PRP Records

Probable Primes Top 10000

(252932 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 (> 50000) Who ? When ?
7251(29*2^230684+1)/139569442Lelio R Paula08/2012
7252(19*10^69424+77)/369425Robert Price08/2016
725319^54287-9669420Lelio R Paula09/2013
72542^230541+5890569400Lelio R Paula04/2012
72552^230506+1270569390Lelio R Paula02/2013
72568*6^89156-569378Lelio R Paula09/2014
72572^230438-11134769369Enzo Doria05/2014
72582^230428-9969366Lelio R Paula02/2012
7259(62^38699+1)/6369362Paul Bourdelais08/2017
72603*10^69354+1769355Robert Price03/2017
7261(493*10^69340-7)/969342Robert Price07/2016
7262(41*10^69321+373)/969322Robert Price04/2017
72636^89072+5369312Lelio R Paula09/2013
7264155^31639+269300Lelio R Paula05/2013
72653*7^81965-469269Lelio R Paula09/2014
7266(16*10^69265+41)/369266Robert Price10/2017
7267(86*10^69260-77)/969261Robert Price05/2016
72689*5^99087+469260Lelio R Paula09/2014
72693^145145+266069252Lelio R Paula09/2013
727111^66492-114069245Enzo Doria11/2012
72705*3^145129-469245Lelio R Paula04/2014
72727*3^145126+869244Lelio R Paula04/2014
727311^66480-237069232Enzo Doria12/2012
72742^229962-6569226Lelio R Paula02/2012
72752^229958-11073369225Enzo Doria05/2014
7276V(332407)69225Serge Batalov03/2015
72776^88959+769224Lelio R Paula09/2013
727815^58855-9469219Lelio R Paula09/2013
7279159773#-p(159773)69212Henri Lifchitz12/2018
7280(2^229838+47)/1208169185Lelio R Paula04/2012
72813^144952+9869160Lelio R Paula09/2013
72825^98941-7269157Lelio R Paula06/2013
7283(17*2^229604-1)/22969117Lelio R Paula01/2014
72842^229585-106369112Yves Minet11/2012
7285(13*2^229567-1)/1969107Lelio R Paula01/2014
7286(13*2^229393-1)/569055Lelio R Paula01/2014
7287(53*10^69050-17)/969051Robert Price09/2015
7288(43*10^69048+47)/969049Robert Price12/2017
72892^229305-186853369028Enzo Doria04/2016
72902^229297+138569026Lelio R Paula04/2012
729118^54986-244169023Enzo Doria03/2013
7292(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
72935^98736-1463669014Enzo Doria02/2013
7294(13^61949-5^61949)/869007Robert Price03/2013
7295(2^229227+5)/61169002Lelio R Paula04/2012
72962^229216-11327969001Enzo Doria07/2014
729710^68994+5191368995Patrick De Geest03/2016
729910^68994-10^5814-168994Serge Batalov01/2011
729810^68994-8294768994Patrick De Geest03/2016
7300(17*2^229136-1)/238168975Lelio R Paula01/2014
73012^229113+10768970Lelio R Paula02/2012
730211^66202-441068943Enzo Doria01/2013
730312^63883+568942Lelio R Paula07/2013
7304(9913*2^229002-1)/39990368935Lelio R Paula04/2015
73052^228962-11158168925Enzo Doria05/2014
73062^228944+8168920Henri Lifchitz01/2007
730711^66174-5468914Lelio R Paula09/2013
73082^228913-11126568910Enzo Doria05/2014
73092^228902+7351968907Enzo Doria04/2016
7310(47*2^228884+1)/6368901Lelio R Paula04/2015
73112^228821+7642768882Enzo Doria05/2016
73123^144340+5068868Lelio R Paula09/2013
73132^228758-11296768864Enzo Doria06/2014
73142^228743-11137968859Enzo Doria05/2014
73152^228741-11091168858Enzo Doria05/2014
7317lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
73163*5^98511-868857Lelio R Paula09/2014
73182^228717+46768851Lelio R Paula02/2011
7319Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
7320(509203*2^228665-1)/3568840Lelio R Paula04/2015
73218^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
732211^66074-105068809Enzo Doria11/2012
7323(68*10^68798-11)/368800Robert Price10/2017
73242^228484+18168781Lelio R Paula02/2012
73252^228479-5869568780Lelio R Paula04/2012
73262^228465-1585368775Enzo Doria04/2013
732711^66040-540068774Enzo Doria01/2013
7328(13*2^228441-1)/57568766Lelio R Paula01/2014
7329(17*2^228393+1)/29568752Lelio R Paula08/2012
73302*10^68744+4168745Robert Price01/2017
733111^66011-15068744Enzo Doria08/2012
7332(13*2^228304-1)/8168726Lelio R Paula01/2014
73332^228295-11107968724Enzo Doria05/2014
