)#/2+1653469Robert Price12/2016
9341(14*10^53465+211)/953466Robert Price11/2017
934237302#*10^(37302+52)+p(37302+1)53457Jason Earls08/2008
934312001^13104-13104^1200153455Norbert Schneider10/2017
93441829^16384+1828^1638453449Henri Lifchitz01/2007
934510^53442+1262153443Patrick De Geest06/2018
934610^53442-200753442Patrick De Geest06/2018
934735^34608-960253438Enzo Doria03/2013
9348(3^111992+8)/1486753430Lelio R Paula03/2012
93502^177480+186966153427Enzo Doria05/2016
934911791^13122-13122^1179153427Norbert Schneider10/2017
9351(8*10^53411+1)/953411Serge Batalov12/2008
93524*5^76410-353409Lelio R Paula09/2014
93532^177380-11304553397Enzo Doria07/2014
93555^76362-2*3^7636253375Mike Oakes11/2009
935472365!6-2453375Robert Price08/2018
93564159^14747-14053370Enzo Doria07/2012
9357(lucasV(1,2,354503)-2)/353358Mike Oakes03/2017
9358p(11586)#/2+3253357Robert Price12/2016
935915^45362-4653350Lelio R Paula01/2013
936014147^5892+5892^1414753338Hans Havermann07/2016
93617^63109+4653334Lelio R Paula10/2012
936220^40986-134353325Enzo Doria03/2013
93634*10^53324-8953325Robert Price08/2017
936420^40977-888353313Enzo Doria03/2013
93653^111711+266053300Lelio R Paula10/2012
93662^177040-1186553295Enzo Doria10/2012
9367(7*10^53287+17)/353288Erik Branger03/2014
936835^34506-1075853280Enzo Doria03/2013
9369(11*10^53274-17)/353275Erik Branger03/2014
9370(1017*2^176971-1)/33553275Lelio R Paula03/2015
93712^176961-283353271Yves Minet09/2014
93723^111642+11053267Lelio R Paula10/2012
937317^43290-9853267Lelio R Paula01/2013
93747^63028+3653265Lelio R Paula10/2012
9375(22*10^53264+71)/353265Robert Price05/2017
93767^63023-3653261Lelio R Paula10/2012
937719783^492+492^1978353256Anatoly F. Selevich02/2007
937813350^9739+9739^1335053247Hans Havermann10/2015
937914394^4993+4993^1439453235Hans Havermann10/2015
93802^176823-11280753230Enzo Doria06/2014
93811684^16495+16495^168453219Serge Batalov05/2014
938215277^3042+3042^1527753213Hans Havermann06/2016
9383(50322^11317-1)/5032153206Serge Batalov04/2015
93842^176742-159553205Lelio R Paula10/2009
9385(27*2^176767-1)/2045505635553204Lelio R Paula01/2014
938672149!6-1253200Robert Price08/2018
9387(-lucasV(1,2,353460)-2)/(3^2*5^2)53199Mike Oakes03/2017
9388(3*2^176696-1)/29953189Lelio R Paula01/2014
9389(7*10^53185-1)/353186Erik Branger03/2014
93902^176629+46553171Lelio R Paula07/2012
9391(3*2^176604-1)/35953162Lelio R Paula01/2014
939210955^13158-13158^1095553154Norbert Schneider11/2017
93935^76038-1436653149Enzo Doria02/2013
939415156^3209+3209^1515653143Hans Havermann06/2016
93952^176532-283753142Yves Minet09/2014
939652^30967-5153140Norbert Schneider08/2014
93979*5^76023-253139Lelio R Paula09/2014
9398(14283!+1)/46421617753135Michael Porter03/2016
93992^176461-16553121Lelio R Paula02/2011
9400(62*10^53111+1)/953112Serge Batalov05/2010
94012^176403-13953103Lelio R Paula02/2011
940255^30508-253095Lelio R Paula08/2013
9403(48591^11329-1)/4859053090Serge Batalov04/2015
94043^111254-8853082Lelio R Paula10/2012
940515^45129-5653076Lelio R Paula01/2013
94062^176293-7353070Lelio R Paula01/2011
9407(67*10^53068+41)/953069Robert Price09/2015
940815271^2986+2986^1527153069Hans Havermann06/2016
94092^176255-66753059Yves Minet01/2012
941036471*2^176221+864753053Paul Vanderveen04/2016
9411(19*10^53049-1)/953050Serge Batalov03/2009
94129*2^176203-553044Lelio R Paula03/2014
94132^176205-9439553043Lelio R Paula08/2011
9414(19*2^176224-1)/21791691353042Lelio R Paula01/2014
94158600^13481-13481^860053041Norbert Schneider05/2018
941617^43103+1453037Lelio R Paula01/2013
9417(31*2^176188-1)/355553036Lelio R Paula01/2014
94182^176177+6094753035David Broadhurst05/2002
9419(22*10^53033-7)/353034Erik Branger09/2014
942013810^6909+6909^1381053023Hans Havermann06/2016
94212^176108+1609553014Lelio R Paula10/2009
