PRP Records

Probable Primes Top 10000

(177649 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 ?
97512^160873+1891548428Lelio R Paula10/2011
975213206^4645+4645^1320648427Hans Havermann04/2016
975310^48420+613948421Patrick De Geest05/2016
975410^48420-2*10^1592-148420Serge Batalov01/2015
975510^48420-2927348420Patrick De Geest03/2016
97572^160822-216348413Yves Minet08/2013
9756(lucasV(1,2,321685)+2)/(571*911)48413Mike Oakes02/2017
975910^48410+9^(48410-1)48411Robert Price03/2016
975810^48410+9016348411Patrick De Geest12/2016
9761(3^101473+4)/26448148410Lelio R Paula03/2012
97629*2^160811+748410Lelio R Paula02/2014
976010^48410-328748410Patrick De Geest12/2016
9763(22699*2^160806+1)/157348409Lelio R Paula05/2014
97643*7^57278-848407Lelio R Paula09/2014
97652^160789-11321548403Enzo Doria07/2014
97666900^12607-12607^690048397Norbert Schneider12/2016
97673^101404+248383Mike Oakes11/2009
97683^101395-11048378Lelio R Paula06/2012
97692^160701+19148376Lelio R Paula01/2011
97706*F(231436)+148368Gilbert Mozzo06/2015
97712^160654-1548362Lelio R Paula08/2010
977220^37167+5348356Lelio R Paula11/2012
9773(799247^8192+1)/248355Lelio R Paula12/2014
9774(238*10^48352-1)/348354Robert Price05/2016
977518661^390+390^1866148352Anatoly F. Selevich01/2007
977621^36566+248349Ray Chandler08/2011
97777^57208-9248347Lelio R Paula06/2012
97795^69165-2^6916648345Mike Oakes10/2010
9778(11867^11867+2981)/2^3/11134148345Makoto Morimoto07/2016
9780(3^101331-4)/467948344Lelio R Paula03/2012
978113^43396-2448341Lelio R Paula10/2012
9783Phi(85113,10)/170227/340453/2080331947/20239360723/57723206898508348339Serge Batalov06/2011
97827*2^160574-948339Lelio R Paula02/2014
9784lucasU(42,1,29781)+lucasU(42,1,29780)48334Mike Oakes04/2009
97853^101296-1931848331Enzo Doria02/2013
9786(lucasV(1,2,321119)+2)/(5*53)48331Mike Oakes01/2017
9788(11863^11863+2822)/3/140681/14848348322Makoto Morimoto07/2016
97875970^12797-12797^597048322Norbert Schneider03/2017
978917^39270+5248320Lelio R Paula11/2012
9790(791013^8192+1)/248318Lelio R Paula12/2014
979110^48314+7146948315Patrick De Geest06/2016
979211^46393-795048314Enzo Doria02/2013
979410^48314-2*10^4988-148314Serge Batalov01/2015
979310^48314-42379748314Patrick De Geest03/2016
97952^160491+8771348313Yves Minet03/2010
97968*6^62084-748312Lelio R Paula09/2014
97972^160477+7297748309Enzo Doria04/2016
97982^160471+9948307Lelio R Paula07/2009
9799(9913*2^160481-1)/419187548307Lelio R Paula03/2015
9801(43^29573+1)/4448305Robert Price11/2013
98002^160463-290748305Yves Minet09/2014
9802(68*10^48304-257)/948305Robert Price06/2017
9803Phi(77061,10)/4151276071/1520798835148301Maksym Voznyy02/2010
98045^69098-1457648298Enzo Doria02/2013
9805(2*10^48297-17)/348297Erik Branger03/2013
980610^48292+10470748293Patrick De Geest06/2016
980810^48292-2*10^392-148292Serge Batalov01/2015
980710^48292-6680348292Patrick De Geest03/2016
980945709!4+248291Robert Price03/2017
98102^160402-112748286Yves Minet05/2013
98112^160398-145148285Yves Minet08/2012
981211^46365+2648285Lelio R Paula10/2012
