PRP Records

Probable Primes Top 10000

(172751 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 ?
65026^83631-7965078Lelio R Paula07/2013
6501572^23601+23601^57265078Norbert Schneider08/2016
6503(3^136399-7)/54422065074Lelio R Paula04/2012
65042^216154-142165069Yves Minet01/2013
65052^216145-11266365067Enzo Doria06/2014
6506132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
6507132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
6508148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
6509194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
6510223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
651282090*10^65050+2^216091-165055Gilbert Mozzo07/2012
651395133*10^65050+2^216091-165055Gilbert Mozzo12/2013
651198142*10^65050+2^216091-165055Gilbert Mozzo12/2013
6514((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
65155977*10^65050+2^216091-165054Gilbert Mozzo03/2012
65167*2^216091+2^298-1365051Peter Lesala03/2007
65172^216091+2*29208-165050Makoto Morimoto10/2013
6518(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
651911^62439-438065024Enzo Doria01/2013
65203^136244+265005Mike Oakes11/2009
652113^58343-5064991Lelio R Paula07/2013
6522331^25791-1000264989Enzo Doria07/2012
65232^215877+13164986Lelio R Paula08/2011
65244*5^92959+964977Lelio R Paula09/2014
65252^215789-1882564959Lelio R Paula09/2011
6526(2^215801-509203)/4132764958Lelio R Paula05/2012
6527U(315311)64954Serge Batalov03/2015
652846072!3-5904964951Robert Price12/2015
65292^215750-595564948Lelio R Paula09/2011
653013^58281+4664922Lelio R Paula07/2013
65312^215623+18364909Lelio R Paula08/2011
6532(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
65335*2^215554+364889Lelio R Paula04/2014
65342^215541-11207564885Enzo Doria06/2014
65352*10^64882-364883Dmitry Domanov11/2010
653610^64862+34233964863Patrick De Geest05/2013
653710^64862-4764862Robert Price05/2011
653819^50718-8464856Lelio R Paula08/2013
6539(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
654010^64843+427869783964844Robert Price05/2015
654110^64843+2196764844Patrick De Geest03/2016
654210^64843-34007364843Patrick De Geest03/2016
654311^62254+7064831Lelio R Paula07/2013
65442^215351-11192564828Enzo Doria05/2014
65452^215310-11764815Lelio R Paula08/2011
6546124^30958-12364809Norbert Schneider02/2015
6547(7*10^64807+17)/364808Erik Branger03/2014
6548(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
65492^215243-1594964795Enzo Doria04/2013
655023^47581-22^4758164793Robert Price08/2012
6551(62*10^64783-17)/964784Robert Price09/2015
65525*3^135747-464769Lelio R Paula04/2014
6553(59*10^64767-41)/964768Robert Price09/2015
6555(2^215140+3)/1964763Lelio R Paula04/2012
65542^215135-1716964763Enzo Doria05/2013
65562^215115-11127764757Enzo Doria05/2014
65579*5^92641+264755Lelio R Paula09/2014
6558(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
6559(5*10^64715-23)/964715Robert Price11/2014
65602^214938-178164703Yves Minet03/2013
656111^62111-42064682Enzo Doria08/2012
65625^92525+4264673Lelio R Paula06/2013
65632^214824+7189364669Enzo Doria04/2016
65642^214799-222164661Yves Minet08/2013
6565(21*2^214688+1)/29364627Lelio R Paula08/2012
656692^32907+32907^9264623Serge Batalov05/2014
65676^83013+10164597Lelio R Paula07/2013
6568p(13775)#/2+864594Robert Price01/2017
6569(7*10^64568-43)/964568Robert Price10/2014
6570Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
6571(24737*2^214476+1)/287764565Lelio R Paula06/2014
6572(47*2^214463+1)/764561Lelio R Paula04/2015
65732^214458+5461564559Lelio R Paula10/2011
6574(3^135322+7)/12291140864557Lelio R Paula04/2012
65752^214389-68311364538Paul Bourdelais03/2013
65762^214369-11124164532Enzo Doria05/2014
6577(19^50461+3^50461)/2264526Robert Price07/2013
657811^61954-366064519Enzo Doria12/2012
6579(23*2^214319-1)/2164517Lelio R Paula01/2014
6580(58695*2^214310-1)/57164516Lelio R Paula04/2015
658135^41779-3464510Norbert Schneider04/2014