7335(3^144039+7)/2268723Lelio R Paula04/2012
7334(8*10^68722+49)/368723Robert Price03/2016
7336(35*10^68718+1)/968719Serge Batalov11/2010
73372^228271-22827168717Henri Lifchitz11/2004
73382^228257+8287568713Lelio R Paula02/2013
73393^144013+4068712Lelio R Paula09/2013
734013^61671-8668699Lelio R Paula09/2013
7341(46*10^68698+683)/968699Robert Price12/2017
734217^55828-7268694Lelio R Paula09/2013
73436^88259+6168679Lelio R Paula09/2013
734418^54699-568663Lelio R Paula09/2013
734533^45216+268662Lelio R Paula05/2013
7347(2^228073-5)/368657Lelio R Paula04/2012
7346(2^(6*38012+1)-5)/368657Kevin Acres11/2013
73482^228055-11160768652Enzo Doria05/2014
73492^228054-11476168652Enzo Doria05/2015
73502^228041+118568648Lelio R Paula04/2012
73512^228040-103768647Yves Minet11/2012
73522*F(328450)-168642Henri Lifchitz12/2009
73535^98201-3468640Lelio R Paula06/2013
73549^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
73557*2^227780-368570Lelio R Paula04/2014
735615327^16382-16382^1532768567Norbert Schneider11/2018
73572^227733-12168555Lelio R Paula02/2012
73582^227702-1696768546Enzo Doria05/2013
73592^227689-11165568542Enzo Doria05/2014
7360gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
73615^98051+268535Ray Chandler07/2011
73625*10^68524+5168525Robert Price01/2017
7363(11*10^68520-149)/368521Robert Price01/2017
736419^53573-7868507Lelio R Paula09/2013
7365(68*10^68504+13)/968505Ray Chandler10/2010
73669*5^98003+468503Lelio R Paula09/2014
73672^227528+5168493Lelio R Paula02/2012
7368(146*28^47316+1)/368476Karsten Bonath06/2018
73693^143497+868466Lelio R Paula04/2012
73702^227430-9568464Lelio R Paula02/2012
7371(8*10^68455+13)/368456Robert Price11/2017
73723*5^97934-268454Lelio R Paula09/2014
737320^52613+7768452Lelio R Paula09/2013
73742^227371+3276968446Lelio R Paula04/2012
7375(3^143465+4)/2127042006768440Lelio R Paula04/2012
7376CopelandErdos(68433)68433Eric W. Weisstein08/2013
73772^227323+7543168432Enzo Doria04/2016
73782^227314-196568429Lelio R Paula04/2012
73792^227303-11061768426Enzo Doria05/2014
73807^80963+6668422Lelio R Paula07/2013
73812^227290+7384968422Enzo Doria04/2016
7382(14^59693-1)/1368415Paul Bourdelais06/2008
73832^227256-278624968411Enzo Doria03/2016
73848*10^68400-768401Dmitry Domanov11/2010
7385(15*2^227228-1)/58368401Lelio R Paula01/2014
73862^227210+186916968398Enzo Doria05/2016
73872^227159-183863568382Enzo Doria05/2015
738844*10^68368+368370Robert Price08/2017
73892^227115-780768369Lelio R Paula10/2009
73902^227078-4735568358Lelio R Paula04/2012
7391(2^227063-1017)/34968351Lelio R Paula04/2012
73922^227057+14809168351Lelio R Paula04/2012
73932^227046+18768348Lelio R Paula02/2012
73942^227009-469368337Yves Minet05/2019
73959*10^68331+5968332Robert Price10/2017
739611^65608-72068324Enzo Doria11/2012
7397(32*10^68320+319)/968321Robert Price10/2017
739833408!2-2^33408-168315Joe McLean05/2017
73992^226894-12368302Lelio R Paula02/2012
740010^68297+14155968298Patrick De Geest05/2013
740110^68297-9368297Robert Price05/2011
7402680^24107-679^2410768284Jean-Louis Charton07/2010
740312^63267+5968277Lelio R Paula07/2013
74042^226785-115968270Yves Minet11/2012
74057^80769+9068258Lelio R Paula07/2013
7406(88*10^68256-1)/368258Robert Price10/2017
74072^226741+6658768256Yves Minet10/2010
74082^226720-11240368250Enzo Doria06/2014
7409(78557*2^226694+1)/368247Lelio R Paula06/2014
7410(83*10^68231+7)/968232Robert Price10/2015
741165^37636+1668231Lelio R Paula01/2016
74125^97615-4^(97615+1)68230Robert Price04/2016
741312^63200-4368205Lelio R Paula07/2013
7414-330*Bern(21940)/22379062073368201Serge Batalov04/2015
74153^142925+868068193Lelio R Paula06/2013
74163*2^226512-768188Lelio R Paula04/2014
741714^59484+5768177Lelio R Paula08/2013
741811^65438-219068147Enzo Doria12/2012
741991^34784-268144Lelio R Paula09/2013
7420(2^226336-3)*6-768135Gilbert Mozzo06/2016
