PRP Records

Probable Primes Top 10000

(252538 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 ?
7751(21*2^214688+1)/29364627Lelio R Paula08/2012
775292^32907+32907^9264623Serge Batalov05/2014
7753(89*10^64608-539)/964609Robert Price11/2017
77546^83013+10164597Lelio R Paula07/2013
7755p(13775)#/2+864594Robert Price01/2017
7756(7*10^64568-43)/964568Robert Price10/2014
7757Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7758(24737*2^214476+1)/287764565Lelio R Paula06/2014
7759(47*2^214463+1)/764561Lelio R Paula04/2015
77602^214458+5461564559Lelio R Paula10/2011
7761(3^135322+7)/12291140864557Lelio R Paula04/2012
77622^214389-68311364538Paul Bourdelais03/2013
7763(76*10^64534+113)/964535Robert Price11/2017
77642^214369-11124164532Enzo Doria05/2014
7765(19^50461+3^50461)/2264526Robert Price07/2013
776611^61954-366064519Enzo Doria12/2012
7767(23*2^214319-1)/2164517Lelio R Paula01/2014
7768(58695*2^214310-1)/57164516Lelio R Paula04/2015
776935^41779-3464510Norbert Schneider04/2014
7770(159^29303+1)/16064506Eric Chen12/2017
7771(89*10^64504-179)/964505Robert Price11/2017
777211^61939-522064503Enzo Doria01/2013
7773(2^214271+78557)/3564501Lelio R Paula05/2012
7774L(308604)+P(308604)64495Robert Price12/2017
7775126^30706-12564494Norbert Schneider02/2015
7776gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
77772^214215+1290964486Lelio R Paula10/2011
77785^92225+6664463Lelio R Paula06/2013
77792^214126-24055164459Paul Bourdelais03/2013
77808*6^82827+564453Lelio R Paula09/2014
7781(31*2^214120-1)/217048564452Lelio R Paula01/2014
7782(31*2^214088-1)/595564445Lelio R Paula01/2014
778314^56227+8964444Lelio R Paula08/2013
77862^214055-15964437Lelio R Paula08/2011
778410^64436+266764437Patrick De Geest05/2013
778565^35543-64^3554364437Robert Price08/2013
778710^64436-5364436Robert Price05/2011
7788(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7789Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
77903^135027+10064425Lelio R Paula05/2013
7791(3^134972-7)/264398Lelio R Paula04/2012
77926*10^64387+764388Dmitry Domanov11/2010
77932^213864-1837764380Enzo Doria05/2013
7794(2^213821+9)/20964365Lelio R Paula04/2012
77952^213788+13564357Lelio R Paula08/2011
7796(3^134883+2)/4831364351Lelio R Paula04/2012
7797(49^38069-46^38069)/364344Serge Batalov12/2016
7798(11^61781+2^61781)/1364338Robert Price02/2013
77996^82670+3764330Lelio R Paula07/2013
7800(3^134839+4)/3231295964328Lelio R Paula04/2012
7801(22*10^64326+161)/364327Robert Price02/2017
780211^61767-405064324Enzo Doria12/2012
78032^213645-11485364314Enzo Doria05/2015
780413^57733+1864312Lelio R Paula07/2013
78052^213621+7270764307Enzo Doria04/2016
780610^64305+13679164306Patrick De Geest05/2011
780710^64305-964305Alexander Gramolin01/2011
7808V(307652)64295Serge Batalov03/2015
78094*10^64286-8964287Robert Price08/2017
7810(2^213546-5)/222164281Lelio R Paula04/2012
78112^213438-5869564252Lelio R Paula10/2011
78122^213367-10564230Lelio R Paula08/2011
7813595^23148+23148^59564225Norbert Schneider07/2016
78143^134601+868064221Lelio R Paula05/2013
7815(26*10^64220+61)/364221Robert Price06/2017
7816500^23793+23793^50064217Norbert Schneider08/2016
7817179^28504-264216Lelio R Paula10/2017
78182^213314-45564214Yves Minet02/2012
781939^40359-3864214Norbert Schneider05/2014
78202^213292-1608564208Enzo Doria04/2013
7821(72524!5+1)/2564203Joe McLean10/2018
78222^213274-7764202Lelio R Paula08/2011
782319^50203+7864198Lelio R Paula08/2013
7824(44*10^64192-233)/964193Robert Price10/2017
78252^213240-11286564192Enzo Doria06/2014
78262^213190-11239164177Enzo Doria06/2014
7827(9913*2^213184-1)/965764175Lelio R Paula04/2015
782814^55991+2764173Lelio R Paula07/2013
78292^213158-11258164167Enzo Doria06/2014
78302^213148+9164164Lelio R Paula08/2011
7831(96^32369+1)/9764163Paul Bourdelais08/2017
78336^82439+12564151Lelio R Paula07/2013
78327*2^213102+964151Lelio R Paula04/2014