9813t(160462)48285Robert Price05/2015
9814(3^50599-75)^2-7748284Jorge Menendez02/2017
98152^160387-372148282Yves Minet04/2017
98163^101192+2^10119348281Mike Oakes10/2009
98175^69063-1848273Lelio R Paula05/2012
98185^69060-1541648271Enzo Doria02/2013
98192^160343-66748269Yves Minet01/2012
98202^160302-214548256Lelio R Paula04/2009
982112^44705-8548245Lelio R Paula10/2012
9822(58695*2^160249-1)/14948243Lelio R Paula03/2015
98232^160218+1270548231Lelio R Paula10/2011
9824(F(14425)^17-F(14424)^17)/F(14423)48230Wayne Halsdorf02/2010
9825(771035^8192+1)/248227Lelio R Paula12/2014
982718348^425+425^1834848226Anatoly F. Selevich12/2006
9826(29*2^160204-1)/6748226Lelio R Paula01/2014
98282^160166+577548215Lelio R Paula04/2009
982911875^11478+11478^1187548211Anatoly F. Selevich10/2009
983017^39177-4048206Lelio R Paula11/2012
9831(5*2^160135-1)/429039948200Lelio R Paula01/2014
9832(763957^8192+1)/248194Lelio R Paula12/2014
9833(11833^11833+1278)/7/89/10748193Makoto Morimoto06/2016
9834gcd(V(576505),5*F(115301)*(F(115301)+1)+1)48192Serge Batalov04/2015
98358788^12217+12217^878848183Norbert Schneider01/2014
9836(11831^11831+1584)/5/23/97/140948181Makoto Morimoto07/2016
9837(760473^8192+1)/248178Lelio R Paula12/2014
9838-lucasV(-1,2,320104)/3148178Mike Oakes01/2017
9839gcd(V(864525),5*F(172905)*(F(172905)-1)+1)48176Serge Batalov04/2015
9840(760135^8192+1)/29491448171Lelio R Paula12/2014
98424357^13236-11048169Enzo Doria06/2012
9841(11827^11827+4120)/1748169Makoto Morimoto07/2016
9843(3*2^160013-1)/242548166Lelio R Paula01/2014
984413^43238+8248165Lelio R Paula11/2012
98452^159992+65748163Lelio R Paula02/2013
98462^159984-38300948160Gary Barnes08/2009
98472^159958-5869548153Lelio R Paula03/2009
98486408*10^48143+11821^11821-2448147Gilbert Mozzo12/2012
9849(755045^8192+1)/22937848147Lelio R Paula12/2014
985011821^11821-2448143Henri Lifchitz10/2011
9851(33*2^159934+1)/193696948141Michael Porter10/2015
9852(11821^11821+1240)/19/1378948138Makoto Morimoto06/2016
985320^36997-5148135Lelio R Paula11/2012
9854(3^100895+7)/2432177503448129Lelio R Paula03/2012
9855(15185*2^159869-1)/182748127Lelio R Paula03/2015
98563*7^56945+848125Lelio R Paula09/2014
9857(749655^8192+1)/13107448122Lelio R Paula12/2014
98584*5^68835+948115Lelio R Paula09/2014
9859(148^22171+1)/14948115Richard Fischer12/2016
9860(2^159841+78557)/92348114Lelio R Paula05/2012
9861(3^50420+59)^2+6148113Jorge Menendez02/2017
986210^48109+948110Jason Earls12/2007
986310^48108+3953148109Patrick De Geest01/2009
986410^48109-10459148109Patrick De Geest07/2009
986810^48107-4810748108Henri Lifchitz07/2002
986510^48107+12622948108Patrick De Geest04/2007
986610^48108-6134348108Patrick De Geest07/2009
986723^35328+2248108Norbert Schneider12/2013
98706213^12682+12682^621348107Norbert Schneider01/2016
9869(64*10^48106+287)/948107Robert Price04/2016
987118^38321-9748104Lelio R Paula11/2012
9872(11813^11813+748)/3/67980748101Makoto Morimoto06/2016
9873(743679^8192+1)/248099Lelio R Paula12/2014
98742^159777-133348098Yves Minet05/2013
