PRP Records

Probable Primes Top 10000

(181746 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 ?
67512^215623+18364909Lelio R Paula08/2011
6752(46*10^64904+521)/964905Robert Price08/2017
6753(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
67545*2^215554+364889Lelio R Paula04/2014
67552^215541-11207564885Enzo Doria06/2014
67562*10^64882-364883Dmitry Domanov11/2010
675710^64862+34233964863Patrick De Geest05/2013
675810^64862-4764862Robert Price05/2011
675919^50718-8464856Lelio R Paula08/2013
6760(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
676210^64843+427869783964844Robert Price05/2015
676110^64843+2196764844Patrick De Geest03/2016
676310^64843-34007364843Patrick De Geest03/2016
676411^62254+7064831Lelio R Paula07/2013
67652^215351-11192564828Enzo Doria05/2014
67662^215310-11764815Lelio R Paula08/2011
6767124^30958-12364809Norbert Schneider02/2015
6768(7*10^64807+17)/364808Erik Branger03/2014
6769(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
67702^215243-1594964795Enzo Doria04/2013
677123^47581-22^4758164793Robert Price08/2012
6772(62*10^64783-17)/964784Robert Price09/2015
67735*3^135747-464769Lelio R Paula04/2014
6774(59*10^64767-41)/964768Robert Price09/2015
6775(2^215140+3)/1964763Lelio R Paula04/2012
67762^215135-1716964763Enzo Doria05/2013
67772^215115-11127764757Enzo Doria05/2014
67789*5^92641+264755Lelio R Paula09/2014
6779(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
6780(5*10^64715-23)/964715Robert Price11/2014
67812^214938-178164703Yves Minet03/2013
678211^62111-42064682Enzo Doria08/2012
67835^92525+4264673Lelio R Paula06/2013
67842^214824+7189364669Enzo Doria04/2016
67852^214799-222164661Yves Minet08/2013
6786(21*2^214688+1)/29364627Lelio R Paula08/2012
678792^32907+32907^9264623Serge Batalov05/2014
67886^83013+10164597Lelio R Paula07/2013
6789p(13775)#/2+864594Robert Price01/2017
6790(7*10^64568-43)/964568Robert Price10/2014
6791Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
6792(24737*2^214476+1)/287764565Lelio R Paula06/2014
6793(47*2^214463+1)/764561Lelio R Paula04/2015
67942^214458+5461564559Lelio R Paula10/2011
6795(3^135322+7)/12291140864557Lelio R Paula04/2012
67962^214389-68311364538Paul Bourdelais03/2013
67972^214369-11124164532Enzo Doria05/2014
6798(19^50461+3^50461)/2264526Robert Price07/2013
679911^61954-366064519Enzo Doria12/2012
6800(23*2^214319-1)/2164517Lelio R Paula01/2014
6801(58695*2^214310-1)/57164516Lelio R Paula04/2015
680235^41779-3464510Norbert Schneider04/2014
680311^61939-522064503Enzo Doria01/2013
6804(2^214271+78557)/3564501Lelio R Paula05/2012
6805126^30706-12564494Norbert Schneider02/2015
6806gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
68072^214215+1290964486Lelio R Paula10/2011
68085^92225+6664463Lelio R Paula06/2013
68092^214126-24055164459Paul Bourdelais03/2013
68108*6^82827+564453Lelio R Paula09/2014
6811(31*2^214120-1)/217048564452Lelio R Paula01/2014
6812(31*2^214088-1)/595564445Lelio R Paula01/2014
681314^56227+8964444Lelio R Paula08/2013
68162^214055-15964437Lelio R Paula08/2011
681410^64436+266764437Patrick De Geest05/2013
681565^35543-64^3554364437Robert Price08/2013
681710^64436-5364436Robert Price05/2011
6818Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
68193^135027+10064425Lelio R Paula05/2013
6820(3^134972-7)/264398Lelio R Paula04/2012
68216*10^64387+764388Dmitry Domanov11/2010
68222^213864-1837764380Enzo Doria05/2013
6823(2^213821+9)/20964365Lelio R Paula04/2012
68242^213788+13564357Lelio R Paula08/2011
6825(3^134883+2)/4831364351Lelio R Paula04/2012
6826(49^38069-46^38069)/364344Serge Batalov12/2016
6827(11^61781+2^61781)/1364338Robert Price02/2013
68286^82670+3764330Lelio R Paula07/2013
6829(3^134839+4)/3231295964328Lelio R Paula04/2012
6830(22*10^64326+161)/364327Robert Price02/2017
683111^61767-405064324Enzo Doria12/2012
68322^213645-11485364314Enzo Doria05/2015