658211^61939-522064503Enzo Doria01/2013
6583(2^214271+78557)/3564501Lelio R Paula05/2012
6584126^30706-12564494Norbert Schneider02/2015
6585gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
65862^214215+1290964486Lelio R Paula10/2011
65875^92225+6664463Lelio R Paula06/2013
65882^214126-24055164459Paul Bourdelais03/2013
65898*6^82827+564453Lelio R Paula09/2014
6590(31*2^214120-1)/217048564452Lelio R Paula01/2014
6591(31*2^214088-1)/595564445Lelio R Paula01/2014
659214^56227+8964444Lelio R Paula08/2013
65952^214055-15964437Lelio R Paula08/2011
659310^64436+266764437Patrick De Geest05/2013
659465^35543-64^3554364437Robert Price08/2013
659610^64436-5364436Robert Price05/2011
6597Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
65983^135027+10064425Lelio R Paula05/2013
6599(3^134972-7)/264398Lelio R Paula04/2012
66006*10^64387+764388Dmitry Domanov11/2010
66012^213864-1837764380Enzo Doria05/2013
6602(2^213821+9)/20964365Lelio R Paula04/2012
66032^213788+13564357Lelio R Paula08/2011
6604(3^134883+2)/4831364351Lelio R Paula04/2012
6605(49^38069-46^38069)/364344Serge Batalov12/2016
6606(11^61781+2^61781)/1364338Robert Price02/2013
66076^82670+3764330Lelio R Paula07/2013
6608(3^134839+4)/3231295964328Lelio R Paula04/2012
6609(22*10^64326+161)/364327Robert Price02/2017
661011^61767-405064324Enzo Doria12/2012
66112^213645-11485364314Enzo Doria05/2015
661213^57733+1864312Lelio R Paula07/2013
66132^213621+7270764307Enzo Doria04/2016
661410^64305+13679164306Patrick De Geest05/2011
661510^64305-964305Alexander Gramolin01/2011
6616V(307652)64295Serge Batalov03/2015
6617(2^213546-5)/222164281Lelio R Paula04/2012
66182^213438-5869564252Lelio R Paula10/2011
66192^213367-10564230Lelio R Paula08/2011
6620595^23148+23148^59564225Norbert Schneider07/2016
66213^134601+868064221Lelio R Paula05/2013
6622500^23793+23793^50064217Norbert Schneider08/2016
66242^213314-45564214Yves Minet02/2012
662339^40359-3864214Norbert Schneider05/2014
66252^213292-1608564208Enzo Doria04/2013
66262^213274-7764202Lelio R Paula08/2011
662719^50203+7864198Lelio R Paula08/2013
66282^213240-11286564192Enzo Doria06/2014
66292^213190-11239164177Enzo Doria06/2014
6630(9913*2^213184-1)/965764175Lelio R Paula04/2015
663114^55991+2764173Lelio R Paula07/2013
66322^213158-11258164167Enzo Doria06/2014
66332^213148+9164164Lelio R Paula08/2011
66356^82439+12564151Lelio R Paula07/2013
66347*2^213102+964151Lelio R Paula04/2014
6636L(306854)+F(306855)64129Henri Lifchitz01/2007
6637610^23017+23017^61064110Norbert Schneider07/2016
66382^212950-6487564105Lelio R Paula10/2011
6639(266*10^64102-17)/364104Robert Price06/2016
6640p(13679)#/2+6464097Robert Price03/2017
664119^50119+9464090Lelio R Paula08/2013
66422^212880-14764084Lelio R Paula08/2011
664311^61523-459064070Enzo Doria01/2013
66445^91663+3864070Lelio R Paula05/2013
66455^91650+5264061Lelio R Paula05/2013
66462^212770+6964051Lelio R Paula08/2011
6647(3^134227+1)/464042Paul Bourdelais11/2007
6648(2*10^64041-17)/364041Robert Price08/2014
6649(15^54449+1)/1664036Paul Bourdelais03/2010
6650(29*10^64027+91)/364028Robert Price03/2016
6651(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
665216878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
66532^212663+5364018Lelio R Paula08/2011
6654(4*10^64014+197)/364015Robert Price03/2017
665510^63986+6363987Robert Price01/2011
665610^63986-3155763986Patrick De Geest05/2013
665731487!2-2^3148763982Robert Price09/2015
6658(21*2^212522-1)/141632363971Lelio R Paula01/2014
66595^91517+9863968Lelio R Paula04/2013
6660(62*10^63954-17)/963955Robert Price09/2015
66625^91493-4^9149363951Predrag Minovic04/2004
6661V(364793)63951Serge Batalov03/2015
666419^50004+5863943Lelio R Paula05/2013
66635*6^82172-763943Lelio R Paula09/2014
6665(56*10^63942+223)/963943Robert Price07/2016
666619^50000-2463938Lelio R Paula05/2013
6667(23*2^212374-1)/2701963928Lelio R Paula01/2014