7834L(306854)+F(306855)64129Henri Lifchitz01/2007
7835610^23017+23017^61064110Norbert Schneider07/2016
78362^212950-6487564105Lelio R Paula10/2011
7837(266*10^64102-17)/364104Robert Price06/2016
7838p(13679)#/2+6464097Robert Price03/2017
783919^50119+9464090Lelio R Paula08/2013
78402^212880-14764084Lelio R Paula08/2011
784111^61523-459064070Enzo Doria01/2013
78425^91663+3864070Lelio R Paula05/2013
78435^91650+5264061Lelio R Paula05/2013
78442^212770+6964051Lelio R Paula08/2011
7845(3^134227+1)/464042Paul Bourdelais11/2007
7846(2*10^64041-17)/364041Robert Price08/2014
7847(15^54449+1)/1664036Paul Bourdelais03/2010
7848(29*10^64027+91)/364028Robert Price03/2016
7849(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
785016878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
78512^212663+5364018Lelio R Paula08/2011
7852(4*10^64014+197)/364015Robert Price03/2017
785385402!6-364014Robert Price08/2018
7854(140^29819+1)/14163994Richard Fischer05/2018
785510^63986+6363987Robert Price01/2011
785610^63986-3155763986Patrick De Geest05/2013
785731487!2-2^3148763982Robert Price09/2015
7858(21*2^212522-1)/141632363971Lelio R Paula01/2014
78595^91517+9863968Lelio R Paula04/2013
7860(19*10^63960-43)/363961Robert Price10/2017
7861(62*10^63954-17)/963955Robert Price09/2015
78635^91493-4^9149363951Predrag Minovic04/2004
7862V(364793)63951Serge Batalov03/2015
786519^50004+5863943Lelio R Paula05/2013
78645*6^82172-763943Lelio R Paula09/2014
7866(56*10^63942+223)/963943Robert Price07/2016
786719^50000-2463938Lelio R Paula05/2013
7868(23*2^212374-1)/2701963928Lelio R Paula01/2014
7869(9*2^212355-1)/76163924Lelio R Paula01/2014
78712^212344-18363922Lelio R Paula08/2011
7870(58695*2^212336-1)/37963922Lelio R Paula04/2015
787210^63916+7963917Robert Price01/2011
787310^63916-7682363916Patrick De Geest05/2013
78742^212295-2563908Lelio R Paula08/2011
78762^212285-238363905Yves Minet10/2013
7875267^26336+26336^26763905Norbert Schneider09/2014
7877(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
787819^49962+6063890Lelio R Paula05/2013
78793^133906-11305663890Enzo Doria07/2014
7880(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
78813*6^82092+563881Lelio R Paula09/2014
788215441^13706+13706^1544163879Hans Havermann02/2017
78832^212154-77635163865Paul Bourdelais03/2013
788435^41359+263862Lelio R Paula05/2013
7885(61*10^63857-43)/963858Robert Price09/2015
7886(2^212131-3)/48563856Lelio R Paula04/2012
78872^212112-45999563853Enzo Doria06/2015
788815^54290+5863850Lelio R Paula05/2013
78893*2^212097-763849Lelio R Paula04/2014
789055^36683-5463842Norbert Schneider08/2014
7891(509203*2^212056-1)/363841Lelio R Paula04/2015
7892(3^133805-7)/17263839Lelio R Paula04/2012
78932^212049+14963834Lelio R Paula08/2011
78945^91318-1863829Lelio R Paula04/2013
789518468^2857+2857^1846863824Hans Havermann03/2017
7896(2^212024-5)/111163823Lelio R Paula04/2012
78972^211961+1291563807Lelio R Paula02/2013
7899(3^133707-7)/578063791Lelio R Paula04/2012
7898(44*10^63790-161)/963791Robert Price11/2017
7900747^22198+22198^74763782Norbert Schneider07/2016
79012^211800-1716963759Enzo Doria05/2013
7902(85*10^63757-1)/363759Robert Price07/2017
790385089!6-863757Robert Price08/2018
7904(14*10^63747-11)/363748Erik Branger09/2014
790591*19^49848+663746Curtis Bright05/2015
790618855^2402+2402^1885563741Hans Havermann03/2017
7907(142*10^63734-7)/963736Robert Price02/2017
79082^211699-11163728Lelio R Paula08/2011
790911^61192-555063725Enzo Doria01/2013
7910(11*10^63718+7)/963719Serge Batalov06/2011
79116^81872-1363709Lelio R Paula04/2013
79123^133522+9863707Lelio R Paula05/2013
79142^211607-6163701Lelio R Paula08/2011
79135^91135+863701Lelio R Paula04/2013
791511^61157-27063689Enzo Doria07/2012
791710^63685+114514191963686Marisa Kirisame03/2015
791610^63685+10383763686Patrick De Geest03/2016
791810^63685-13079763685Patrick De Geest03/2016