98752^159765+71748095Lelio R Paula02/2013
987635^31143-395848087Enzo Doria03/2013
98778*10^48081-948082Dmitry Domanov11/2010
987812^44553-5948081Lelio R Paula10/2012
987935086!3+218748080Robert Price12/2015
9880(11807^11807+9647)/2/548079Makoto Morimoto07/2016
98811338^15377+15377^133848076Serge Batalov05/2014
98822^159692-125948073Yves Minet08/2012
9883(lucasV(1,2,319367)+2)/(5*11)48068Mike Oakes01/2017
98842^159669+94148066Lelio R Paula02/2013
98852^159660-287948063Yves Minet09/2014
98862^159647+57348059Lelio R Paula02/2013
988719^37581+9448057Lelio R Paula11/2012
98882^159633-57706348055Paul Bourdelais11/2012
98895436^12865-12865^543648055Norbert Schneider04/2017
9890(11801^11801+8503)/2^4/3/17/13748048Makoto Morimoto07/2016
9891(23*2^159599+1)/2548045Lelio R Paula07/2012
98922^159597+130748044Lelio R Paula07/2008
98933^100693-3448043Lelio R Paula06/2012
9894(349*10^48036-7)/948038Robert Price03/2017
9895(68*10^48032+7)/348034Robert Price03/2016
989724^34797-120748028Enzo Doria03/2013
9896(106*10^48026-1)/348028Serge Batalov12/2014
98982^159522+67948021Lelio R Paula02/2013
9899(726998^8192+1)/14745748013Lelio R Paula11/2014
9900(725753^8192+1)/13107448007Lelio R Paula12/2014
990110^48003+2148004Robert Price01/2011
990210^48003-3652148003Patrick De Geest01/2012
990320^36896-404348003Enzo Doria03/2013
990410^48000+7390948001Patrick De Geest05/2012
990510^48000-8240748000Patrick De Geest05/2012
990610^47999+7809348000Patrick De Geest05/2012
990710^47999-122747999Patrick De Geest05/2012
99082^159440-1260947997Enzo Doria10/2012
9909(11789^11789+297)/2/17/2347996Makoto Morimoto06/2016
9910(40^29959+1)/4147995Robert Price09/2013
9913(49*10^47989+41)/947990Erik Branger05/2013
991110^47989+2*47989-147990Robert Price03/2015
991210^47989+3028347990Patrick De Geest01/2016
991410^47989-1046347989Patrick De Geest01/2016
9915(11*2^159409-1)/2147987Lelio R Paula01/2014
9916(298*10^47983-7)/347985Robert Price06/2017
99175^68644+9447981Lelio R Paula05/2012
99182^159386-214547980Lelio R Paula03/2009
9919Linear(0,1,1,-1,318751)47977Henri Lifchitz04/2007
9920(720710^8192+1)/966388940947977Lelio R Paula11/2014
9921(2^159392+5)/11779866947974Lelio R Paula01/2012
99226576^12565-12565^657647973Norbert Schneider11/2016
992310^47969+58504347970Robert Price03/2015
992410^47969+15329147970Patrick De Geest01/2016
992510^47969-15140747969Patrick De Geest01/2016
9926(9*2^159332+1)/547964Lelio R Paula07/2012
9927(11783^11783+65)/2^3/89/268603747963Makoto Morimoto06/2016
992820^36864+3147962Lelio R Paula11/2012
9929(2^159324+78557)/240947958Lelio R Paula05/2012
99312^159293-105147952Yves Minet05/2009
9930(355*29^32789-61)/1447952Curtis Bright05/2015
9932lucasU(1856,1,14670)-lucasU(1856,1,14669)47947Mike Oakes05/2009
9933(11779^11779+1425)/2^2/11/545679147946Makoto Morimoto07/2016
99343^100482-31047943Lelio R Paula06/2012
9935(11777^11777+5123)/2^2/5/13/225147939Makoto Morimoto07/2016
993617^38959+847938Lelio R Paula11/2012
99377*10^47936-6947937Robert Price01/2017
