PRP Records

Probable Primes Top 10000

(252675 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 ?
72512^228041+118568648Lelio R Paula04/2012
72522^228040-103768647Yves Minet11/2012
72532*F(328450)-168642Henri Lifchitz12/2009
72545^98201-3468640Lelio R Paula06/2013
72559^71910+3*8^71910-2*4^71910-3*2^7191068620Mike Oakes12/2010
72567*2^227780-368570Lelio R Paula04/2014
725715327^16382-16382^1532768567Norbert Schneider11/2018
72582^227733-12168555Lelio R Paula02/2012
72592^227702-1696768546Enzo Doria05/2013
72602^227689-11165568542Enzo Doria05/2014
7261gcd(V(823915),5*F(164783)*(F(164783)-1)+1)68536Serge Batalov04/2015
72625^98051+268535Ray Chandler07/2011
72635*10^68524+5168525Robert Price01/2017
7264(11*10^68520-149)/368521Robert Price01/2017
726519^53573-7868507Lelio R Paula09/2013
7266(68*10^68504+13)/968505Ray Chandler10/2010
72679*5^98003+468503Lelio R Paula09/2014
72682^227528+5168493Lelio R Paula02/2012
7269(146*28^47316+1)/368476Karsten Bonath06/2018
72703^143497+868466Lelio R Paula04/2012
72712^227430-9568464Lelio R Paula02/2012
7272(8*10^68455+13)/368456Robert Price11/2017
72733*5^97934-268454Lelio R Paula09/2014
727420^52613+7768452Lelio R Paula09/2013
72752^227371+3276968446Lelio R Paula04/2012
7276(3^143465+4)/2127042006768440Lelio R Paula04/2012
7277CopelandErdos(68433)68433Eric W. Weisstein08/2013
72782^227323+7543168432Enzo Doria04/2016
72792^227314-196568429Lelio R Paula04/2012
72802^227303-11061768426Enzo Doria05/2014
72817^80963+6668422Lelio R Paula07/2013
72822^227290+7384968422Enzo Doria04/2016
7283(14^59693-1)/1368415Paul Bourdelais06/2008
72842^227256-278624968411Enzo Doria03/2016
72858*10^68400-768401Dmitry Domanov11/2010
7286(15*2^227228-1)/58368401Lelio R Paula01/2014
72872^227210+186916968398Enzo Doria05/2016
72882^227159-183863568382Enzo Doria05/2015
728944*10^68368+368370Robert Price08/2017
72902^227115-780768369Lelio R Paula10/2009
72912^227078-4735568358Lelio R Paula04/2012
7292(2^227063-1017)/34968351Lelio R Paula04/2012
72932^227057+14809168351Lelio R Paula04/2012
72942^227046+18768348Lelio R Paula02/2012
72959*10^68331+5968332Robert Price10/2017
729611^65608-72068324Enzo Doria11/2012
7297(32*10^68320+319)/968321Robert Price10/2017
729833408!2-2^33408-168315Joe McLean05/2017
72992^226894-12368302Lelio R Paula02/2012
730010^68297+14155968298Patrick De Geest05/2013
730110^68297-9368297Robert Price05/2011
7302680^24107-679^2410768284Jean-Louis Charton07/2010
730312^63267+5968277Lelio R Paula07/2013
73042^226785-115968270Yves Minet11/2012
73057^80769+9068258Lelio R Paula07/2013
7306(88*10^68256-1)/368258Robert Price10/2017
73072^226741+6658768256Yves Minet10/2010
73082^226720-11240368250Enzo Doria06/2014
7309(78557*2^226694+1)/368247Lelio R Paula06/2014
7310(83*10^68231+7)/968232Robert Price10/2015
731165^37636+1668231Lelio R Paula01/2016
73125^97615-4^(97615+1)68230Robert Price04/2016
731312^63200-4368205Lelio R Paula07/2013
7314-330*Bern(21940)/22379062073368201Serge Batalov04/2015
73153^142925+868068193Lelio R Paula06/2013
73163*2^226512-768188Lelio R Paula04/2014
731714^59484+5768177Lelio R Paula08/2013
731811^65438-219068147Enzo Doria12/2012
731991^34784-268144Lelio R Paula09/2013
7320(2^226336-3)*6-768135Gilbert Mozzo06/2016
7321(22*10^68133-37)/368134Robert Price05/2017
73225^97476+3668133Lelio R Paula06/2013
73233*5^97474-268132Lelio R Paula09/2014
732412^63130+4968129Lelio R Paula07/2013
73252^226281+538568118Lelio R Paula04/2012
73262^226257-304968111Yves Minet10/2014
7327(28*10^68107-43)/368108Robert Price04/2016
73282^226243-258768106Yves Minet07/2014
732920^52346-1168104Lelio R Paula09/2013
73302^226205-9968095Lelio R Paula02/2012
73312^226187-4968090Lelio R Paula02/2012
73323^142708+7668090Lelio R Paula06/2013
73337*10^68088-8968089Robert Price01/2017
73342^226154+7183968080Enzo Doria04/2016