79192^211547+1155*21154763682Henri Lifchitz02/2005
79202^211543+4563681Lelio R Paula08/2011
79212^211534+4363679Lelio R Paula08/2011
792211^61140-6063671Enzo Doria07/2012
79232^211491-11232163666Enzo Doria06/2014
792419085^2164+2164^1908563654Hans Havermann03/2017
7925(2^211430-5)/85963644Lelio R Paula04/2012
79262^211401-9163639Lelio R Paula08/2011
7927(6883*2^211378-1)/6963634Lelio R Paula04/2015
7928(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7929(29*2^211384-1)/5012262163627Lelio R Paula01/2014
79302^211333+1501563618Lelio R Paula01/2013
793133^41889-3263610Norbert Schneider03/2014
793213^57093+1863599Lelio R Paula05/2013
7933(5*2^211219-1)/963583Lelio R Paula01/2014
7934(107*10^63576-17)/963578Robert Price02/2017
793523^46687-102063575Enzo Doria08/2012
7936(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7937(3^133243+7)/1072663570Lelio R Paula04/2012
7938(7*2^211181+1)/274563570Lelio R Paula06/2012
7940(20^48859-1)/1963566Paul Bourdelais03/2010
79392*3^133227+563566Lelio R Paula04/2014
79412^211155+11363564Lelio R Paula08/2011
79422^211134+34563558Lelio R Paula09/2011
79432^211121+1638563554Lelio R Paula09/2011
794416996^5483+5483^1699663549Hans Havermann02/2017
7945(2^211079+9)/36428363536Lelio R Paula03/2012
79463*10^63522+1363523Robert Price08/2017
794715852^10157+10157^1585263516Hans Havermann02/2017
79482^210948-1587363502Enzo Doria04/2013
79497^75136+663498Lelio R Paula04/2013
79502^210928+1291563496Lelio R Paula02/2013
79517*10^63493+3963494Robert Price07/2016
79522^210909+13563490Lelio R Paula08/2011
7953(3*2^210832+1)/763467Lelio R Paula07/2012
79548*7^75098-363467Lelio R Paula09/2014
795517683^3882+3882^1768363466Hans Havermann03/2017
7957Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
79562^210820-1690563464Enzo Doria05/2013
79585^90795-3663463Lelio R Paula04/2013
795984731!6-4863463Robert Price08/2018
79602^210816-1319763462Enzo Doria10/2012
79612^210750+13363443Lelio R Paula08/2011
7962291^25742+25742^29163426Norbert Schneider09/2014
7963(3^132908+8)/27985963408Lelio R Paula04/2012
79646^81480-13963404Lelio R Paula04/2013
79652^210576-17363390Lelio R Paula08/2011
796618^50497+5563388Lelio R Paula05/2013
79672^210545+1163381Lelio R Paula08/2011
79682^210543+6363380Lelio R Paula08/2011
7969155^28929-15463365Norbert Schneider12/2018
797083^33016+8263361Norbert Schneider04/2015
79712^210464+9876533163356Jason Earls12/2008
79727*10^63351+963352Dmitry Domanov11/2010
7973p(13534)#/2+51263348Robert Price05/2017
79741741^19546+19546^174163345Serge Batalov05/2014
797510^63336+1981963337Patrick De Geest12/2013
797610^63336-12288363336Patrick De Geest12/2013
7977(19^49523-2^49523)/1763327Robert Price09/2013
7978(2^210378+47)/9551693163323Lelio R Paula03/2012
797931191!2+25663316Robert Price01/2015
798016458^7031+7031^1645863315Hans Havermann01/2017
7981(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7982156^28864+15563303Norbert Schneider12/2018
7983(2^210283+7)/169114563296Lelio R Paula03/2012
79842^210217+129963282Lelio R Paula09/2011
7985(2^210221-3)/26963281Lelio R Paula04/2012
7986Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
798796^31913-9563261Norbert Schneider04/2016
79883^132572+28063253Lelio R Paula04/2013
79893^132570-2^(132570-1)63252Robert Price01/2016
799011^60734-492063248Enzo Doria01/2013
79922^210061+2163235Donovan Johnson06/2006
799118^50375+9563235Lelio R Paula05/2013
799385^32773-263233Lelio R Paula08/2013
7994(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7995(2^210054-1017)/67163230Lelio R Paula04/2012
79963*2^210022+563224Lelio R Paula04/2014
799715^53756+3263222Lelio R Paula05/2013
799917^51380+2263221Lelio R Paula05/2013
7998(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
800043^38700+4263216Norbert Schneider06/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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