PRP Records

Probable Primes Top 10000

(173006 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 ?
97516408*10^48143+11821^11821-2448147Gilbert Mozzo12/2012
9752(755045^8192+1)/22937848147Lelio R Paula12/2014
975311821^11821-2448143Henri Lifchitz10/2011
9754(33*2^159934+1)/193696948141Michael Porter10/2015
9755(11821^11821+1240)/19/1378948138Makoto Morimoto06/2016
975620^36997-5148135Lelio R Paula11/2012
9757(3^100895+7)/2432177503448129Lelio R Paula03/2012
9758(15185*2^159869-1)/182748127Lelio R Paula03/2015
97593*7^56945+848125Lelio R Paula09/2014
9760(749655^8192+1)/13107448122Lelio R Paula12/2014
97614*5^68835+948115Lelio R Paula09/2014
9762(148^22171+1)/14948115Richard Fischer12/2016
9763(2^159841+78557)/92348114Lelio R Paula05/2012
9764(3^50420+59)^2+6148113Jorge Menendez02/2017
976510^48109+948110Jason Earls12/2007
976610^48108+3953148109Patrick De Geest01/2009
976710^48109-10459148109Patrick De Geest07/2009
977110^48107-4810748108Henri Lifchitz07/2002
976810^48107+12622948108Patrick De Geest04/2007
976910^48108-6134348108Patrick De Geest07/2009
977023^35328+2248108Norbert Schneider12/2013
97726213^12682+12682^621348107Norbert Schneider01/2016
9773(64*10^48106+287)/948107Robert Price04/2016
977418^38321-9748104Lelio R Paula11/2012
9775(11813^11813+748)/3/67980748101Makoto Morimoto06/2016
9776(743679^8192+1)/248099Lelio R Paula12/2014
97772^159777-133348098Yves Minet05/2013
97782^159765+71748095Lelio R Paula02/2013
977935^31143-395848087Enzo Doria03/2013
97808*10^48081-948082Dmitry Domanov11/2010
978112^44553-5948081Lelio R Paula10/2012
978235086!3+218748080Robert Price12/2015
9783(11807^11807+9647)/2/548079Makoto Morimoto07/2016
97841338^15377+15377^133848076Serge Batalov05/2014
97852^159692-125948073Yves Minet08/2012
9786(lucasV(1,2,319367)+2)/(5*11)48068Mike Oakes01/2017
97872^159669+94148066Lelio R Paula02/2013
97882^159660-287948063Yves Minet09/2014
97892^159647+57348059Lelio R Paula02/2013
979019^37581+9448057Lelio R Paula11/2012
97912^159633-57706348055Paul Bourdelais11/2012
97925436^12865-12865^543648055Norbert Schneider04/2017
9793(11801^11801+8503)/2^4/3/17/13748048Makoto Morimoto07/2016
9794(23*2^159599+1)/2548045Lelio R Paula07/2012
97952^159597+130748044Lelio R Paula07/2008
97963^100693-3448043Lelio R Paula06/2012
9797(349*10^48036-7)/948038Robert Price03/2017
9798(68*10^48032+7)/348034Robert Price03/2016
979924^34797-120748028Enzo Doria03/2013
9800(106*10^48026-1)/348028Serge Batalov12/2014
98012^159522+67948021Lelio R Paula02/2013
9802(726998^8192+1)/14745748013Lelio R Paula11/2014
9803(725753^8192+1)/13107448007Lelio R Paula12/2014
980410^48003+2148004Robert Price01/2011
980510^48003-3652148003Patrick De Geest01/2012
980620^36896-404348003Enzo Doria03/2013
980710^48000+7390948001Patrick De Geest05/2012
980810^48000-8240748000Patrick De Geest05/2012
980910^47999+7809348000Patrick De Geest05/2012
981010^47999-122747999Patrick De Geest05/2012
98112^159440-1260947997Enzo Doria10/2012
9812(11789^11789+297)/2/17/2347996Makoto Morimoto06/2016
