PRP Records

Probable Primes Top 10000

(224660 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 ?
750111^61954-366064519Enzo Doria12/2012
7502(23*2^214319-1)/2164517Lelio R Paula01/2014
7503(58695*2^214310-1)/57164516Lelio R Paula04/2015
750435^41779-3464510Norbert Schneider04/2014
7505(159^29303+1)/16064506Eric Chen12/2017
7506(89*10^64504-179)/964505Robert Price11/2017
750711^61939-522064503Enzo Doria01/2013
7508(2^214271+78557)/3564501Lelio R Paula05/2012
7509L(308604)+P(308604)64495Robert Price12/2017
7510126^30706-12564494Norbert Schneider02/2015
7511gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
75122^214215+1290964486Lelio R Paula10/2011
75135^92225+6664463Lelio R Paula06/2013
75142^214126-24055164459Paul Bourdelais03/2013
75158*6^82827+564453Lelio R Paula09/2014
7516(31*2^214120-1)/217048564452Lelio R Paula01/2014
7517(31*2^214088-1)/595564445Lelio R Paula01/2014
751814^56227+8964444Lelio R Paula08/2013
75212^214055-15964437Lelio R Paula08/2011
751910^64436+266764437Patrick De Geest05/2013
752065^35543-64^3554364437Robert Price08/2013
752210^64436-5364436Robert Price05/2011
7523(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7524Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
75253^135027+10064425Lelio R Paula05/2013
7526(3^134972-7)/264398Lelio R Paula04/2012
75276*10^64387+764388Dmitry Domanov11/2010
75282^213864-1837764380Enzo Doria05/2013
7529(2^213821+9)/20964365Lelio R Paula04/2012
75302^213788+13564357Lelio R Paula08/2011
7531(3^134883+2)/4831364351Lelio R Paula04/2012
7532(49^38069-46^38069)/364344Serge Batalov12/2016
7533(11^61781+2^61781)/1364338Robert Price02/2013
75346^82670+3764330Lelio R Paula07/2013
7535(3^134839+4)/3231295964328Lelio R Paula04/2012
7536(22*10^64326+161)/364327Robert Price02/2017
753711^61767-405064324Enzo Doria12/2012
75382^213645-11485364314Enzo Doria05/2015
753913^57733+1864312Lelio R Paula07/2013
75402^213621+7270764307Enzo Doria04/2016
754110^64305+13679164306Patrick De Geest05/2011
754210^64305-964305Alexander Gramolin01/2011
7543V(307652)64295Serge Batalov03/2015
75444*10^64286-8964287Robert Price08/2017
7545(2^213546-5)/222164281Lelio R Paula04/2012
75462^213438-5869564252Lelio R Paula10/2011
75472^213367-10564230Lelio R Paula08/2011
7548595^23148+23148^59564225Norbert Schneider07/2016
75493^134601+868064221Lelio R Paula05/2013
7550(26*10^64220+61)/364221Robert Price06/2017
7551500^23793+23793^50064217Norbert Schneider08/2016
7552179^28504-264216Lelio R Paula10/2017
75542^213314-45564214Yves Minet02/2012
755339^40359-3864214Norbert Schneider05/2014
75552^213292-1608564208Enzo Doria04/2013
75562^213274-7764202Lelio R Paula08/2011
755719^50203+7864198Lelio R Paula08/2013
7558(44*10^64192-233)/964193Robert Price10/2017
75592^213240-11286564192Enzo Doria06/2014
75602^213190-11239164177Enzo Doria06/2014
7561(9913*2^213184-1)/965764175Lelio R Paula04/2015
756214^55991+2764173Lelio R Paula07/2013
75632^213158-11258164167Enzo Doria06/2014
75642^213148+9164164Lelio R Paula08/2011
7565(96^32369+1)/9764163Paul Bourdelais08/2017
75676^82439+12564151Lelio R Paula07/2013
75667*2^213102+964151Lelio R Paula04/2014
7568L(306854)+F(306855)64129Henri Lifchitz01/2007
7569610^23017+23017^61064110Norbert Schneider07/2016
75702^212950-6487564105Lelio R Paula10/2011
7571(266*10^64102-17)/364104Robert Price06/2016
7572p(13679)#/2+6464097Robert Price03/2017
757319^50119+9464090Lelio R Paula08/2013
75742^212880-14764084Lelio R Paula08/2011
757511^61523-459064070Enzo Doria01/2013
75765^91663+3864070Lelio R Paula05/2013
75775^91650+5264061Lelio R Paula05/2013
75782^212770+6964051Lelio R Paula08/2011
7579(3^134227+1)/464042Paul Bourdelais11/2007
7580(2*10^64041-17)/364041Robert Price08/2014
7581(15^54449+1)/1664036Paul Bourdelais03/2010
7582(29*10^64027+91)/364028Robert Price03/2016
7583(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