94222^176107+1891553014Lelio R Paula07/2012
94233^111080-962852999Enzo Doria02/2013
94242^176047-155152996Yves Minet08/2012
94252^176042+7351952994Enzo Doria04/2016
9426lucasV(1715,1,2^14)/6553752986Mike Oakes04/2009
94272^175984-11225952977Enzo Doria06/2014
942811^50870+1052976Lelio R Paula01/2013
9429(11*10^52956+19)/352957Robert Price03/2016
9430gcd(V(949965),5*F(189993)*(F(189993)+1)+1)52941Serge Batalov04/2015
9431(-lucasV(1,2,351735)+2)/(3*7*263)52938Mike Oakes03/2017
9433(98*10^52931-89)/9952931Ray Chandler11/2010
943213774^6963+6963^1377452931Hans Havermann06/2016
94342^175812-136752925Yves Minet05/2013
94352^175801+1155*17580152922Henri Lifchitz01/2005
943611^50801-909052904Enzo Doria02/2013
94377803^13592-13592^780352904Norbert Schneider07/2018
943843^32374+1252882Robert Price11/2013
94392^175628+1352870Lelio R Paula01/2011
94402^175615-174752866Yves Minet09/2012
9441(13*10^52861+107)/352862Robert Price11/2017
94429*2^175586-752858Lelio R Paula03/2014
944312174^12937+12937^1217452854Norbert Schneider04/2016
9444(15*2^175565+1)/835952848Lelio R Paula07/2012
9445(2^175631-1)/330463093135534238072561/9273316952839Robert Kinser03/2017
944614256^5077+5077^1425652828Hans Havermann06/2016
94472^175467+8287552821Lelio R Paula07/2012
9448(7*10^52819+167)/352820Robert Kinser10/2017
9449(67607*2^175426+1)/352813Lelio R Paula05/2014
945071671!6-3252813Robert Price08/2018
945113^47400-6052801Lelio R Paula01/2013
94524*10^52792+6352793Robert Price06/2016
9454(78557*2^175360+1)/308752791Lelio R Paula06/2014
945318^42055-292952791Enzo Doria03/2013
94559*5^75521+252788Lelio R Paula09/2014
94566^67814+3152770Lelio R Paula10/2012
945770^28600+6952770Norbert Schneider10/2012
945814^46038+9752766Lelio R Paula01/2013
9459(61*10^52763-7)/952764Serge Batalov02/2009
94602*5^75474+952755Lelio R Paula09/2014
946110^52753+282643060952754Robert Price05/2015
946210^52753+18399752754Patrick De Geest01/2016
946310^52753-5015352753Patrick De Geest03/2016
946419846^455+455^1984652751Anatoly F. Selevich02/2007
94652^175217+7297752746Enzo Doria04/2016
9466p(11466)#/2-25652746Robert Price05/2017
9467(4*10^52740+41)/952740Robert Price11/2014
94682^175189+538552738Lelio R Paula08/2009
94692^175160+938552729Lelio R Paula07/2008
947012356^12885+12885^1235652724Norbert Schneider03/2016
94712^175137+1152722Lelio R Paula01/2011
947265^29077-64^2907752715Robert Price08/2013
94732*10^52713-8752714Robert Price06/2016
94742^175106-46552713Lelio R Paula08/2009
94752^175089-5869552708Lelio R Paula08/2009
94772^175045+19552694Lelio R Paula02/2011
9476195^23010-252694Lelio R Paula10/2017
94782^175025+14952688Lelio R Paula02/2011
9479(19^41201+1)/2052685Paul Bourdelais03/2010
9480(436*10^52683-13)/952685Robert Price10/2017
94812*12^48815-5^4881552681Mike Oakes10/2010
9482335^20862-20862^33552678Norbert Schneider09/2015
94832^174983-760552676Lelio R Paula07/2009
94844*10^52667+1952668Robert Price04/2016
9485(10^52667+77)/352667Robert Price01/2017
948611434^12977+12977^1143452664Norbert Schneider04/2016
94872^174941-120352663Lelio R Paula07/2009
94888501^13400-13400^850152655Norbert Schneider03/2018
94892^174910+1270552654Lelio R Paula07/2012
94903^110338+7452645Lelio R Paula10/2012
94915^75303+1252635Lelio R Paula10/2012
94922^174836+25525552631Lelio R Paula07/2009
9493(66^28921+1)/6752622Paul Bourdelais08/2017
949420^40443+952618Lelio R Paula01/2013
9495(11*2^174788+1)/952617Lelio R Paula01/2012
9496(11*2^174786-1)/70352615Lelio R Paula01/2014
949711^50520-129052612Enzo Doria11/2012
9498(10^52608-19)/952608Robert Price10/2017
9499(9913*2^174736-1)/33352603Lelio R Paula03/2015
950013145^10024+10024^1314552594Hans Havermann05/2016


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

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