9813(40^29959+1)/4147995Robert Price09/2013
9816(49*10^47989+41)/947990Erik Branger05/2013
981410^47989+2*47989-147990Robert Price03/2015
981510^47989+3028347990Patrick De Geest01/2016
981710^47989-1046347989Patrick De Geest01/2016
9818(11*2^159409-1)/2147987Lelio R Paula01/2014
98195^68644+9447981Lelio R Paula05/2012
98202^159386-214547980Lelio R Paula03/2009
9821Linear(0,1,1,-1,318751)47977Henri Lifchitz04/2007
9822(720710^8192+1)/966388940947977Lelio R Paula11/2014
9823(2^159392+5)/11779866947974Lelio R Paula01/2012
98246576^12565-12565^657647973Norbert Schneider11/2016
982510^47969+58504347970Robert Price03/2015
982610^47969+15329147970Patrick De Geest01/2016
982710^47969-15140747969Patrick De Geest01/2016
9828(9*2^159332+1)/547964Lelio R Paula07/2012
9829(11783^11783+65)/2^3/89/268603747963Makoto Morimoto06/2016
983020^36864+3147962Lelio R Paula11/2012
9831(2^159324+78557)/240947958Lelio R Paula05/2012
98332^159293-105147952Yves Minet05/2009
9832(355*29^32789-61)/1447952Curtis Bright05/2015
9834lucasU(1856,1,14670)-lucasU(1856,1,14669)47947Mike Oakes05/2009
9835(11779^11779+1425)/2^2/11/545679147946Makoto Morimoto07/2016
98363^100482-31047943Lelio R Paula06/2012
9837(11777^11777+5123)/2^2/5/13/225147939Makoto Morimoto07/2016
983817^38959+847938Lelio R Paula11/2012
98397*10^47936-6947937Robert Price01/2017
9840(708709^8192+1)/247927Lelio R Paula12/2014
9841(709609^8192+1)/29491447927Lelio R Paula12/2014
9843Phi(104749,3)47923Lelio R Paula02/2012
984224^34721-169147923Enzo Doria03/2013
98447*5^68554+647919Lelio R Paula09/2014
9845(16*10^47918-19)/347919Robert Price03/2016
984711836^11179+11179^1183647917Anatoly F. Selevich07/2009
9846Phi(65680,67)47917Enzo Doria04/2012
98483^100418-5247912Lelio R Paula06/2012
98492^159145-11281347908Enzo Doria06/2014
98506*F(229213)+147904Gilbert Mozzo06/2015
98516750^12509-12509^675047901Norbert Schneider10/2016
9852(5*2^159123-1)/3947900Lelio R Paula01/2014
98532^159105-11251347896Enzo Doria06/2014
9854(11*2^159097-1)/2147893Lelio R Paula01/2014
98552^159092+21147892Lelio R Paula02/2013
985610^47890+22490147891Patrick De Geest06/2016
985710^47890-2*10^4844-147890Serge Batalov01/2015
985810^47890-5791147890Patrick De Geest03/2016
98592^159078+115547888Lelio R Paula10/2011
9860(5*2^159081+1)/14347887Lelio R Paula07/2012
9861Phi(69053,5)47885Lelio R Paula01/2012
98623^100362-9847885Lelio R Paula06/2012
9863(9913*2^159034-1)/947878Lelio R Paula03/2015
98645^68484-68484^547869Donovan Johnson08/2005
98652^159001-27871347865Gary Barnes08/2009
98662^159003-1409547865Enzo Doria04/2013
98675^68476-2103647863Enzo Doria03/2013
9868(695277^8192+1)/247859Lelio R Paula12/2014
98692^158977+7471747857Yves Minet12/2009
98703*5^68464-847855Lelio R Paula09/2014
987113855^2844+2844^1385547855Hans Havermann08/2015
987212030^9503+9503^1203047854Jens K. Andersen01/2009
9873110597#+13131747853Nicolas PALAU09/2016
9874(3*2^158960+1)/49947850Lelio R Paula07/2012
98752^158948+1968347849Lelio R Paula10/2011
9876lucasU(1873,1,14622)-lucasU(1873,1,14621)47848Mike Oakes05/2009