683313^57733+1864312Lelio R Paula07/2013
68342^213621+7270764307Enzo Doria04/2016
683510^64305+13679164306Patrick De Geest05/2011
683610^64305-964305Alexander Gramolin01/2011
6837V(307652)64295Serge Batalov03/2015
68384*10^64286-8964287Robert Price08/2017
6839(2^213546-5)/222164281Lelio R Paula04/2012
68402^213438-5869564252Lelio R Paula10/2011
68412^213367-10564230Lelio R Paula08/2011
6842595^23148+23148^59564225Norbert Schneider07/2016
68443^134601+868064221Lelio R Paula05/2013
6843(26*10^64220+61)/364221Robert Price06/2017
6845500^23793+23793^50064217Norbert Schneider08/2016
68462^213314-45564214Yves Minet02/2012
684739^40359-3864214Norbert Schneider05/2014
68482^213292-1608564208Enzo Doria04/2013
68492^213274-7764202Lelio R Paula08/2011
685019^50203+7864198Lelio R Paula08/2013
68512^213240-11286564192Enzo Doria06/2014
68522^213190-11239164177Enzo Doria06/2014
6853(9913*2^213184-1)/965764175Lelio R Paula04/2015
685414^55991+2764173Lelio R Paula07/2013
68552^213158-11258164167Enzo Doria06/2014
68562^213148+9164164Lelio R Paula08/2011
6857(96^32369+1)/9764163Paul Bourdelais08/2017
68596^82439+12564151Lelio R Paula07/2013
68587*2^213102+964151Lelio R Paula04/2014
6860L(306854)+F(306855)64129Henri Lifchitz01/2007
6861610^23017+23017^61064110Norbert Schneider07/2016
68622^212950-6487564105Lelio R Paula10/2011
6863(266*10^64102-17)/364104Robert Price06/2016
6864p(13679)#/2+6464097Robert Price03/2017
686519^50119+9464090Lelio R Paula08/2013
68662^212880-14764084Lelio R Paula08/2011
686711^61523-459064070Enzo Doria01/2013
68685^91663+3864070Lelio R Paula05/2013
68695^91650+5264061Lelio R Paula05/2013
68702^212770+6964051Lelio R Paula08/2011
6871(3^134227+1)/464042Paul Bourdelais11/2007
6872(2*10^64041-17)/364041Robert Price08/2014
6873(15^54449+1)/1664036Paul Bourdelais03/2010
6874(29*10^64027+91)/364028Robert Price03/2016
6875(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
687616878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
68772^212663+5364018Lelio R Paula08/2011
6878(4*10^64014+197)/364015Robert Price03/2017
687910^63986+6363987Robert Price01/2011
688010^63986-3155763986Patrick De Geest05/2013
688131487!2-2^3148763982Robert Price09/2015
6882(21*2^212522-1)/141632363971Lelio R Paula01/2014
68835^91517+9863968Lelio R Paula04/2013
6884(62*10^63954-17)/963955Robert Price09/2015
68865^91493-4^9149363951Predrag Minovic04/2004
6885V(364793)63951Serge Batalov03/2015
688819^50004+5863943Lelio R Paula05/2013
68875*6^82172-763943Lelio R Paula09/2014
6889(56*10^63942+223)/963943Robert Price07/2016
689019^50000-2463938Lelio R Paula05/2013
6891(23*2^212374-1)/2701963928Lelio R Paula01/2014
6892(9*2^212355-1)/76163924Lelio R Paula01/2014
68942^212344-18363922Lelio R Paula08/2011
6893(58695*2^212336-1)/37963922Lelio R Paula04/2015
689510^63916+7963917Robert Price01/2011
689610^63916-7682363916Patrick De Geest05/2013
68972^212295-2563908Lelio R Paula08/2011
68992^212285-238363905Yves Minet10/2013
6898267^26336+26336^26763905Norbert Schneider09/2014
6900(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
690119^49962+6063890Lelio R Paula05/2013
69023^133906-11305663890Enzo Doria07/2014
6903(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
69043*6^82092+563881Lelio R Paula09/2014
690515441^13706+13706^1544163879Hans Havermann02/2017
69062^212154-77635163865Paul Bourdelais03/2013
690735^41359+263862Lelio R Paula05/2013
6908(61*10^63857-43)/963858Robert Price09/2015
6909(2^212131-3)/48563856Lelio R Paula04/2012
69102^212112-45999563853Enzo Doria06/2015
691115^54290+5863850Lelio R Paula05/2013
69123*2^212097-763849Lelio R Paula04/2014
691355^36683-5463842Norbert Schneider08/2014
6914(509203*2^212056-1)/363841Lelio R Paula04/2015
6915(3^133805-7)/17263839Lelio R Paula04/2012
69162^212049+14963834Lelio R Paula08/2011
69175^91318-1863829Lelio R Paula04/2013
