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 ?
67517*2^232381+369955Lelio R Paula04/2014
67522^232362-11054169948Enzo Doria05/2014
67532^232326-11239169938Enzo Doria06/2014
67543^146575+23669935Lelio R Paula09/2013
675530^47341-2969929Norbert Schneider02/2014
67565^100040-6869925Lelio R Paula09/2013
6757(35*10^69866-593)/969867Robert Price08/2017
67582^232045-1729569853Lelio R Paula04/2012
6759(2^231987+78557)/9569834Lelio R Paula05/2012
67602^231955+7424369826Yves Minet03/2011
67612^231946-1587369823Enzo Doria04/2013
676218^55618+9569816Lelio R Paula09/2013
67636^89712+5^(89712-1)69810Robert Price02/2016
67642^231870+13569800Lelio R Paula02/2012
6765(23*2^231827-1)/417969785Lelio R Paula01/2014
67662^231778+5461569773Lelio R Paula04/2012
6767(19*2^231780+1)/23569772Lelio R Paula08/2012
676814^60866+2769761Lelio R Paula09/2013
676913^62619-4469755Lelio R Paula09/2013
6770(2^231715-509203)/3569752Lelio R Paula05/2012
67712^231711-11046769752Enzo Doria05/2014
6772(19^54547+18^54547)/3769751Robert Price08/2013
6773(23*2^231697-1)/4569748Lelio R Paula01/2014
67742^231696-186149969748Enzo Doria03/2016
67752^231684-14769744Lelio R Paula02/2012
6776(23*2^231686-1)/118369743Lelio R Paula01/2014
67772^231591-47739769716Paul Bourdelais03/2013
677811^66916-42069686Enzo Doria08/2012
67795^99680-1370669674Enzo Doria02/2013
6780(8*10^69674-53)/969674Robert Price11/2014
6781(44*10^69663-413)/969664Robert Price10/2017
6782(77*10^69656-23)/969657Robert Price10/2015
67836^89509+13169652Lelio R Paula09/2013
6784(78557*2^231349+1)/3569647Lelio R Paula06/2014
6785(11*10^69645+19)/369646Robert Price03/2016
678611^66875-2869644Lelio R Paula09/2013
67872^231347+7148369643Enzo Doria04/2016
6788(14^60763+3^60763)/1769641Robert Price04/2013
6789(4*10^69626+173)/369627Robert Price01/2017
67902^231289+25569625Lelio R Paula04/2012
67912^231234-11291369609Enzo Doria06/2014
6792(265*10^69602-7)/369604Robert Price07/2016
67932^231182-11284169593Enzo Doria06/2014
6794(15*2^231129+1)/2369577Lelio R Paula08/2012
67953^145806-2869568Lelio R Paula09/2013
6796(265*10^69554-7)/369556Robert Price07/2016
67972^231052-11315969554Enzo Doria07/2014
679811^66784-869549Lelio R Paula09/2013
6799Phi(104409,10)/229699969546Maksym Voznyy07/2015
68002^231016-11052369543Enzo Doria05/2014
68012^231014+57729457569543Lelio R Paula02/2016
680214^60658+6769522Lelio R Paula09/2013
68035^99418+3669491Lelio R Paula06/2013
68047^82203-3069470Lelio R Paula09/2013
6805(63^38609-1)/6269469Paul Bourdelais08/2017
68065^99359-2^9936069449Mike Oakes12/2010
6807(29*2^230684+1)/139569442Lelio R Paula08/2012
6808(19*10^69424+77)/369425Robert Price08/2016
680919^54287-9669420Lelio R Paula09/2013
68102^230541+5890569400Lelio R Paula04/2012
68112^230506+1270569390Lelio R Paula02/2013
68128*6^89156-569378Lelio R Paula09/2014
68132^230438-11134769369Enzo Doria05/2014
68142^230428-9969366Lelio R Paula02/2012
6815(62^38699+1)/6369362Paul Bourdelais08/2017
68163*10^69354+1769355Robert Price03/2017
6817(493*10^69340-7)/969342Robert Price07/2016
6818(41*10^69321+373)/969322Robert Price04/2017
68196^89072+5369312Lelio R Paula09/2013
6820155^31639+269300Lelio R Paula05/2013
68213*7^81965-469269Lelio R Paula09/2014
6822(16*10^69265+41)/369266Robert Price10/2017
6823(86*10^69260-77)/969261Robert Price05/2016
68249*5^99087+469260Lelio R Paula09/2014
68253^145145+266069252Lelio R Paula09/2013
682611^66492-114069245Enzo Doria11/2012
68275*3^145129-469245Lelio R Paula04/2014
68287*3^145126+869244Lelio R Paula04/2014
682911^66480-237069232Enzo Doria12/2012
68302^229962-6569226Lelio R Paula02/2012
68312^229958-11073369225Enzo Doria05/2014
6832V(332407)69225Serge Batalov03/2015
68336^88959+769224Lelio R Paula09/2013
683415^58855-9469219Lelio R Paula09/2013
