PRP Records

Probable Primes Top 10000

(253466 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 (> 50000) Who ? When ?
75012^229305-186853369028Enzo Doria04/2016
75022^229297+138569026Lelio R Paula04/2012
750318^54986-244169023Enzo Doria03/2013
7504(34*10^69021-7)/9/3/6769020Makoto Morimoto04/2016
75055^98736-1463669014Enzo Doria02/2013
7506(13^61949-5^61949)/869007Robert Price03/2013
7507(2^229227+5)/61169002Lelio R Paula04/2012
75082^229216-11327969001Enzo Doria07/2014
750910^68994+5191368995Patrick De Geest03/2016
751110^68994-10^5814-168994Serge Batalov01/2011
751010^68994-8294768994Patrick De Geest03/2016
7512(17*2^229136-1)/238168975Lelio R Paula01/2014
75132^229113+10768970Lelio R Paula02/2012
751411^66202-441068943Enzo Doria01/2013
751512^63883+568942Lelio R Paula07/2013
7516(9913*2^229002-1)/39990368935Lelio R Paula04/2015
75172^228962-11158168925Enzo Doria05/2014
75182^228944+8168920Henri Lifchitz01/2007
751911^66174-5468914Lelio R Paula09/2013
75202^228913-11126568910Enzo Doria05/2014
75212^228902+7351968907Enzo Doria04/2016
7522(47*2^228884+1)/6368901Lelio R Paula04/2015
75232^228821+7642768882Enzo Doria05/2016
75243^144340+5068868Lelio R Paula09/2013
75252^228758-11296768864Enzo Doria06/2014
75262^228743-11137968859Enzo Doria05/2014
75272^228741-11091168858Enzo Doria05/2014
7529lucasU(1926,1,20964)-lucasU(1926,1,20963)68857Mike Oakes05/2009
75283*5^98511-868857Lelio R Paula09/2014
75302^228717+46768851Lelio R Paula02/2011
7531Phi(153218,10)/2211855049/23592660859/49771411729168849Maksym Voznyy10/2011
7532(509203*2^228665-1)/3568840Lelio R Paula04/2015
75338^76213-7^7621368828Ananda Tallur & Jean-Louis Charton11/2003
753411^66074-105068809Enzo Doria11/2012
7535(68*10^68798-11)/368800Robert Price10/2017
75362^228484+18168781Lelio R Paula02/2012
75372^228479-5869568780Lelio R Paula04/2012
75382^228465-1585368775Enzo Doria04/2013
753911^66040-540068774Enzo Doria01/2013
7540(13*2^228441-1)/57568766Lelio R Paula01/2014
7541(17*2^228393+1)/29568752Lelio R Paula08/2012
75422*10^68744+4168745Robert Price01/2017
754311^66011-15068744Enzo Doria08/2012
7544(13*2^228304-1)/8168726Lelio R Paula01/2014
75452^228295-11107968724Enzo Doria05/2014
7547(3^144039+7)/2268723Lelio R Paula04/2012
7546(8*10^68722+49)/368723Robert Price03/2016
7548(35*10^68718+1)/968719Serge Batalov11/2010
75492^228271-22827168717Henri Lifchitz11/2004
75502^228257+8287568713Lelio R Paula02/2013
75513^144013+4068712Lelio R Paula09/2013
755213^61671-8668699Lelio R Paula09/2013
7553(46*10^68698+683)/968699Robert Price12/2017
755417^55828-7268694Lelio R Paula09/2013
75556^88259+6168679Lelio R Paula09/2013
755618^54699-568663Lelio R Paula09/2013
755733^45216+268662Lelio R Paula05/2013
7559(2^228073-5)/368657Lelio R Paula04/2012
7558(2^(6*38012+1)-5)/368657Kevin Acres11/2013
75602^228055-11160768652Enzo Doria05/2014
75612^228054-11476168652Enzo Doria05/2015
75622^228041+118568648Lelio R Paula04/2012
75632^228040-103768647Yves Minet11/2012
75642*F(328450)-168642Henri Lifchitz12/2009
75655^98201-3468640Lelio R Paula06/2013
75669^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
75677*2^227780-368570Lelio R Paula04/2014
756815327^16382-16382^1532768567Norbert Schneider11/2018
75692^227733-12168555Lelio R Paula02/2012
75702^227702-1696768546Enzo Doria05/2013
75712^227689-11165568542Enzo Doria05/2014
7572gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
75735^98051+268535Ray Chandler07/2011
75745*10^68524+5168525Robert Price01/2017
7575(11*10^68520-149)/368521Robert Price01/2017
757619^53573-7868507Lelio R Paula09/2013
7577(68*10^68504+13)/968505Ray Chandler10/2010
75789*5^98003+468503Lelio R Paula09/2014
75792^227528+5168493Lelio R Paula02/2012
7580(146*28^47316+1)/368476Karsten Bonath06/2018
75813^143497+868466Lelio R Paula04/2012
75822^227430-9568464Lelio R Paula02/2012
