PRP Records

Probable Primes Top 10000

(211563 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 ?
72512^215351-11192564828Enzo Doria05/2014
72522^215310-11764815Lelio R Paula08/2011
7253124^30958-12364809Norbert Schneider02/2015
7254(7*10^64807+17)/364808Erik Branger03/2014
7255(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
72562^215243-1594964795Enzo Doria04/2013
725723^47581-22^4758164793Robert Price08/2012
7258(62*10^64783-17)/964784Robert Price09/2015
72595*3^135747-464769Lelio R Paula04/2014
7260(59*10^64767-41)/964768Robert Price09/2015
7262(2^215140+3)/1964763Lelio R Paula04/2012
72612^215135-1716964763Enzo Doria05/2013
72632^215115-11127764757Enzo Doria05/2014
72649*5^92641+264755Lelio R Paula09/2014
7265(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7266(5*10^64715-23)/964715Robert Price11/2014
72672^214938-178164703Yves Minet03/2013
726811^62111-42064682Enzo Doria08/2012
72695^92525+4264673Lelio R Paula06/2013
72702^214824+7189364669Enzo Doria04/2016
72712^214799-222164661Yves Minet08/2013
7272(21*2^214688+1)/29364627Lelio R Paula08/2012
727392^32907+32907^9264623Serge Batalov05/2014
7274(89*10^64608-539)/964609Robert Price11/2017
72756^83013+10164597Lelio R Paula07/2013
7276p(13775)#/2+864594Robert Price01/2017
7277(7*10^64568-43)/964568Robert Price10/2014
7278Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7279(24737*2^214476+1)/287764565Lelio R Paula06/2014
7280(47*2^214463+1)/764561Lelio R Paula04/2015
72812^214458+5461564559Lelio R Paula10/2011
7282(3^135322+7)/12291140864557Lelio R Paula04/2012
72832^214389-68311364538Paul Bourdelais03/2013
7284(76*10^64534+113)/964535Robert Price11/2017
72852^214369-11124164532Enzo Doria05/2014
7286(19^50461+3^50461)/2264526Robert Price07/2013
728711^61954-366064519Enzo Doria12/2012
7288(23*2^214319-1)/2164517Lelio R Paula01/2014
7289(58695*2^214310-1)/57164516Lelio R Paula04/2015
729035^41779-3464510Norbert Schneider04/2014
7291(159^29303+1)/16064506Eric Chen12/2017
7292(89*10^64504-179)/964505Robert Price11/2017
729311^61939-522064503Enzo Doria01/2013
7294(2^214271+78557)/3564501Lelio R Paula05/2012
7295L(308604)+P(308604)64495Robert Price12/2017
7296126^30706-12564494Norbert Schneider02/2015
7297gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
72982^214215+1290964486Lelio R Paula10/2011
72995^92225+6664463Lelio R Paula06/2013
73002^214126-24055164459Paul Bourdelais03/2013
73018*6^82827+564453Lelio R Paula09/2014
7302(31*2^214120-1)/217048564452Lelio R Paula01/2014
7303(31*2^214088-1)/595564445Lelio R Paula01/2014
730414^56227+8964444Lelio R Paula08/2013
73072^214055-15964437Lelio R Paula08/2011
730510^64436+266764437Patrick De Geest05/2013
730665^35543-64^3554364437Robert Price08/2013
730810^64436-5364436Robert Price05/2011
7309(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7310Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
73113^135027+10064425Lelio R Paula05/2013
7312(3^134972-7)/264398Lelio R Paula04/2012
73136*10^64387+764388Dmitry Domanov11/2010
73142^213864-1837764380Enzo Doria05/2013
7315(2^213821+9)/20964365Lelio R Paula04/2012
73162^213788+13564357Lelio R Paula08/2011
7317(3^134883+2)/4831364351Lelio R Paula04/2012
7318(49^38069-46^38069)/364344Serge Batalov12/2016
7319(11^61781+2^61781)/1364338Robert Price02/2013
73206^82670+3764330Lelio R Paula07/2013
7321(3^134839+4)/3231295964328Lelio R Paula04/2012
7322(22*10^64326+161)/364327Robert Price02/2017
732311^61767-405064324Enzo Doria12/2012
73242^213645-11485364314Enzo Doria05/2015
732513^57733+1864312Lelio R Paula07/2013
73262^213621+7270764307Enzo Doria04/2016
732710^64305+13679164306Patrick De Geest05/2011
732810^64305-964305Alexander Gramolin01/2011
7329V(307652)64295Serge Batalov03/2015
73304*10^64286-8964287Robert Price08/2017
7331(2^213546-5)/222164281Lelio R Paula04/2012
73322^213438-5869564252Lelio R Paula10/2011