7421(22*10^68133-37)/368134Robert Price05/2017
74225^97476+3668133Lelio R Paula06/2013
74233*5^97474-268132Lelio R Paula09/2014
742412^63130+4968129Lelio R Paula07/2013
74252^226281+538568118Lelio R Paula04/2012
74262^226257-304968111Yves Minet10/2014
7427(28*10^68107-43)/368108Robert Price04/2016
74282^226243-258768106Yves Minet07/2014
742920^52346-1168104Lelio R Paula09/2013
74302^226205-9968095Lelio R Paula02/2012
74312^226187-4968090Lelio R Paula02/2012
74323^142708+7668090Lelio R Paula06/2013
74337*10^68088-8968089Robert Price01/2017
74342^226154+7183968080Enzo Doria04/2016
7435(10^68078+59)/368078Serge Batalov12/2014
743714^59387+6968066Lelio R Paula08/2013
74362^226108-11342968066Enzo Doria07/2014
7438(62*10^68059-197)/968060Robert Price10/2017
7439(24^49307-1)/2368053Robert Price04/2012
744015^57859-2868048Lelio R Paula08/2013
7441(509203*2^226003-1)/1368039Lelio R Paula04/2015
74422^226015-11136168038Enzo Doria05/2014
7443(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
74444*10^68020+9168021Robert Price11/2017
7445156*(10^(4*17000)-1)/101-168001Robert Price05/2014
74462^225878-101767997Lelio R Paula04/2012
74473*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
74483*2^225865+567993Lelio R Paula04/2014
745011^65284-582067987Enzo Doria01/2013
744919^53166+7067987Lelio R Paula08/2013
74512^225837+7540767984Enzo Doria04/2016
74523^142464-11265467973Enzo Doria06/2014
74532^225777+9567966Lelio R Paula02/2012
7454(2^225641-1017)/13881567920Lelio R Paula04/2012
74552^225609-1844567916Enzo Doria05/2013
74562^225542-17767895Lelio R Paula02/2012
74572^225536-2967894Henri Lifchitz05/2005
745811^65190-339067889Enzo Doria12/2012
74593^142249-2^(142249-1)67871Robert Price01/2016
746011^65168-483067866Enzo Doria01/2013
746110^67863+5862767864Patrick De Geest01/2016
746210^67863-1167863Robert Price05/2011
7463(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
7464(19*2^225357-1)/1167840Lelio R Paula01/2014
74659*6^87164-767828Lelio R Paula09/2014
7466131^32034+13067825Norbert Schneider03/2015
7467(29*2^225314+1)/1088167824Lelio R Paula08/2012
7468(134*10^67816+7)/367818Robert Price02/2017
74692^225261+85567811Lelio R Paula04/2012
7470(29*2^225252-1)/293367806Lelio R Paula01/2014
7471(4*10^67796+23)/967796Robert Price11/2014
747215477^16180-16180^1547767790Norbert Schneider09/2018
7473(23*2^225177+1)/3167785Lelio R Paula08/2012
7474(4*10^67784+149)/967784Robert Price03/2017
74758177^17322+17322^817767774Norbert Schneider03/2019
74762^225120+15167768Lelio R Paula02/2012
7477(44^41233+1)/4567763Robert Price11/2013
747889933!6-1667747Robert Price08/2018
74798*10^67742+967743Dmitry Domanov11/2010
74802^224977+108967725Lelio R Paula04/2012
7481(2^224950+5)/1950967713Lelio R Paula04/2012
748211^65011-597067702Enzo Doria01/2013
748388*10^67691+767693Robert Price11/2016
748411^65000-714067691Enzo Doria01/2013
74862^224841+5967684Lelio R Paula02/2012
748533129!2+2^3312967684Robert Price09/2015
74872^224827+841567680Lelio R Paula02/2013
7488(9913*2^224821-1)/1982567678Lelio R Paula04/2015
74892^224815-4978967677Henri Lifchitz04/2005
7490(43*10^67664+11)/967665Robert Price06/2015
7491(292*10^67659-1)/367661Robert Price01/2017
7492(17*2^224766+1)/2900767659Lelio R Paula06/2012
74932^224744+57729457567655Lelio R Paula02/2016
7494((1+sqrt(7)+sqrt(6))^45863-1)*((1+sqrt(7)-sqrt(6))^45863-1)*((1-sqrt(7)+sqrt(6))^45863-1)*((1-sqrt(767653Mike Oakes05/2009
7495(2^224721+78557)/173967645Lelio R Paula05/2012
74962^224700+191567642Lelio R Paula04/2012
7497(29*2^224694-1)/19890567636Lelio R Paula01/2014
74982^224658-9367629Lelio R Paula02/2012
74992^224624-1307767619Enzo Doria10/2012
750018^53860-331967609Enzo Doria03/2013


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2019 07:14 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!