9878(266*10^47844-17)/347846Robert Price06/2016
98776411^12568-12568^641147846Norbert Schneider11/2016
9879lucasU(1656,1,14862)-lucasU(1656,1,14861)47839Mike Oakes05/2009
9880(2^158894-3)/3747831Lelio R Paula01/2012
988134918!3-2747826Robert Price09/2014
98822*10^47823+8947824Robert Price07/2016
98836950^12447-12447^695047822Norbert Schneider03/2013
98842^158838-1385347816Enzo Doria04/2013
988518^38087+3747810Lelio R Paula11/2012
9886(685559^8192+1)/247809Lelio R Paula12/2014
9887(684701^8192+1)/247805Lelio R Paula12/2014
9889(11*2^158796+1)/347803Lelio R Paula01/2012
9888(684463^8192+1)/247803Lelio R Paula12/2014
9890110503#+20839147798Makoto Morimoto12/2015
9892(11^45893-4^45893)/747792Robert Price03/2013
9893(58*10^47791+23)/947792Erik Branger05/2013
9891(11743^11743+5271)/247792Makoto Morimoto07/2016
98962^158757+2947791Henri Lifchitz05/2005
98942^158758+20547791Lelio R Paula02/2013
989535^30951-3647791Enzo Doria03/2013
989710^47784+14147785Patrick De Geest06/2016
989910^47784-2*10^10720-147784Serge Batalov01/2015
989810^47784-13192747784Patrick De Geest03/2016
99002^158710-11260747777Enzo Doria06/2014
9901(677621^8192+1)/247768Lelio R Paula12/2014
99022^158656+66147761Lelio R Paula02/2013
9903(14^41669+13^41669)/2747757Robert Price04/2013
9904(676199^8192+1)/13107447755Lelio R Paula12/2014
9905(675075^8192+1)/247754Lelio R Paula12/2014
99067^56505-2647753Lelio R Paula06/2012
9907(lucasV(1,2,317394)-2)/(7^2*23*43*67*127*463*9619*35267*45343)47749Mike Oakes01/2017
99082^158603+75547745Lelio R Paula02/2013
99093*2^158583+547739Lelio R Paula02/2014
991010^47738+2508347739Patrick De Geest06/2016
991110^47738-2*10^408-147738Serge Batalov01/2015
991210^47738-7817747738Patrick De Geest03/2016
99132^158564+8785547733Lelio R Paula11/2008
99142^158559-150747732Yves Minet08/2012
991510^47728+7947729Robert Price01/2011
99162^158552-11261947729Enzo Doria06/2014
991710^47728-7187947728Patrick De Geest10/2011
99187^56474+6447727Lelio R Paula06/2012
9919(2^158557+47)/2893147726Lelio R Paula01/2012
99202^158535-70647747724Paul Bourdelais11/2012
992110^47722-2*10^7928-147722Serge Batalov01/2015
9922(7*10^47719+71)/347720Robert Price03/2016
99232^158497+2147713Donovan Johnson02/2006
9924((19541*3^50000)^2+(3^100000-19541*3^50000)^2)/3^10000047713Robert Price07/2014
9925((148735*3^50000)^2+(3^100000-148735*3^50000)^2)/3^10000047713Robert Price08/2014
9926((155921*3^50000)^2+(3^100000-155921*3^50000)^2)/3^10000047713Robert Price08/2014
9927((228248*3^50000)^2+(3^100000-228248*3^50000)^2)/3^10000047713Robert Price08/2014
9928(666459^8192+1)/13107447704Lelio R Paula12/2014
9929(22*10^47701-19)/347702Robert Price02/2017
99312^158451+10547699Lelio R Paula03/2009
99323^99972-11047699Lelio R Paula04/2012
9930(664661^8192+1)/247699Lelio R Paula12/2014
9933(664063^8192+1)/247696Lelio R Paula12/2014
99347800^12253+12253^780047690Norbert Schneider02/2014
9936(2^158420+3)/4209147685Lelio R Paula01/2012
9935(662996^8192+1)/63897747685Lelio R Paula11/2014
99375755^12682+12682^575547685Norbert Schneider01/2016