9938(708709^8192+1)/247927Lelio R Paula12/2014
9939(709609^8192+1)/29491447927Lelio R Paula12/2014
9941Phi(104749,3)47923Lelio R Paula02/2012
994024^34721-169147923Enzo Doria03/2013
99427*5^68554+647919Lelio R Paula09/2014
9943(16*10^47918-19)/347919Robert Price03/2016
994511836^11179+11179^1183647917Anatoly F. Selevich07/2009
9944Phi(65680,67)47917Enzo Doria04/2012
99463^100418-5247912Lelio R Paula06/2012
99472^159145-11281347908Enzo Doria06/2014
99486*F(229213)+147904Gilbert Mozzo06/2015
99496750^12509-12509^675047901Norbert Schneider10/2016
9950(5*2^159123-1)/3947900Lelio R Paula01/2014
99512^159105-11251347896Enzo Doria06/2014
9952(11*2^159097-1)/2147893Lelio R Paula01/2014
99532^159092+21147892Lelio R Paula02/2013
995410^47890+22490147891Patrick De Geest06/2016
995510^47890-2*10^4844-147890Serge Batalov01/2015
995610^47890-5791147890Patrick De Geest03/2016
99572^159078+115547888Lelio R Paula10/2011
9958(5*2^159081+1)/14347887Lelio R Paula07/2012
9959Phi(69053,5)47885Lelio R Paula01/2012
99603^100362-9847885Lelio R Paula06/2012
9961(9913*2^159034-1)/947878Lelio R Paula03/2015
99625^68484-68484^547869Donovan Johnson08/2005
99642^159001-27871347865Gary Barnes08/2009
99632^159003-1409547865Enzo Doria04/2013
99655^68476-2103647863Enzo Doria03/2013
9966(695277^8192+1)/247859Lelio R Paula12/2014
99672^158977+7471747857Yves Minet12/2009
99683*5^68464-847855Lelio R Paula09/2014
996913855^2844+2844^1385547855Hans Havermann08/2015
997012030^9503+9503^1203047854Jens K. Andersen01/2009
9971110597#+13131747853Nicolas PALAU09/2016
9972(3*2^158960+1)/49947850Lelio R Paula07/2012
99732^158948+1968347849Lelio R Paula10/2011
9974lucasU(1873,1,14622)-lucasU(1873,1,14621)47848Mike Oakes05/2009
9976(266*10^47844-17)/347846Robert Price06/2016
99756411^12568-12568^641147846Norbert Schneider11/2016
9977lucasU(1656,1,14862)-lucasU(1656,1,14861)47839Mike Oakes05/2009
9978(2^158894-3)/3747831Lelio R Paula01/2012
997934918!3-2747826Robert Price09/2014
99802*10^47823+8947824Robert Price07/2016
99816950^12447-12447^695047822Norbert Schneider03/2013
99822^158838-1385347816Enzo Doria04/2013
998318^38087+3747810Lelio R Paula11/2012
9984(685559^8192+1)/247809Lelio R Paula12/2014
9985(684701^8192+1)/247805Lelio R Paula12/2014
9987(11*2^158796+1)/347803Lelio R Paula01/2012
9986(684463^8192+1)/247803Lelio R Paula12/2014
9988110503#+20839147798Makoto Morimoto12/2015
9989(11^45893-4^45893)/747792Robert Price03/2013
9990(58*10^47791+23)/947792Erik Branger05/2013
9991(11743^11743+5271)/247792Makoto Morimoto07/2016
99942^158757+2947791Henri Lifchitz05/2005
99922^158758+20547791Lelio R Paula02/2013
999335^30951-3647791Enzo Doria03/2013
999510^47784+14147785Patrick De Geest06/2016
999710^47784-2*10^10720-147784Serge Batalov01/2015
999610^47784-13192747784Patrick De Geest03/2016
99982^158710-11260747777Enzo Doria06/2014
9999(677621^8192+1)/247768Lelio R Paula12/2014
100002^158656+66147761Lelio R Paula02/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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