73332^213367-10564230Lelio R Paula08/2011
7334595^23148+23148^59564225Norbert Schneider07/2016
73353^134601+868064221Lelio R Paula05/2013
7336(26*10^64220+61)/364221Robert Price06/2017
7337500^23793+23793^50064217Norbert Schneider08/2016
7338179^28504-264216Lelio R Paula10/2017
73402^213314-45564214Yves Minet02/2012
733939^40359-3864214Norbert Schneider05/2014
73412^213292-1608564208Enzo Doria04/2013
73422^213274-7764202Lelio R Paula08/2011
734319^50203+7864198Lelio R Paula08/2013
7344(44*10^64192-233)/964193Robert Price10/2017
73452^213240-11286564192Enzo Doria06/2014
73462^213190-11239164177Enzo Doria06/2014
7347(9913*2^213184-1)/965764175Lelio R Paula04/2015
734814^55991+2764173Lelio R Paula07/2013
73492^213158-11258164167Enzo Doria06/2014
73502^213148+9164164Lelio R Paula08/2011
7351(96^32369+1)/9764163Paul Bourdelais08/2017
73536^82439+12564151Lelio R Paula07/2013
73527*2^213102+964151Lelio R Paula04/2014
7354L(306854)+F(306855)64129Henri Lifchitz01/2007
7355610^23017+23017^61064110Norbert Schneider07/2016
73562^212950-6487564105Lelio R Paula10/2011
7357(266*10^64102-17)/364104Robert Price06/2016
7358p(13679)#/2+6464097Robert Price03/2017
735919^50119+9464090Lelio R Paula08/2013
73602^212880-14764084Lelio R Paula08/2011
736111^61523-459064070Enzo Doria01/2013
73625^91663+3864070Lelio R Paula05/2013
73635^91650+5264061Lelio R Paula05/2013
73642^212770+6964051Lelio R Paula08/2011
7365(3^134227+1)/464042Paul Bourdelais11/2007
7366(2*10^64041-17)/364041Robert Price08/2014
7367(15^54449+1)/1664036Paul Bourdelais03/2010
7368(29*10^64027+91)/364028Robert Price03/2016
7369(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
737016878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
73712^212663+5364018Lelio R Paula08/2011
7372(4*10^64014+197)/364015Robert Price03/2017
7373(140^29819+1)/14163994Richard Fischer05/2018
737410^63986+6363987Robert Price01/2011
737510^63986-3155763986Patrick De Geest05/2013
737631487!2-2^3148763982Robert Price09/2015
7377(21*2^212522-1)/141632363971Lelio R Paula01/2014
73785^91517+9863968Lelio R Paula04/2013
7379(19*10^63960-43)/363961Robert Price10/2017
7380(62*10^63954-17)/963955Robert Price09/2015
73825^91493-4^9149363951Predrag Minovic04/2004
7381V(364793)63951Serge Batalov03/2015
738419^50004+5863943Lelio R Paula05/2013
73835*6^82172-763943Lelio R Paula09/2014
7385(56*10^63942+223)/963943Robert Price07/2016
738619^50000-2463938Lelio R Paula05/2013
7387(23*2^212374-1)/2701963928Lelio R Paula01/2014
7388(9*2^212355-1)/76163924Lelio R Paula01/2014
73902^212344-18363922Lelio R Paula08/2011
7389(58695*2^212336-1)/37963922Lelio R Paula04/2015
739110^63916+7963917Robert Price01/2011
739210^63916-7682363916Patrick De Geest05/2013
73932^212295-2563908Lelio R Paula08/2011
73952^212285-238363905Yves Minet10/2013
7394267^26336+26336^26763905Norbert Schneider09/2014
7396(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
739719^49962+6063890Lelio R Paula05/2013
73983^133906-11305663890Enzo Doria07/2014
7399(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
74003*6^82092+563881Lelio R Paula09/2014
740115441^13706+13706^1544163879Hans Havermann02/2017
74022^212154-77635163865Paul Bourdelais03/2013
740335^41359+263862Lelio R Paula05/2013
7404(61*10^63857-43)/963858Robert Price09/2015
7405(2^212131-3)/48563856Lelio R Paula04/2012
74062^212112-45999563853Enzo Doria06/2015
740715^54290+5863850Lelio R Paula05/2013
74083*2^212097-763849Lelio R Paula04/2014
740955^36683-5463842Norbert Schneider08/2014
7410(509203*2^212056-1)/363841Lelio R Paula04/2015
7411(3^133805-7)/17263839Lelio R Paula04/2012
74122^212049+14963834Lelio R Paula08/2011
74135^91318-1863829Lelio R Paula04/2013
741418468^2857+2857^1846863824Hans Havermann03/2017
7415(2^212024-5)/111163823Lelio R Paula04/2012
74162^211961+1291563807Lelio R Paula02/2013
7417(3^133707-7)/578063791Lelio R Paula04/2012
7418(44*10^63790-161)/963791Robert Price11/2017