99383^99932+3^49967+547680Mike Oakes12/2010
9939(661141^8192+1)/247680Lelio R Paula12/2014
9940(11719^11719+2293)/2^2/31/220347678Makoto Morimoto07/2016
994113^42800-8047677Lelio R Paula10/2012
9942F(228223)/12285369586644810752947676Donovan Johnson05/2007
99432^158361-11269347672Enzo Doria06/2014
99442^158351-215547669Yves Minet08/2013
9945(11717^11717+4778)/5/11/4123347668Makoto Morimoto07/2016
99462^158345+67747667Lelio R Paula02/2013
99472^158337-1155*15833747665Henri Lifchitz01/2005
9948(656137^8192+1)/247653Lelio R Paula12/2014
99497^56386-247652Lelio R Paula06/2012
995011783^11062+11062^1178347649Anatoly F. Selevich04/2009
995255^27370-5447634Norbert Schneider08/2012
9951(653670^8192+1)/73728147634Lelio R Paula11/2014
99532^158227+70147632Lelio R Paula02/2013
99552^158222-46747630Yves Minet01/2012
995435^30847-1007847630Enzo Doria03/2013
99562^158216+64347628Lelio R Paula02/2013
9957(652648^8192+1)/4831918489747624Lelio R Paula11/2014
99582^158199-1515747623Enzo Doria04/2013
9959177^21182+247617Lelio R Paula05/2013
9960(7*2^158168-1)/8793947610Lelio R Paula01/2014
99617473^12290+12290^747347606Norbert Schneider03/2014
99622^158132-11480947603Enzo Doria05/2015
9963(11701^11701+6384)/547602Makoto Morimoto07/2016
99648345^12138+12138^834547599Norbert Schneider11/2013
996511^45703-78047595Enzo Doria11/2012
99662^158095+95347592Lelio R Paula02/2013
99675^68086-1715647591Enzo Doria02/2013
9968(11699^11699+1688)/166347591Makoto Morimoto06/2016
996912855^5032+5032^1285547586Hans Havermann02/2016
99705779^12648-12648^577947580Norbert Schneider12/2016
9971PIPrime(47577)47577Eric W. Weisstein05/2006
99725^68048-1808647564Enzo Doria02/2013
997314^41494+6747558Lelio R Paula11/2012
997424^34456-201547557Enzo Doria03/2013
9975(11689^11689+2459)/2^2/3^247547Makoto Morimoto06/2016
9976(635947^8192+1)/247542Lelio R Paula12/2014
99772^157921+65947539Lelio R Paula02/2013
9978(2^157929-5)/2546747537Lelio R Paula01/2012
9979(146^21961-1)/14547530Richard Fischer10/2016
99805552^12691-12691^555247521Norbert Schneider01/2017
998113233^3896+3896^1323347515Hans Havermann02/2016
99822^157838+90747514Lelio R Paula02/2013
9983(11*2^157828+1)/68747510Lelio R Paula01/2012
9984(11681^11681+2011)/2^2/3/11104947507Makoto Morimoto06/2016
998512^44020-4347506Lelio R Paula10/2012
9986(266*10^47499-11)/347501Robert Price09/2016
99873^99541+5647494Lelio R Paula04/2012
998835^30758-800447493Enzo Doria03/2013
99892^157753-382347489Yves Minet04/2009
9990(11677^11677+3717)/2/43/9697947488Makoto Morimoto07/2016
9991(625575^8192+1)/247483Lelio R Paula12/2014
999212913!-12913#+14748103/2005
999331^31835-3047478Theodore Burton12/2005
99942^157716+90147478Lelio R Paula01/2013
99952^157710+425747476Lelio R Paula03/2009
9996(623727^8192+1)/247473Lelio R Paula12/2014
9997(623697^8192+1)/247473Lelio R Paula12/2014
99987*2^157683-347469Henri Lifchitz06/2003
99995^67892-1550647455Enzo Doria02/2013
100002^157637-1360947454Enzo Doria04/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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