6835(2^229838+47)/1208169185Lelio R Paula04/2012
68363^144952+9869160Lelio R Paula09/2013
68375^98941-7269157Lelio R Paula06/2013
6838(17*2^229604-1)/22969117Lelio R Paula01/2014
68392^229585-106369112Yves Minet11/2012
6840(13*2^229567-1)/1969107Lelio R Paula01/2014
6841(13*2^229393-1)/569055Lelio R Paula01/2014
6842(53*10^69050-17)/969051Robert Price09/2015
6843(43*10^69048+47)/969049Robert Price12/2017
68442^229305-186853369028Enzo Doria04/2016
68452^229297+138569026Lelio R Paula04/2012
684618^54986-244169023Enzo Doria03/2013
6847(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
68485^98736-1463669014Enzo Doria02/2013
6849(13^61949-5^61949)/869007Robert Price03/2013
6850(2^229227+5)/61169002Lelio R Paula04/2012
68512^229216-11327969001Enzo Doria07/2014
685210^68994+5191368995Patrick De Geest03/2016
685410^68994-10^5814-168994Serge Batalov01/2011
685310^68994-8294768994Patrick De Geest03/2016
6855(17*2^229136-1)/238168975Lelio R Paula01/2014
68562^229113+10768970Lelio R Paula02/2012
685711^66202-441068943Enzo Doria01/2013
685812^63883+568942Lelio R Paula07/2013
6859(9913*2^229002-1)/39990368935Lelio R Paula04/2015
68602^228962-11158168925Enzo Doria05/2014
68612^228944+8168920Henri Lifchitz01/2007
686211^66174-5468914Lelio R Paula09/2013
68632^228913-11126568910Enzo Doria05/2014
68642^228902+7351968907Enzo Doria04/2016
6865(47*2^228884+1)/6368901Lelio R Paula04/2015
68662^228821+7642768882Enzo Doria05/2016
68673^144340+5068868Lelio R Paula09/2013
68682^228758-11296768864Enzo Doria06/2014
68692^228743-11137968859Enzo Doria05/2014
68702^228741-11091168858Enzo Doria05/2014
6872lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
68713*5^98511-868857Lelio R Paula09/2014
68732^228717+46768851Lelio R Paula02/2011
6874Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
6875(509203*2^228665-1)/3568840Lelio R Paula04/2015
68768^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
687711^66074-105068809Enzo Doria11/2012
6878(68*10^68798-11)/368800Robert Price10/2017
68792^228484+18168781Lelio R Paula02/2012
68802^228479-5869568780Lelio R Paula04/2012
68812^228465-1585368775Enzo Doria04/2013
688211^66040-540068774Enzo Doria01/2013
6883(13*2^228441-1)/57568766Lelio R Paula01/2014
6884(17*2^228393+1)/29568752Lelio R Paula08/2012
68852*10^68744+4168745Robert Price01/2017
688611^66011-15068744Enzo Doria08/2012
6887(13*2^228304-1)/8168726Lelio R Paula01/2014
68882^228295-11107968724Enzo Doria05/2014
6890(3^144039+7)/2268723Lelio R Paula04/2012
6889(8*10^68722+49)/368723Robert Price03/2016
6891(35*10^68718+1)/968719Serge Batalov11/2010
68922^228271-22827168717Henri Lifchitz11/2004
68932^228257+8287568713Lelio R Paula02/2013
68943^144013+4068712Lelio R Paula09/2013
689513^61671-8668699Lelio R Paula09/2013
6896(46*10^68698+683)/968699Robert Price12/2017
689717^55828-7268694Lelio R Paula09/2013
68986^88259+6168679Lelio R Paula09/2013
689918^54699-568663Lelio R Paula09/2013
690033^45216+268662Lelio R Paula05/2013
6902(2^228073-5)/368657Lelio R Paula04/2012
6901(2^(6*38012+1)-5)/368657Kevin Acres11/2013
69032^228055-11160768652Enzo Doria05/2014
69042^228054-11476168652Enzo Doria05/2015
69052^228041+118568648Lelio R Paula04/2012
69062^228040-103768647Yves Minet11/2012
69072*F(328450)-168642Henri Lifchitz12/2009
69085^98201-3468640Lelio R Paula06/2013
69099^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
69107*2^227780-368570Lelio R Paula04/2014
69112^227733-12168555Lelio R Paula02/2012
69122^227702-1696768546Enzo Doria05/2013
69132^227689-11165568542Enzo Doria05/2014
6914gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
69155^98051+268535Ray Chandler07/2011
69165*10^68524+5168525Robert Price01/2017
6917(11*10^68520-149)/368521Robert Price01/2017
691819^53573-7868507Lelio R Paula09/2013
6919(68*10^68504+13)/968505Ray Chandler10/2010