7419747^22198+22198^74763782Norbert Schneider07/2016
74202^211800-1716963759Enzo Doria05/2013
7421(85*10^63757-1)/363759Robert Price07/2017
7422(14*10^63747-11)/363748Erik Branger09/2014
742391*19^49848+663746Curtis Bright05/2015
742418855^2402+2402^1885563741Hans Havermann03/2017
7425(142*10^63734-7)/963736Robert Price02/2017
74262^211699-11163728Lelio R Paula08/2011
742711^61192-555063725Enzo Doria01/2013
7428(11*10^63718+7)/963719Serge Batalov06/2011
74296^81872-1363709Lelio R Paula04/2013
74303^133522+9863707Lelio R Paula05/2013
74322^211607-6163701Lelio R Paula08/2011
74315^91135+863701Lelio R Paula04/2013
743311^61157-27063689Enzo Doria07/2012
743510^63685+114514191963686Marisa Kirisame03/2015
743410^63685+10383763686Patrick De Geest03/2016
743610^63685-13079763685Patrick De Geest03/2016
74372^211547+1155*21154763682Henri Lifchitz02/2005
74382^211543+4563681Lelio R Paula08/2011
74392^211534+4363679Lelio R Paula08/2011
744011^61140-6063671Enzo Doria07/2012
74412^211491-11232163666Enzo Doria06/2014
744219085^2164+2164^1908563654Hans Havermann03/2017
7443(2^211430-5)/85963644Lelio R Paula04/2012
74442^211401-9163639Lelio R Paula08/2011
7445(6883*2^211378-1)/6963634Lelio R Paula04/2015
7446(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
7447(29*2^211384-1)/5012262163627Lelio R Paula01/2014
74482^211333+1501563618Lelio R Paula01/2013
744933^41889-3263610Norbert Schneider03/2014
745013^57093+1863599Lelio R Paula05/2013
7451(5*2^211219-1)/963583Lelio R Paula01/2014
7452(107*10^63576-17)/963578Robert Price02/2017
745323^46687-102063575Enzo Doria08/2012
7454(67607*2^211188+1)/523431963573Lelio R Paula06/2014
7455(3^133243+7)/1072663570Lelio R Paula04/2012
7456(7*2^211181+1)/274563570Lelio R Paula06/2012
7458(20^48859-1)/1963566Paul Bourdelais03/2010
74572*3^133227+563566Lelio R Paula04/2014
74592^211155+11363564Lelio R Paula08/2011
74602^211134+34563558Lelio R Paula09/2011
74612^211121+1638563554Lelio R Paula09/2011
746216996^5483+5483^1699663549Hans Havermann02/2017
7463(2^211079+9)/36428363536Lelio R Paula03/2012
74643*10^63522+1363523Robert Price08/2017
746515852^10157+10157^1585263516Hans Havermann02/2017
74662^210948-1587363502Enzo Doria04/2013
74677^75136+663498Lelio R Paula04/2013
74682^210928+1291563496Lelio R Paula02/2013
74697*10^63493+3963494Robert Price07/2016
74702^210909+13563490Lelio R Paula08/2011
7471(3*2^210832+1)/763467Lelio R Paula07/2012
74728*7^75098-363467Lelio R Paula09/2014
747317683^3882+3882^1768363466Hans Havermann03/2017
7474Pell-LucasQ(165799)/263464Eric W. Weisstein11/2006
74752^210820-1690563464Enzo Doria05/2013
74765^90795-3663463Lelio R Paula04/2013
74772^210816-1319763462Enzo Doria10/2012
74782^210750+13363443Lelio R Paula08/2011
7479291^25742+25742^29163426Norbert Schneider09/2014
7480(3^132908+8)/27985963408Lelio R Paula04/2012
74816^81480-13963404Lelio R Paula04/2013
74822^210576-17363390Lelio R Paula08/2011
748318^50497+5563388Lelio R Paula05/2013
74842^210545+1163381Lelio R Paula08/2011
74852^210543+6363380Lelio R Paula08/2011
748683^33016+8263361Norbert Schneider04/2015
74872^210464+9876533163356Jason Earls12/2008
74887*10^63351+963352Dmitry Domanov11/2010
7489p(13534)#/2+51263348Robert Price05/2017
74901741^19546+19546^174163345Serge Batalov05/2014
749110^63336+1981963337Patrick De Geest12/2013
749210^63336-12288363336Patrick De Geest12/2013
7493(19^49523-2^49523)/1763327Robert Price09/2013
7494(2^210378+47)/9551693163323Lelio R Paula03/2012
749531191!2+25663316Robert Price01/2015
749616458^7031+7031^1645863315Hans Havermann01/2017
7497(lucasV(1,2,420636)-2)/(7*31^2*210319)63303Mike Oakes03/2017
7498(2^210283+7)/169114563296Lelio R Paula03/2012
74992^210217+129963282Lelio R Paula09/2011
7500(2^210221-3)/26963281Lelio R Paula04/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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