7583(8*10^68455+13)/368456Robert Price11/2017
75843*5^97934-268454Lelio R Paula09/2014
758520^52613+7768452Lelio R Paula09/2013
75862^227371+3276968446Lelio R Paula04/2012
7587(3^143465+4)/2127042006768440Lelio R Paula04/2012
7588CopelandErdos(68433)68433Eric W. Weisstein08/2013
75892^227323+7543168432Enzo Doria04/2016
75902^227314-196568429Lelio R Paula04/2012
75912^227303-11061768426Enzo Doria05/2014
75927^80963+6668422Lelio R Paula07/2013
75932^227290+7384968422Enzo Doria04/2016
7594(14^59693-1)/1368415Paul Bourdelais06/2008
75952^227256-278624968411Enzo Doria03/2016
75978*10^68400-768401Dmitry Domanov11/2010
7596(15*2^227228-1)/58368401Lelio R Paula01/2014
75982^227210+186916968398Enzo Doria05/2016
75992^227159-183863568382Enzo Doria05/2015
760044*10^68368+368370Robert Price08/2017
76012^227115-780768369Lelio R Paula10/2009
76022^227078-4735568358Lelio R Paula04/2012
7603(2^227063-1017)/34968351Lelio R Paula04/2012
76042^227057+14809168351Lelio R Paula04/2012
76052^227046+18768348Lelio R Paula02/2012
76062^227009-469368337Yves Minet05/2019
76079*10^68331+5968332Robert Price10/2017
760811^65608-72068324Enzo Doria11/2012
7609(32*10^68320+319)/968321Robert Price10/2017
761033408!2-2^33408-168315Joe McLean05/2017
76112^226894-12368302Lelio R Paula02/2012
761210^68297+14155968298Patrick De Geest05/2013
761310^68297-9368297Robert Price05/2011
7614680^24107-679^2410768284Jean-Louis Charton07/2010
761512^63267+5968277Lelio R Paula07/2013
76162^226785-115968270Yves Minet11/2012
76177^80769+9068258Lelio R Paula07/2013
7618(88*10^68256-1)/368258Robert Price10/2017
76192^226741+6658768256Yves Minet10/2010
76202^226720-11240368250Enzo Doria06/2014
7621(78557*2^226694+1)/368247Lelio R Paula06/2014
7622(83*10^68231+7)/968232Robert Price10/2015
762365^37636+1668231Lelio R Paula01/2016
76245^97615-4^(97615+1)68230Robert Price04/2016
762512^63200-4368205Lelio R Paula07/2013
7626-330*Bern(21940)/22379062073368201Serge Batalov04/2015
76273^142925+868068193Lelio R Paula06/2013
76283*2^226512-768188Lelio R Paula04/2014
762914^59484+5768177Lelio R Paula08/2013
763011^65438-219068147Enzo Doria12/2012
763191^34784-268144Lelio R Paula09/2013
7632(2^226336-3)*6-768135Gilbert Mozzo06/2016
7633(22*10^68133-37)/368134Robert Price05/2017
76345^97476+3668133Lelio R Paula06/2013
76353*5^97474-268132Lelio R Paula09/2014
763612^63130+4968129Lelio R Paula07/2013
76372^226281+538568118Lelio R Paula04/2012
76382^226257-304968111Yves Minet10/2014
7639(28*10^68107-43)/368108Robert Price04/2016
76402^226243-258768106Yves Minet07/2014
764120^52346-1168104Lelio R Paula09/2013
76422^226205-9968095Lelio R Paula02/2012
76432^226187-4968090Lelio R Paula02/2012
76443^142708+7668090Lelio R Paula06/2013
76457*10^68088-8968089Robert Price01/2017
76462^226154+7183968080Enzo Doria04/2016
7647(10^68078+59)/368078Serge Batalov12/2014
764914^59387+6968066Lelio R Paula08/2013
76482^226108-11342968066Enzo Doria07/2014
7650(62*10^68059-197)/968060Robert Price10/2017
7651(24^49307-1)/2368053Robert Price04/2012
765215^57859-2868048Lelio R Paula08/2013
7653(509203*2^226003-1)/1368039Lelio R Paula04/2015
76542^226015-11136168038Enzo Doria05/2014
7655(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
76564*10^68020+9168021Robert Price11/2017
7657156*(10^(4*17000)-1)/101-168001Robert Price05/2014
76582^225878-101767997Lelio R Paula04/2012
76593*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
76603*2^225865+567993Lelio R Paula04/2014
766211^65284-582067987Enzo Doria01/2013
766119^53166+7067987Lelio R Paula08/2013
76632^225837+7540767984Enzo Doria04/2016
76643^142464-11265467973Enzo Doria06/2014
76652^225777+9567966Lelio R Paula02/2012
7666(2^225641-1017)/13881567920Lelio R Paula04/2012
76672^225609-1844567916Enzo Doria05/2013
76682^225542-17767895Lelio R Paula02/2012
76692^225536-2967894Henri Lifchitz05/2005