758416878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
75852^212663+5364018Lelio R Paula08/2011
7586(4*10^64014+197)/364015Robert Price03/2017
758785402!6-364014Robert Price08/2018
7588(140^29819+1)/14163994Richard Fischer05/2018
758910^63986+6363987Robert Price01/2011
759010^63986-3155763986Patrick De Geest05/2013
759131487!2-2^3148763982Robert Price09/2015
7592(21*2^212522-1)/141632363971Lelio R Paula01/2014
75935^91517+9863968Lelio R Paula04/2013
7594(19*10^63960-43)/363961Robert Price10/2017
7595(62*10^63954-17)/963955Robert Price09/2015
75975^91493-4^9149363951Predrag Minovic04/2004
7596V(364793)63951Serge Batalov03/2015
759919^50004+5863943Lelio R Paula05/2013
75985*6^82172-763943Lelio R Paula09/2014
7600(56*10^63942+223)/963943Robert Price07/2016
760119^50000-2463938Lelio R Paula05/2013
7602(23*2^212374-1)/2701963928Lelio R Paula01/2014
7603(9*2^212355-1)/76163924Lelio R Paula01/2014
76052^212344-18363922Lelio R Paula08/2011
7604(58695*2^212336-1)/37963922Lelio R Paula04/2015
760610^63916+7963917Robert Price01/2011
760710^63916-7682363916Patrick De Geest05/2013
76082^212295-2563908Lelio R Paula08/2011
76102^212285-238363905Yves Minet10/2013
7609267^26336+26336^26763905Norbert Schneider09/2014
7611(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
761219^49962+6063890Lelio R Paula05/2013
76133^133906-11305663890Enzo Doria07/2014
7614(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
76153*6^82092+563881Lelio R Paula09/2014
761615441^13706+13706^1544163879Hans Havermann02/2017
76172^212154-77635163865Paul Bourdelais03/2013
761835^41359+263862Lelio R Paula05/2013
7619(61*10^63857-43)/963858Robert Price09/2015
7620(2^212131-3)/48563856Lelio R Paula04/2012
76212^212112-45999563853Enzo Doria06/2015
762215^54290+5863850Lelio R Paula05/2013
76233*2^212097-763849Lelio R Paula04/2014
762455^36683-5463842Norbert Schneider08/2014
7625(509203*2^212056-1)/363841Lelio R Paula04/2015
7626(3^133805-7)/17263839Lelio R Paula04/2012
76272^212049+14963834Lelio R Paula08/2011
76285^91318-1863829Lelio R Paula04/2013
762918468^2857+2857^1846863824Hans Havermann03/2017
7630(2^212024-5)/111163823Lelio R Paula04/2012
76312^211961+1291563807Lelio R Paula02/2013
7633(3^133707-7)/578063791Lelio R Paula04/2012
7632(44*10^63790-161)/963791Robert Price11/2017
7634747^22198+22198^74763782Norbert Schneider07/2016
76352^211800-1716963759Enzo Doria05/2013
7636(85*10^63757-1)/363759Robert Price07/2017
763785089!6-863757Robert Price08/2018
7638(14*10^63747-11)/363748Erik Branger09/2014
763991*19^49848+663746Curtis Bright05/2015
764018855^2402+2402^1885563741Hans Havermann03/2017
7641(142*10^63734-7)/963736Robert Price02/2017
76422^211699-11163728Lelio R Paula08/2011
764311^61192-555063725Enzo Doria01/2013
7644(11*10^63718+7)/963719Serge Batalov06/2011
76456^81872-1363709Lelio R Paula04/2013
76463^133522+9863707Lelio R Paula05/2013
76482^211607-6163701Lelio R Paula08/2011
76475^91135+863701Lelio R Paula04/2013
764911^61157-27063689Enzo Doria07/2012
765010^63685+114514191963686Marisa Kirisame03/2015
765110^63685+10383763686Patrick De Geest03/2016
765210^63685-13079763685Patrick De Geest03/2016
76532^211547+1155*21154763682Henri Lifchitz02/2005
76542^211543+4563681Lelio R Paula08/2011
76552^211534+4363679Lelio R Paula08/2011
765611^61140-6063671Enzo Doria07/2012
76572^211491-11232163666Enzo Doria06/2014
765819085^2164+2164^1908563654Hans Havermann03/2017
7659(2^211430-5)/85963644Lelio R Paula04/2012
76602^211401-9163639Lelio R Paula08/2011
7661(6883*2^211378-1)/6963634Lelio R Paula04/2015
7662(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7663(29*2^211384-1)/5012262163627Lelio R Paula01/2014
76642^211333+1501563618Lelio R Paula01/2013
766533^41889-3263610Norbert Schneider03/2014
766613^57093+1863599Lelio R Paula05/2013
7667(5*2^211219-1)/963583Lelio R Paula01/2014
7668(107*10^63576-17)/963578Robert Price02/2017