7335(10^68078+59)/368078Serge Batalov12/2014
733714^59387+6968066Lelio R Paula08/2013
73362^226108-11342968066Enzo Doria07/2014
7338(62*10^68059-197)/968060Robert Price10/2017
7339(24^49307-1)/2368053Robert Price04/2012
734015^57859-2868048Lelio R Paula08/2013
7341(509203*2^226003-1)/1368039Lelio R Paula04/2015
73422^226015-11136168038Enzo Doria05/2014
7343(10^(2*34016+1)+72*10^34016-1)/968033Robert Price09/2017
73444*10^68020+9168021Robert Price11/2017
7345156*(10^(4*17000)-1)/101-168001Robert Price05/2014
73462^225878-101767997Lelio R Paula04/2012
73473*8^75289+5^75289-3*4^75289+3*2^7528967994Mike Oakes11/2010
73483*2^225865+567993Lelio R Paula04/2014
735011^65284-582067987Enzo Doria01/2013
734919^53166+7067987Lelio R Paula08/2013
73512^225837+7540767984Enzo Doria04/2016
73523^142464-11265467973Enzo Doria06/2014
73532^225777+9567966Lelio R Paula02/2012
7354(2^225641-1017)/13881567920Lelio R Paula04/2012
73552^225609-1844567916Enzo Doria05/2013
73562^225542-17767895Lelio R Paula02/2012
73572^225536-2967894Henri Lifchitz05/2005
735811^65190-339067889Enzo Doria12/2012
73593^142249-2^(142249-1)67871Robert Price01/2016
736011^65168-483067866Enzo Doria01/2013
736110^67863+5862767864Patrick De Geest01/2016
736210^67863-1167863Robert Price05/2011
7363(1!)^2+(2!)^2+(3!)^2+...+(9566!)^267856T. D. Noe02/2006
7364(19*2^225357-1)/1167840Lelio R Paula01/2014
73659*6^87164-767828Lelio R Paula09/2014
7366131^32034+13067825Norbert Schneider03/2015
7367(29*2^225314+1)/1088167824Lelio R Paula08/2012
7368(134*10^67816+7)/367818Robert Price02/2017
73692^225261+85567811Lelio R Paula04/2012
7370(29*2^225252-1)/293367806Lelio R Paula01/2014
7371(4*10^67796+23)/967796Robert Price11/2014
737215477^16180-16180^1547767790Norbert Schneider09/2018
7373(23*2^225177+1)/3167785Lelio R Paula08/2012
7374(4*10^67784+149)/967784Robert Price03/2017
73758177^17322+17322^817767774Norbert Schneider03/2019
73762^225120+15167768Lelio R Paula02/2012
7377(44^41233+1)/4567763Robert Price11/2013
737889933!6-1667747Robert Price08/2018
73798*10^67742+967743Dmitry Domanov11/2010
73802^224977+108967725Lelio R Paula04/2012
7381(2^224950+5)/1950967713Lelio R Paula04/2012
738211^65011-597067702Enzo Doria01/2013
738388*10^67691+767693Robert Price11/2016
738411^65000-714067691Enzo Doria01/2013
73862^224841+5967684Lelio R Paula02/2012
738533129!2+2^3312967684Robert Price09/2015
73872^224827+841567680Lelio R Paula02/2013
7388(9913*2^224821-1)/1982567678Lelio R Paula04/2015
73892^224815-4978967677Henri Lifchitz04/2005
7390(43*10^67664+11)/967665Robert Price06/2015
7391(292*10^67659-1)/367661Robert Price01/2017
7392(17*2^224766+1)/2900767659Lelio R Paula06/2012
73932^224744+57729457567655Lelio R Paula02/2016
7394((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
7395(2^224721+78557)/173967645Lelio R Paula05/2012
73962^224700+191567642Lelio R Paula04/2012
7397(29*2^224694-1)/19890567636Lelio R Paula01/2014
73982^224658-9367629Lelio R Paula02/2012
73992^224624-1307767619Enzo Doria10/2012
740018^53860-331967609Enzo Doria03/2013
7401(21181*2^224570+1)/567606Lelio R Paula06/2014
740289762!6-367606Robert Price08/2018
74032^224578-11104167605Enzo Doria05/2014
74042^224569-11323367603Enzo Doria07/2014
74052^224562-11317167600Enzo Doria07/2014
74062^224556-11312967599Enzo Doria07/2014
74076*7^79980-567592Lelio R Paula09/2014
7408(6883*2^224523-1)/1603167588Lelio R Paula04/2015
740910^67579+16477967580Patrick De Geest07/2017
7411(52*10^67578-61)/967579Robert Price09/2015
741010^67579-40167579Robert Price06/2017
7412(17^54919-1)/1667574Paul Bourdelais03/2010
7413(2^224363-9)/195167537Lelio R Paula04/2012
7414(709*10^67517-7)/967519Robert Price09/2017
741547719!3-5904967516Robert Price12/2015
7416(22^50287+1)/2367506Robert Price06/2013
74173*10^67499+6767500Robert Price11/2017
741811^64811-582067494Enzo Doria01/2013