767011^65190-339067889Enzo Doria12/2012
76713^142249-2^(142249-1)67871Robert Price01/2016
767211^65168-483067866Enzo Doria01/2013
767310^67863+5862767864Patrick De Geest01/2016
767410^67863-1167863Robert Price05/2011
7675(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
7676(19*2^225357-1)/1167840Lelio R Paula01/2014
76779*6^87164-767828Lelio R Paula09/2014
7678131^32034+13067825Norbert Schneider03/2015
7679(29*2^225314+1)/1088167824Lelio R Paula08/2012
7680(134*10^67816+7)/367818Robert Price02/2017
76812^225261+85567811Lelio R Paula04/2012
7682(29*2^225252-1)/293367806Lelio R Paula01/2014
7683(4*10^67796+23)/967796Robert Price11/2014
768415477^16180-16180^1547767790Norbert Schneider09/2018
7685(23*2^225177+1)/3167785Lelio R Paula08/2012
7686(4*10^67784+149)/967784Robert Price03/2017
76878177^17322+17322^817767774Norbert Schneider03/2019
76882^225120+15167768Lelio R Paula02/2012
7689(44^41233+1)/4567763Robert Price11/2013
769089933!6-1667747Robert Price08/2018
76918*10^67742+967743Dmitry Domanov11/2010
76922^224977+108967725Lelio R Paula04/2012
7693(2^224950+5)/1950967713Lelio R Paula04/2012
769411^65011-597067702Enzo Doria01/2013
769588*10^67691+767693Robert Price11/2016
769611^65000-714067691Enzo Doria01/2013
76982^224841+5967684Lelio R Paula02/2012
769733129!2+2^3312967684Robert Price09/2015
76992^224827+841567680Lelio R Paula02/2013
7700(9913*2^224821-1)/1982567678Lelio R Paula04/2015
77012^224815-4978967677Henri Lifchitz04/2005
7702(43*10^67664+11)/967665Robert Price06/2015
7703(292*10^67659-1)/367661Robert Price01/2017
7704(17*2^224766+1)/2900767659Lelio R Paula06/2012
77052^224744+57729457567655Lelio R Paula02/2016
7706((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
7707(2^224721+78557)/173967645Lelio R Paula05/2012
77082^224700+191567642Lelio R Paula04/2012
7709(29*2^224694-1)/19890567636Lelio R Paula01/2014
77102^224658-9367629Lelio R Paula02/2012
77112^224624-1307767619Enzo Doria10/2012
771218^53860-331967609Enzo Doria03/2013
7713(21181*2^224570+1)/567606Lelio R Paula06/2014
771489762!6-367606Robert Price08/2018
77152^224578-11104167605Enzo Doria05/2014
77162^224569-11323367603Enzo Doria07/2014
77172^224562-11317167600Enzo Doria07/2014
77182^224556-11312967599Enzo Doria07/2014
77196*7^79980-567592Lelio R Paula09/2014
7720(6883*2^224523-1)/1603167588Lelio R Paula04/2015
772110^67579+16477967580Patrick De Geest07/2017
7723(52*10^67578-61)/967579Robert Price09/2015
772210^67579-40167579Robert Price06/2017
7724(17^54919-1)/1667574Paul Bourdelais03/2010
7725((10^33771-1)*10000/9+6389)*10^33771+(10^33771-1)/967546Hans Havermann05/2019
7726(2^224363-9)/195167537Lelio R Paula04/2012
7727(709*10^67517-7)/967519Robert Price09/2017
772847719!3-5904967516Robert Price12/2015
7729(22^50287+1)/2367506Robert Price06/2013
77303*10^67499+6767500Robert Price11/2017
773111^64811-582067494Enzo Doria01/2013
7732131^31870+31870^13167478Serge Batalov05/2014
77339*10^67468+767469Dmitry Domanov11/2010
7734(31*2^224115-1)/4772367463Lelio R Paula01/2014
7735128^32001+32001^12867433Serge Batalov05/2014
7736(89*10^67431-17)/967432Robert Price11/2015
77372^223912-11105967405Enzo Doria05/2014
77392^223913+7369767405Enzo Doria04/2016
7738(2*10^67405-23)/367405Robert Price09/2017
7741(10^67404+179)/967404Serge Batalov12/2014
774018738^3955+3955^1873867404Hans Havermann09/2016
77429*7^79728-267379Lelio R Paula09/2014
7743(28*10^67378-43)/367379Robert Price04/2016
7744(3^141234-7)/43024128267378Lelio R Paula04/2012
7745211^28988-267377Lelio R Paula09/2013
77464*10^67375+9167376Robert Price11/2017
77472^223793-1806967369Enzo Doria05/2013
77482^223777-252167364Yves Minet07/2014
7749(15185*2^223775-1)/1518367363Lelio R Paula04/2015
7750(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 20 2019 14:10 (Time in France)

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