6668(9*2^212355-1)/76163924Lelio R Paula01/2014
66702^212344-18363922Lelio R Paula08/2011
6669(58695*2^212336-1)/37963922Lelio R Paula04/2015
667110^63916+7963917Robert Price01/2011
667210^63916-7682363916Patrick De Geest05/2013
66732^212295-2563908Lelio R Paula08/2011
66742^212285-238363905Yves Minet10/2013
6675267^26336+26336^26763905Norbert Schneider09/2014
6676(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
667819^49962+6063890Lelio R Paula05/2013
66773^133906-11305663890Enzo Doria07/2014
6679(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
66803*6^82092+563881Lelio R Paula09/2014
668115441^13706+13706^1544163879Hans Havermann02/2017
66822^212154-77635163865Paul Bourdelais03/2013
668335^41359+263862Lelio R Paula05/2013
6684(61*10^63857-43)/963858Robert Price09/2015
6685(2^212131-3)/48563856Lelio R Paula04/2012
66862^212112-45999563853Enzo Doria06/2015
668715^54290+5863850Lelio R Paula05/2013
66883*2^212097-763849Lelio R Paula04/2014
668955^36683-5463842Norbert Schneider08/2014
6690(509203*2^212056-1)/363841Lelio R Paula04/2015
6691(3^133805-7)/17263839Lelio R Paula04/2012
66922^212049+14963834Lelio R Paula08/2011
66935^91318-1863829Lelio R Paula04/2013
669418468^2857+2857^1846863824Hans Havermann03/2017
6695(2^212024-5)/111163823Lelio R Paula04/2012
66962^211961+1291563807Lelio R Paula02/2013
6697(3^133707-7)/578063791Lelio R Paula04/2012
6698747^22198+22198^74763782Norbert Schneider07/2016
66992^211800-1716963759Enzo Doria05/2013
6700(14*10^63747-11)/363748Erik Branger09/2014
670191*19^49848+663746Curtis Bright05/2015
670218855^2402+2402^1885563741Hans Havermann03/2017
6703(142*10^63734-7)/963736Robert Price02/2017
67042^211699-11163728Lelio R Paula08/2011
670511^61192-555063725Enzo Doria01/2013
6706(11*10^63718+7)/963719Serge Batalov06/2011
67076^81872-1363709Lelio R Paula04/2013
67083^133522+9863707Lelio R Paula05/2013
67102^211607-6163701Lelio R Paula08/2011
67095^91135+863701Lelio R Paula04/2013
671111^61157-27063689Enzo Doria07/2012
671210^63685+114514191963686Marisa Kirisame03/2015
671310^63685+10383763686Patrick De Geest03/2016
671410^63685-13079763685Patrick De Geest03/2016
67152^211547+1155*21154763682Henri Lifchitz02/2005
67162^211543+4563681Lelio R Paula08/2011
67172^211534+4363679Lelio R Paula08/2011
671811^61140-6063671Enzo Doria07/2012
67192^211491-11232163666Enzo Doria06/2014
672019085^2164+2164^1908563654Hans Havermann03/2017
6721(2^211430-5)/85963644Lelio R Paula04/2012
67222^211401-9163639Lelio R Paula08/2011
6723(6883*2^211378-1)/6963634Lelio R Paula04/2015
6724(F(152232)^3-F(152231)^3)/F(152230)63629Wayne Halsdorf03/2012
6725(29*2^211384-1)/5012262163627Lelio R Paula01/2014
67262^211333+1501563618Lelio R Paula01/2013
672733^41889-3263610Norbert Schneider03/2014
672813^57093+1863599Lelio R Paula05/2013
6729(5*2^211219-1)/963583Lelio R Paula01/2014
6730(107*10^63576-17)/963578Robert Price02/2017
673123^46687-102063575Enzo Doria08/2012
6732(67607*2^211188+1)/523431963573Lelio R Paula06/2014
6733(3^133243+7)/1072663570Lelio R Paula04/2012
6734(7*2^211181+1)/274563570Lelio R Paula06/2012
6736(20^48859-1)/1963566Paul Bourdelais03/2010
67352*3^133227+563566Lelio R Paula04/2014
67372^211155+11363564Lelio R Paula08/2011
67382^211134+34563558Lelio R Paula09/2011
67392^211121+1638563554Lelio R Paula09/2011
674016996^5483+5483^1699663549Hans Havermann02/2017
6741(2^211079+9)/36428363536Lelio R Paula03/2012
674215852^10157+10157^1585263516Hans Havermann02/2017
67432^210948-1587363502Enzo Doria04/2013
67447^75136+663498Lelio R Paula04/2013
67452^210928+1291563496Lelio R Paula02/2013
67467*10^63493+3963494Robert Price07/2016
67472^210909+13563490Lelio R Paula08/2011
6748(3*2^210832+1)/763467Lelio R Paula07/2012
67498*7^75098-363467Lelio R Paula09/2014
675017683^3882+3882^1768363466Hans Havermann03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 24 2017 22:44 (Time in France)

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