PRP Records

Probable Primes Top 10000

(193407 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 ?
7001331^25791-1000264989Enzo Doria07/2012
70022^215877+13164986Lelio R Paula08/2011
70034*5^92959+964977Lelio R Paula09/2014
70042^215789-1882564959Lelio R Paula09/2011
7005(2^215801-509203)/4132764958Lelio R Paula05/2012
7006U(315311)64954Serge Batalov03/2015
700746072!3-5904964951Robert Price12/2015
70082^215750-595564948Lelio R Paula09/2011
700913^58281+4664922Lelio R Paula07/2013
70102^215623+18364909Lelio R Paula08/2011
7011(46*10^64904+521)/964905Robert Price08/2017
7012(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
70135*2^215554+364889Lelio R Paula04/2014
70142^215541-11207564885Enzo Doria06/2014
70152*10^64882-364883Dmitry Domanov11/2010
701610^64862+34233964863Patrick De Geest05/2013
701710^64862-4764862Robert Price05/2011
701819^50718-8464856Lelio R Paula08/2013
7019(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
702110^64843+427869783964844Robert Price05/2015
702010^64843+2196764844Patrick De Geest03/2016
702210^64843-34007364843Patrick De Geest03/2016
702311^62254+7064831Lelio R Paula07/2013
70242^215351-11192564828Enzo Doria05/2014
70252^215310-11764815Lelio R Paula08/2011
7026124^30958-12364809Norbert Schneider02/2015
7027(7*10^64807+17)/364808Erik Branger03/2014
7028(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
70292^215243-1594964795Enzo Doria04/2013
703023^47581-22^4758164793Robert Price08/2012
7031(62*10^64783-17)/964784Robert Price09/2015
70325*3^135747-464769Lelio R Paula04/2014
7033(59*10^64767-41)/964768Robert Price09/2015
7035(2^215140+3)/1964763Lelio R Paula04/2012
70342^215135-1716964763Enzo Doria05/2013
70362^215115-11127764757Enzo Doria05/2014
70379*5^92641+264755Lelio R Paula09/2014
7038(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7039(5*10^64715-23)/964715Robert Price11/2014
70402^214938-178164703Yves Minet03/2013
704111^62111-42064682Enzo Doria08/2012
70425^92525+4264673Lelio R Paula06/2013
70432^214824+7189364669Enzo Doria04/2016
70442^214799-222164661Yves Minet08/2013
7045(21*2^214688+1)/29364627Lelio R Paula08/2012
704692^32907+32907^9264623Serge Batalov05/2014
7047(89*10^64608-539)/964609Robert Price11/2017
70486^83013+10164597Lelio R Paula07/2013
7049p(13775)#/2+864594Robert Price01/2017
7050(7*10^64568-43)/964568Robert Price10/2014
7051Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7052(24737*2^214476+1)/287764565Lelio R Paula06/2014
7053(47*2^214463+1)/764561Lelio R Paula04/2015
70542^214458+5461564559Lelio R Paula10/2011
7055(3^135322+7)/12291140864557Lelio R Paula04/2012
70562^214389-68311364538Paul Bourdelais03/2013
7057(76*10^64534+113)/964535Robert Price11/2017
70582^214369-11124164532Enzo Doria05/2014
7059(19^50461+3^50461)/2264526Robert Price07/2013
706011^61954-366064519Enzo Doria12/2012
7061(23*2^214319-1)/2164517Lelio R Paula01/2014
7062(58695*2^214310-1)/57164516Lelio R Paula04/2015
706335^41779-3464510Norbert Schneider04/2014
7064(89*10^64504-179)/964505Robert Price11/2017
706511^61939-522064503Enzo Doria01/2013
7066(2^214271+78557)/3564501Lelio R Paula05/2012
7067126^30706-12564494Norbert Schneider02/2015
7068gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
70692^214215+1290964486Lelio R Paula10/2011
70705^92225+6664463Lelio R Paula06/2013
70712^214126-24055164459Paul Bourdelais03/2013
70728*6^82827+564453Lelio R Paula09/2014
7073(31*2^214120-1)/217048564452Lelio R Paula01/2014
7074(31*2^214088-1)/595564445Lelio R Paula01/2014
707514^56227+8964444Lelio R Paula08/2013
70782^214055-15964437Lelio R Paula08/2011
707610^64436+266764437Patrick De Geest05/2013
707765^35543-64^3554364437Robert Price08/2013
707910^64436-5364436Robert Price05/2011
7080(3^135043-lucasV(1,3,135043)+1)/364431Paul Vanderveen11/2017
7081Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
70823^135027+10064425Lelio R Paula05/2013