766923^46687-102063575Enzo Doria08/2012
7670(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7671(3^133243+7)/1072663570Lelio R Paula04/2012
7672(7*2^211181+1)/274563570Lelio R Paula06/2012
7674(20^48859-1)/1963566Paul Bourdelais03/2010
76732*3^133227+563566Lelio R Paula04/2014
76752^211155+11363564Lelio R Paula08/2011
76762^211134+34563558Lelio R Paula09/2011
76772^211121+1638563554Lelio R Paula09/2011
767816996^5483+5483^1699663549Hans Havermann02/2017
7679(2^211079+9)/36428363536Lelio R Paula03/2012
76803*10^63522+1363523Robert Price08/2017
768115852^10157+10157^1585263516Hans Havermann02/2017
76822^210948-1587363502Enzo Doria04/2013
76837^75136+663498Lelio R Paula04/2013
76842^210928+1291563496Lelio R Paula02/2013
76857*10^63493+3963494Robert Price07/2016
76862^210909+13563490Lelio R Paula08/2011
7687(3*2^210832+1)/763467Lelio R Paula07/2012
76888*7^75098-363467Lelio R Paula09/2014
768917683^3882+3882^1768363466Hans Havermann03/2017
7691Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
76902^210820-1690563464Enzo Doria05/2013
76925^90795-3663463Lelio R Paula04/2013
769384731!6-4863463Robert Price08/2018
76942^210816-1319763462Enzo Doria10/2012
76952^210750+13363443Lelio R Paula08/2011
7696291^25742+25742^29163426Norbert Schneider09/2014
7697(3^132908+8)/27985963408Lelio R Paula04/2012
76986^81480-13963404Lelio R Paula04/2013
76992^210576-17363390Lelio R Paula08/2011
770018^50497+5563388Lelio R Paula05/2013
77012^210545+1163381Lelio R Paula08/2011
77022^210543+6363380Lelio R Paula08/2011
770383^33016+8263361Norbert Schneider04/2015
77042^210464+9876533163356Jason Earls12/2008
77057*10^63351+963352Dmitry Domanov11/2010
7706p(13534)#/2+51263348Robert Price05/2017
77071741^19546+19546^174163345Serge Batalov05/2014
770810^63336+1981963337Patrick De Geest12/2013
770910^63336-12288363336Patrick De Geest12/2013
7710(19^49523-2^49523)/1763327Robert Price09/2013
7711(2^210378+47)/9551693163323Lelio R Paula03/2012
771231191!2+25663316Robert Price01/2015
771316458^7031+7031^1645863315Hans Havermann01/2017
7714(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7715(2^210283+7)/169114563296Lelio R Paula03/2012
77162^210217+129963282Lelio R Paula09/2011
7717(2^210221-3)/26963281Lelio R Paula04/2012
7718Phi(193404,10)/386809/812296963268Maksym Voznyy10/2011
771996^31913-9563261Norbert Schneider04/2016
77203^132572+28063253Lelio R Paula04/2013
77213^132570-2^(132570-1)63252Robert Price01/2016
772211^60734-492063248Enzo Doria01/2013
77242^210061+2163235Donovan Johnson06/2006
772318^50375+9563235Lelio R Paula05/2013
772585^32773-263233Lelio R Paula08/2013
7726(-lucasV(1,2,420115)-2)/(3*5^3)63232Mike Oakes02/2017
7727(2^210054-1017)/67163230Lelio R Paula04/2012
77283*2^210022+563224Lelio R Paula04/2014
772915^53756+3263222Lelio R Paula05/2013
773117^51380+2263221Lelio R Paula05/2013
7730(lucasV(1,2,420045)+2)/25763221Mike Oakes02/2017
773243^38700+4263216Norbert Schneider06/2014
77335^90431-9663209Lelio R Paula04/2013
7734(172*10^63202-1)/963204Serge Batalov12/2014
7735(43*10^63200+83)/963201Robert Price08/2017
77362^209914-1600563191Enzo Doria04/2013
77373*6^81190-563179Lelio R Paula09/2014
77382^209820+425763163Lelio R Paula10/2011
774099^31648+263158Lelio R Paula05/2013
773916976^5253+5253^1697663158Hans Havermann01/2017
77412^209790+6763154Lelio R Paula08/2011
77422^209759+9019563144Lelio R Paula02/2013
7743145823#+21150763142Arkadiusz Wesolowski03/2013
77442^209707+51363129Lelio R Paula10/2011
7745(3^132314-8)/1763129Lelio R Paula04/2012
7746(2*10^63117+7)/963117Erik Branger03/2011
77479*2^209654-763114Lelio R Paula04/2014
774884304!6-963112Robert Price08/2018
774911^60598-1463107Lelio R Paula05/2013
775015103^15078+15078^1510363106Hans Havermann01/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 15 2018 21:33 (Time in France)

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