7419131^31870+31870^13167478Serge Batalov05/2014
74209*10^67468+767469Dmitry Domanov11/2010
7421(31*2^224115-1)/4772367463Lelio R Paula01/2014
7422128^32001+32001^12867433Serge Batalov05/2014
7423(89*10^67431-17)/967432Robert Price11/2015
74242^223912-11105967405Enzo Doria05/2014
74252^223913+7369767405Enzo Doria04/2016
7426(2*10^67405-23)/367405Robert Price09/2017
7427(10^67404+179)/967404Serge Batalov12/2014
742818738^3955+3955^1873867404Hans Havermann09/2016
74299*7^79728-267379Lelio R Paula09/2014
7430(28*10^67378-43)/367379Robert Price04/2016
7431(3^141234-7)/43024128267378Lelio R Paula04/2012
7432211^28988-267377Lelio R Paula09/2013
74334*10^67375+9167376Robert Price11/2017
74342^223793-1806967369Enzo Doria05/2013
74352^223777-252167364Yves Minet07/2014
7436(15185*2^223775-1)/1518367363Lelio R Paula04/2015
7437(2^223759-lucasV(1,2,223759)+1)/267358Mike Oakes11/2016
7438V(340138)67336Serge Batalov03/2015
743943125^14528-10667334Enzo Doria07/2012
744015275^16086-16086^1527567304Norbert Schneider09/2018
74418*10^67302-5167303Robert Price10/2017
744217458^7153+7153^1745867292Hans Havermann08/2016
744316366^12925+12925^1636667288Hans Havermann08/2016
744437^42906-267286Lelio R Paula08/2013
744518^53592-1367273Lelio R Paula08/2013
7446V(396221)67256Serge Batalov03/2015
7448(34*10^67245-7)/9/3^4/193/138153767236Makoto Morimoto04/2016
7447(14*10^67235-101)/367236Robert Price04/2017
744953^38993-52^3899367235Robert Price01/2013
7450(2^223349-7)/648567231Lelio R Paula04/2012
74512^223333+31567230Lelio R Paula04/2012
74522^223278-11104167214Enzo Doria05/2014
7453(2347*2^223281+1)/(3*5*197*1213*1783)67208Jens K. Andersen09/2007
74542^223256-4567207Lelio R Paula02/2012
74552^223253-11211167206Enzo Doria06/2014
745618407^4474+4474^1840767199Hans Havermann08/2016
745747^40182+40182^4767189Norbert Schneider11/2014
745813^60309+9467181Lelio R Paula07/2013
745911^64503-8467173Lelio R Paula07/2013
74603^140781+23667170Lelio R Paula06/2013
74612^223107-86505767162Paul Bourdelais03/2013
74622^223100-5967160Lelio R Paula02/2012
74632^223087+7196367156Enzo Doria04/2016
746418^53481-377967134Enzo Doria03/2013
7465(326^26713-1)/32567134Eric Chen09/2017
74664^111473-6257367114Mike Oakes02/2011
74672^222943+2967113Henri Lifchitz08/2005
7468(2^222939-9)/10367110Lelio R Paula04/2012
74692^222862-45916167089Enzo Doria05/2015
74702^222828+819367078Lelio R Paula04/2012
74713^140570+266067069Lelio R Paula06/2013
74722^222744+85567053Lelio R Paula04/2012
747313^60189+8467048Lelio R Paula07/2013
74742*10^67043-5167044Robert Price11/2017
74752^222701+57729457567040Lelio R Paula02/2016
7476(13*10^67038-31)/967039Serge Batalov11/2008
7477(151*10^67027-7)/967029Robert Price07/2017
7478(58695*2^222620-1)/6167019Lelio R Paula04/2015
74792^222614-11104167014Enzo Doria05/2014
7480118^32333-11766991Norbert Schneider08/2018
74812^222520-190766986Yves Minet03/2013
7482(4^111231+23)/366968Robert Price02/2017
74832^222408-11127566952Enzo Doria05/2014
748410^66949-9^6694966949Jean-Louis Charton12/2005
74852^222378-100566943Lelio R Paula04/2012
7486(9*2^222366+1)/7366938Lelio R Paula08/2012
74877^79202-6^(79202+1)66934Robert Price06/2016
74882^222325-11225566927Enzo Doria06/2014
748920^51428+3366910Lelio R Paula08/2013
74912^222224-1850966897Enzo Doria05/2013
7490(38*10^66896+187)/966897Robert Price11/2017
74922^222192-86968810566887Lelio R Paula02/2016
7493(19*10^66878-43)/366879Robert Price10/2017
749411^64219-6466878Lelio R Paula07/2013
74952^222151-1729566875Lelio R Paula04/2012
7496gcd(V(799885),5*F(159977)*(F(159977)+1)+1)66867Serge Batalov04/2015
74972^222085-11103166855Enzo Doria05/2014
74988*10^66848-1366849Robert Price05/2017
7499(3^140087+4)/1366838Lelio R Paula04/2012
7500(3^140102+4)/884360943766836Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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