7083(3^134972-7)/264398Lelio R Paula04/2012
70846*10^64387+764388Dmitry Domanov11/2010
70852^213864-1837764380Enzo Doria05/2013
7086(2^213821+9)/20964365Lelio R Paula04/2012
70872^213788+13564357Lelio R Paula08/2011
7088(3^134883+2)/4831364351Lelio R Paula04/2012
7089(49^38069-46^38069)/364344Serge Batalov12/2016
7090(11^61781+2^61781)/1364338Robert Price02/2013
70916^82670+3764330Lelio R Paula07/2013
7092(3^134839+4)/3231295964328Lelio R Paula04/2012
7093(22*10^64326+161)/364327Robert Price02/2017
709411^61767-405064324Enzo Doria12/2012
70952^213645-11485364314Enzo Doria05/2015
709613^57733+1864312Lelio R Paula07/2013
70972^213621+7270764307Enzo Doria04/2016
709810^64305+13679164306Patrick De Geest05/2011
709910^64305-964305Alexander Gramolin01/2011
7100V(307652)64295Serge Batalov03/2015
71014*10^64286-8964287Robert Price08/2017
7102(2^213546-5)/222164281Lelio R Paula04/2012
71032^213438-5869564252Lelio R Paula10/2011
71042^213367-10564230Lelio R Paula08/2011
7105595^23148+23148^59564225Norbert Schneider07/2016
71073^134601+868064221Lelio R Paula05/2013
7106(26*10^64220+61)/364221Robert Price06/2017
7108500^23793+23793^50064217Norbert Schneider08/2016
7109179^28504-264216Lelio R Paula10/2017
71112^213314-45564214Yves Minet02/2012
711039^40359-3864214Norbert Schneider05/2014
71122^213292-1608564208Enzo Doria04/2013
71132^213274-7764202Lelio R Paula08/2011
711419^50203+7864198Lelio R Paula08/2013
7115(44*10^64192-233)/964193Robert Price10/2017
71162^213240-11286564192Enzo Doria06/2014
71172^213190-11239164177Enzo Doria06/2014
7118(9913*2^213184-1)/965764175Lelio R Paula04/2015
711914^55991+2764173Lelio R Paula07/2013
71202^213158-11258164167Enzo Doria06/2014
71212^213148+9164164Lelio R Paula08/2011
7122(96^32369+1)/9764163Paul Bourdelais08/2017
71246^82439+12564151Lelio R Paula07/2013
71237*2^213102+964151Lelio R Paula04/2014
7125L(306854)+F(306855)64129Henri Lifchitz01/2007
7126610^23017+23017^61064110Norbert Schneider07/2016
71272^212950-6487564105Lelio R Paula10/2011
7128(266*10^64102-17)/364104Robert Price06/2016
7129p(13679)#/2+6464097Robert Price03/2017
713019^50119+9464090Lelio R Paula08/2013
71312^212880-14764084Lelio R Paula08/2011
713211^61523-459064070Enzo Doria01/2013
71335^91663+3864070Lelio R Paula05/2013
71345^91650+5264061Lelio R Paula05/2013
71352^212770+6964051Lelio R Paula08/2011
7136(3^134227+1)/464042Paul Bourdelais11/2007
7137(2*10^64041-17)/364041Robert Price08/2014
7138(15^54449+1)/1664036Paul Bourdelais03/2010
7139(29*10^64027+91)/364028Robert Price03/2016
7140(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
714116878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
71422^212663+5364018Lelio R Paula08/2011
7143(4*10^64014+197)/364015Robert Price03/2017
714410^63986+6363987Robert Price01/2011
714510^63986-3155763986Patrick De Geest05/2013
714631487!2-2^3148763982Robert Price09/2015
7147(21*2^212522-1)/141632363971Lelio R Paula01/2014
71485^91517+9863968Lelio R Paula04/2013
7149(19*10^63960-43)/363961Robert Price10/2017
7150(62*10^63954-17)/963955Robert Price09/2015
71525^91493-4^9149363951Predrag Minovic04/2004
7151V(364793)63951Serge Batalov03/2015
715419^50004+5863943Lelio R Paula05/2013
71535*6^82172-763943Lelio R Paula09/2014
7155(56*10^63942+223)/963943Robert Price07/2016
715619^50000-2463938Lelio R Paula05/2013
7157(23*2^212374-1)/2701963928Lelio R Paula01/2014
7158(9*2^212355-1)/76163924Lelio R Paula01/2014
71602^212344-18363922Lelio R Paula08/2011
7159(58695*2^212336-1)/37963922Lelio R Paula04/2015
716110^63916+7963917Robert Price01/2011
716210^63916-7682363916Patrick De Geest05/2013
71632^212295-2563908Lelio R Paula08/2011
71652^212285-238363905Yves Minet10/2013
7164267^26336+26336^26763905Norbert Schneider09/2014
7166(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
716719^49962+6063890Lelio R Paula05/2013
71683^133906-11305663890Enzo Doria07/2014