691818468^2857+2857^1846863824Hans Havermann03/2017
6919(2^212024-5)/111163823Lelio R Paula04/2012
69202^211961+1291563807Lelio R Paula02/2013
6921(3^133707-7)/578063791Lelio R Paula04/2012
6922747^22198+22198^74763782Norbert Schneider07/2016
69232^211800-1716963759Enzo Doria05/2013
6924(85*10^63757-1)/363759Robert Price07/2017
6925(14*10^63747-11)/363748Erik Branger09/2014
692691*19^49848+663746Curtis Bright05/2015
692718855^2402+2402^1885563741Hans Havermann03/2017
6928(142*10^63734-7)/963736Robert Price02/2017
69292^211699-11163728Lelio R Paula08/2011
693011^61192-555063725Enzo Doria01/2013
6931(11*10^63718+7)/963719Serge Batalov06/2011
69326^81872-1363709Lelio R Paula04/2013
69333^133522+9863707Lelio R Paula05/2013
69352^211607-6163701Lelio R Paula08/2011
69345^91135+863701Lelio R Paula04/2013
693611^61157-27063689Enzo Doria07/2012
693810^63685+114514191963686Marisa Kirisame03/2015
693710^63685+10383763686Patrick De Geest03/2016
693910^63685-13079763685Patrick De Geest03/2016
69402^211547+1155*21154763682Henri Lifchitz02/2005
69412^211543+4563681Lelio R Paula08/2011
69422^211534+4363679Lelio R Paula08/2011
694311^61140-6063671Enzo Doria07/2012
69442^211491-11232163666Enzo Doria06/2014
694519085^2164+2164^1908563654Hans Havermann03/2017
6946(2^211430-5)/85963644Lelio R Paula04/2012
69472^211401-9163639Lelio R Paula08/2011
6948(6883*2^211378-1)/6963634Lelio R Paula04/2015
6949(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
6950(29*2^211384-1)/5012262163627Lelio R Paula01/2014
69512^211333+1501563618Lelio R Paula01/2013
695233^41889-3263610Norbert Schneider03/2014
695313^57093+1863599Lelio R Paula05/2013
6954(5*2^211219-1)/963583Lelio R Paula01/2014
6955(107*10^63576-17)/963578Robert Price02/2017
695623^46687-102063575Enzo Doria08/2012
6957(67607*2^211188+1)/523431963573Lelio R Paula06/2014
6958(3^133243+7)/1072663570Lelio R Paula04/2012
6959(7*2^211181+1)/274563570Lelio R Paula06/2012
6961(20^48859-1)/1963566Paul Bourdelais03/2010
69602*3^133227+563566Lelio R Paula04/2014
69622^211155+11363564Lelio R Paula08/2011
69632^211134+34563558Lelio R Paula09/2011
69642^211121+1638563554Lelio R Paula09/2011
696516996^5483+5483^1699663549Hans Havermann02/2017
6966(2^211079+9)/36428363536Lelio R Paula03/2012
69673*10^63522+1363523Robert Price08/2017
696815852^10157+10157^1585263516Hans Havermann02/2017
69692^210948-1587363502Enzo Doria04/2013
69707^75136+663498Lelio R Paula04/2013
69712^210928+1291563496Lelio R Paula02/2013
69727*10^63493+3963494Robert Price07/2016
69732^210909+13563490Lelio R Paula08/2011
6974(3*2^210832+1)/763467Lelio R Paula07/2012
69758*7^75098-363467Lelio R Paula09/2014
697617683^3882+3882^1768363466Hans Havermann03/2017
6977Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
69782^210820-1690563464Enzo Doria05/2013
69795^90795-3663463Lelio R Paula04/2013
69802^210816-1319763462Enzo Doria10/2012
69812^210750+13363443Lelio R Paula08/2011
6982291^25742+25742^29163426Norbert Schneider09/2014
6983(3^132908+8)/27985963408Lelio R Paula04/2012
69846^81480-13963404Lelio R Paula04/2013
69852^210576-17363390Lelio R Paula08/2011
698618^50497+5563388Lelio R Paula05/2013
69872^210545+1163381Lelio R Paula08/2011
69882^210543+6363380Lelio R Paula08/2011
698983^33016+8263361Norbert Schneider04/2015
69902^210464+9876533163356Jason Earls12/2008
69917*10^63351+963352Dmitry Domanov11/2010
6992p(13534)#/2+51263348Robert Price05/2017
69931741^19546+19546^174163345Serge Batalov05/2014
699410^63336+1981963337Patrick De Geest12/2013
699510^63336-12288363336Patrick De Geest12/2013
6996(19^49523-2^49523)/1763327Robert Price09/2013
6997(2^210378+47)/9551693163323Lelio R Paula03/2012
699831191!2+25663316Robert Price01/2015
699916458^7031+7031^1645863315Hans Havermann01/2017
7000(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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