69209*5^98003+468503Lelio R Paula09/2014
69212^227528+5168493Lelio R Paula02/2012
6922(146*28^47316+1)/368476Karsten Bonath06/2018
69233^143497+868466Lelio R Paula04/2012
69242^227430-9568464Lelio R Paula02/2012
6925(8*10^68455+13)/368456Robert Price11/2017
69263*5^97934-268454Lelio R Paula09/2014
692720^52613+7768452Lelio R Paula09/2013
69282^227371+3276968446Lelio R Paula04/2012
6929(3^143465+4)/2127042006768440Lelio R Paula04/2012
6930CopelandErdos(68433)68433Eric W. Weisstein08/2013
69312^227323+7543168432Enzo Doria04/2016
69322^227314-196568429Lelio R Paula04/2012
69332^227303-11061768426Enzo Doria05/2014
69347^80963+6668422Lelio R Paula07/2013
69352^227290+7384968422Enzo Doria04/2016
6936(14^59693-1)/1368415Paul Bourdelais06/2008
69372^227256-278624968411Enzo Doria03/2016
69398*10^68400-768401Dmitry Domanov11/2010
6938(15*2^227228-1)/58368401Lelio R Paula01/2014
69402^227210+186916968398Enzo Doria05/2016
69412^227159-183863568382Enzo Doria05/2015
694244*10^68368+368370Robert Price08/2017
69432^227115-780768369Lelio R Paula10/2009
69442^227078-4735568358Lelio R Paula04/2012
6945(2^227063-1017)/34968351Lelio R Paula04/2012
69462^227057+14809168351Lelio R Paula04/2012
69472^227046+18768348Lelio R Paula02/2012
69489*10^68331+5968332Robert Price10/2017
694911^65608-72068324Enzo Doria11/2012
6950(32*10^68320+319)/968321Robert Price10/2017
695133408!2-2^33408-168315Joe McLean05/2017
69522^226894-12368302Lelio R Paula02/2012
695310^68297+14155968298Patrick De Geest05/2013
695410^68297-9368297Robert Price05/2011
6955680^24107-679^2410768284Jean-Louis Charton07/2010
695612^63267+5968277Lelio R Paula07/2013
69572^226785-115968270Yves Minet11/2012
69587^80769+9068258Lelio R Paula07/2013
6959(88*10^68256-1)/368258Robert Price10/2017
69602^226741+6658768256Yves Minet10/2010
69612^226720-11240368250Enzo Doria06/2014
6962(78557*2^226694+1)/368247Lelio R Paula06/2014
6963(83*10^68231+7)/968232Robert Price10/2015
696465^37636+1668231Lelio R Paula01/2016
69655^97615-4^(97615+1)68230Robert Price04/2016
696612^63200-4368205Lelio R Paula07/2013
6967-330*Bern(21940)/22379062073368201Serge Batalov04/2015
69683^142925+868068193Lelio R Paula06/2013
69693*2^226512-768188Lelio R Paula04/2014
697014^59484+5768177Lelio R Paula08/2013
697111^65438-219068147Enzo Doria12/2012
697291^34784-268144Lelio R Paula09/2013
6973(2^226336-3)*6-768135Gilbert Mozzo06/2016
6974(22*10^68133-37)/368134Robert Price05/2017
69755^97476+3668133Lelio R Paula06/2013
69763*5^97474-268132Lelio R Paula09/2014
697712^63130+4968129Lelio R Paula07/2013
69782^226281+538568118Lelio R Paula04/2012
69792^226257-304968111Yves Minet10/2014
6980(28*10^68107-43)/368108Robert Price04/2016
69812^226243-258768106Yves Minet07/2014
698220^52346-1168104Lelio R Paula09/2013
69832^226205-9968095Lelio R Paula02/2012
69842^226187-4968090Lelio R Paula02/2012
69853^142708+7668090Lelio R Paula06/2013
69867*10^68088-8968089Robert Price01/2017
69872^226154+7183968080Enzo Doria04/2016
6988(10^68078+59)/368078Serge Batalov12/2014
699014^59387+6968066Lelio R Paula08/2013
69892^226108-11342968066Enzo Doria07/2014
6991(62*10^68059-197)/968060Robert Price10/2017
6992(24^49307-1)/2368053Robert Price04/2012
699315^57859-2868048Lelio R Paula08/2013
6994(509203*2^226003-1)/1368039Lelio R Paula04/2015
69952^226015-11136168038Enzo Doria05/2014
6996(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
69974*10^68020+9168021Robert Price11/2017
6998156*(10^(4*17000)-1)/101-168001Robert Price05/2014
69992^225878-101767997Lelio R Paula04/2012
70003*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010


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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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