7169(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
71703*6^82092+563881Lelio R Paula09/2014
717115441^13706+13706^1544163879Hans Havermann02/2017
71722^212154-77635163865Paul Bourdelais03/2013
717335^41359+263862Lelio R Paula05/2013
7174(61*10^63857-43)/963858Robert Price09/2015
7175(2^212131-3)/48563856Lelio R Paula04/2012
71762^212112-45999563853Enzo Doria06/2015
717715^54290+5863850Lelio R Paula05/2013
71783*2^212097-763849Lelio R Paula04/2014
717955^36683-5463842Norbert Schneider08/2014
7180(509203*2^212056-1)/363841Lelio R Paula04/2015
7181(3^133805-7)/17263839Lelio R Paula04/2012
71822^212049+14963834Lelio R Paula08/2011
71835^91318-1863829Lelio R Paula04/2013
718418468^2857+2857^1846863824Hans Havermann03/2017
7185(2^212024-5)/111163823Lelio R Paula04/2012
71862^211961+1291563807Lelio R Paula02/2013
7188(3^133707-7)/578063791Lelio R Paula04/2012
7187(44*10^63790-161)/963791Robert Price11/2017
7189747^22198+22198^74763782Norbert Schneider07/2016
71902^211800-1716963759Enzo Doria05/2013
7191(85*10^63757-1)/363759Robert Price07/2017
7192(14*10^63747-11)/363748Erik Branger09/2014
719391*19^49848+663746Curtis Bright05/2015
719418855^2402+2402^1885563741Hans Havermann03/2017
7195(142*10^63734-7)/963736Robert Price02/2017
71962^211699-11163728Lelio R Paula08/2011
719711^61192-555063725Enzo Doria01/2013
7198(11*10^63718+7)/963719Serge Batalov06/2011
71996^81872-1363709Lelio R Paula04/2013
72003^133522+9863707Lelio R Paula05/2013
72022^211607-6163701Lelio R Paula08/2011
72015^91135+863701Lelio R Paula04/2013
720311^61157-27063689Enzo Doria07/2012
720410^63685+114514191963686Marisa Kirisame03/2015
720510^63685+10383763686Patrick De Geest03/2016
720610^63685-13079763685Patrick De Geest03/2016
72072^211547+1155*21154763682Henri Lifchitz02/2005
72082^211543+4563681Lelio R Paula08/2011
72092^211534+4363679Lelio R Paula08/2011
721011^61140-6063671Enzo Doria07/2012
72112^211491-11232163666Enzo Doria06/2014
721219085^2164+2164^1908563654Hans Havermann03/2017
7213(2^211430-5)/85963644Lelio R Paula04/2012
72142^211401-9163639Lelio R Paula08/2011
7215(6883*2^211378-1)/6963634Lelio R Paula04/2015
7216(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7217(29*2^211384-1)/5012262163627Lelio R Paula01/2014
72182^211333+1501563618Lelio R Paula01/2013
721933^41889-3263610Norbert Schneider03/2014
722013^57093+1863599Lelio R Paula05/2013
7221(5*2^211219-1)/963583Lelio R Paula01/2014
7222(107*10^63576-17)/963578Robert Price02/2017
722323^46687-102063575Enzo Doria08/2012
7224(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7225(3^133243+7)/1072663570Lelio R Paula04/2012
7226(7*2^211181+1)/274563570Lelio R Paula06/2012
7228(20^48859-1)/1963566Paul Bourdelais03/2010
72272*3^133227+563566Lelio R Paula04/2014
72292^211155+11363564Lelio R Paula08/2011
72302^211134+34563558Lelio R Paula09/2011
72312^211121+1638563554Lelio R Paula09/2011
723216996^5483+5483^1699663549Hans Havermann02/2017
7233(2^211079+9)/36428363536Lelio R Paula03/2012
72343*10^63522+1363523Robert Price08/2017
723515852^10157+10157^1585263516Hans Havermann02/2017
72362^210948-1587363502Enzo Doria04/2013
72377^75136+663498Lelio R Paula04/2013
72382^210928+1291563496Lelio R Paula02/2013
72397*10^63493+3963494Robert Price07/2016
72402^210909+13563490Lelio R Paula08/2011
7241(3*2^210832+1)/763467Lelio R Paula07/2012
72428*7^75098-363467Lelio R Paula09/2014
724317683^3882+3882^1768363466Hans Havermann03/2017
7245Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
72442^210820-1690563464Enzo Doria05/2013
72465^90795-3663463Lelio R Paula04/2013
72472^210816-1319763462Enzo Doria10/2012
72482^210750+13363443Lelio R Paula08/2011
7249291^25742+25742^29163426Norbert Schneider09/2014
7250(3^132908+8)/27985963408Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 12 2017 10:35 (Time in France)

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