PRP Records

Probable Primes Top 10000

(202622 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 ?
7001-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
7002(13*10^65297+83)/365298Robert Price09/2016
70035^93400-865284Lelio R Paula06/2013
70042^216802-16565264Lelio R Paula08/2011
70052^216799-2863565264Lelio R Paula10/2011
70065*10^65255+5165256Robert Price01/2017
70072^216762-16765252Lelio R Paula08/2011
700811^62657-579065251Enzo Doria01/2013
70093^136756-11288065250Enzo Doria06/2014
70102^216752+2165249Lelio R Paula08/2011
70113*10^65247+1165248Robert Price11/2017
701211^62651-270065245Enzo Doria12/2012
7014Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7013gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7015(2^216676-1017)/63765224Lelio R Paula04/2012
70162^216652-232765219Yves Minet10/2013
7017(9179*2^216648-1)/466765218Lelio R Paula04/2015
7018(5*10^65203-119)/365204Robert Price04/2016
70192^216555-11326965190Enzo Doria07/2014
7020(9513^16384+1)/265181Henri Lifchitz02/2007
70212^216474+1291565166Lelio R Paula02/2013
702219^50958-3265163Lelio R Paula08/2013
70232^216442-11213365156Enzo Doria06/2014
70242^216437-11221365155Enzo Doria06/2014
70252^216435-11276765154Enzo Doria06/2014
70262^216420+1270565149Lelio R Paula02/2013
70278*3^136507-765132Lelio R Paula04/2014
7028(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
70295*10^65086-5165087Robert Price10/2017
70302^216197-11176965082Enzo Doria05/2014
70326^83631-7965078Lelio R Paula07/2013
7031572^23601+23601^57265078Norbert Schneider08/2016
7033(3^136399-7)/54422065074Lelio R Paula04/2012
70342^216154-142165069Yves Minet01/2013
70352^216145-11266365067Enzo Doria06/2014
7036(7*10^65064+53)/365065Robert Price10/2017
7037132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7038132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7039148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7040194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7041223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
704382090*10^65050+2^216091-165055Gilbert Mozzo07/2012
704495133*10^65050+2^216091-165055Gilbert Mozzo12/2013
704298142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7045((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
70465977*10^65050+2^216091-165054Gilbert Mozzo03/2012
70477*2^216091+2^298-1365051Peter Lesala03/2007
70482^216091+2*29208-165050Makoto Morimoto10/2013
7049(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7050p(13861)#/2+25665039Robert Price05/2017
7051(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
705211^62439-438065024Enzo Doria01/2013
70533^136244+265005Mike Oakes11/2009
705413^58343-5064991Lelio R Paula07/2013
7055331^25791-1000264989Enzo Doria07/2012
70562^215877+13164986Lelio R Paula08/2011
70574*5^92959+964977Lelio R Paula09/2014
70582^215789-1882564959Lelio R Paula09/2011
7059(2^215801-509203)/4132764958Lelio R Paula05/2012
7060U(315311)64954Serge Batalov03/2015
706146072!3-5904964951Robert Price12/2015
70622^215750-595564948Lelio R Paula09/2011
706313^58281+4664922Lelio R Paula07/2013
70642^215623+18364909Lelio R Paula08/2011
7065(46*10^64904+521)/964905Robert Price08/2017
7066(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
70675*2^215554+364889Lelio R Paula04/2014
70682^215541-11207564885Enzo Doria06/2014
70692*10^64882-364883Dmitry Domanov11/2010
707010^64862+34233964863Patrick De Geest05/2013
707110^64862-4764862Robert Price05/2011
707219^50718-8464856Lelio R Paula08/2013
7073(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
707510^64843+427869783964844Robert Price05/2015
707410^64843+2196764844Patrick De Geest03/2016
707610^64843-34007364843Patrick De Geest03/2016
707711^62254+7064831Lelio R Paula07/2013
70782^215351-11192564828Enzo Doria05/2014
70792^215310-11764815Lelio R Paula08/2011
7080124^30958-12364809Norbert Schneider02/2015
7081(7*10^64807+17)/364808Erik Branger03/2014
7082(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
70832^215243-1594964795Enzo Doria04/2013
708423^47581-22^4758164793Robert Price08/2012
7085(62*10^64783-17)/964784Robert Price09/2015
70865*3^135747-464769Lelio R Paula04/2014
7087(59*10^64767-41)/964768Robert Price09/2015
7089(2^215140+3)/1964763Lelio R Paula04/2012
70882^215135-1716964763Enzo Doria05/2013
70902^215115-11127764757Enzo Doria05/2014
70919*5^92641+264755Lelio R Paula09/2014
7092(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
7093(5*10^64715-23)/964715Robert Price11/2014
70942^214938-178164703Yves Minet03/2013
709511^62111-42064682Enzo Doria08/2012
70965^92525+4264673Lelio R Paula06/2013
70972^214824+7189364669Enzo Doria04/2016
70982^214799-222164661Yves Minet08/2013
7099(21*2^214688+1)/29364627Lelio R Paula08/2012
710092^32907+32907^9264623Serge Batalov05/2014
7101(89*10^64608-539)/964609Robert Price11/2017
71026^83013+10164597Lelio R Paula07/2013
7103p(13775)#/2+864594Robert Price01/2017
7104(7*10^64568-43)/964568Robert Price10/2014
7105Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7106(24737*2^214476+1)/287764565Lelio R Paula06/2014
7107(47*2^214463+1)/764561Lelio R Paula04/2015
71082^214458+5461564559Lelio R Paula10/2011
7109(3^135322+7)/12291140864557Lelio R Paula04/2012
71102^214389-68311364538Paul Bourdelais03/2013
7111(76*10^64534+113)/964535Robert Price11/2017
71122^214369-11124164532Enzo Doria05/2014
7113(19^50461+3^50461)/2264526Robert Price07/2013
711411^61954-366064519Enzo Doria12/2012
7115(23*2^214319-1)/2164517Lelio R Paula01/2014
7116(58695*2^214310-1)/57164516Lelio R Paula04/2015
711735^41779-3464510Norbert Schneider04/2014
7118(159^29303+1)/16064506Eric Chen12/2017
7119(89*10^64504-179)/964505Robert Price11/2017
712011^61939-522064503Enzo Doria01/2013
7121(2^214271+78557)/3564501Lelio R Paula05/2012
7122L(308604)+P(308604)64495Robert Price12/2017
7123126^30706-12564494Norbert Schneider02/2015
7124gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
71252^214215+1290964486Lelio R Paula10/2011
71265^92225+6664463Lelio R Paula06/2013
71272^214126-24055164459Paul Bourdelais03/2013
71288*6^82827+564453Lelio R Paula09/2014
7129(31*2^214120-1)/217048564452Lelio R Paula01/2014
7130(31*2^214088-1)/595564445Lelio R Paula01/2014
713114^56227+8964444Lelio R Paula08/2013
71342^214055-15964437Lelio R Paula08/2011
713210^64436+266764437Patrick De Geest05/2013
713365^35543-64^3554364437Robert Price08/2013
713510^64436-5364436Robert Price05/2011
7136(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7137Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
71383^135027+10064425Lelio R Paula05/2013
7139(3^134972-7)/264398Lelio R Paula04/2012
71406*10^64387+764388Dmitry Domanov11/2010
71412^213864-1837764380Enzo Doria05/2013
7142(2^213821+9)/20964365Lelio R Paula04/2012
71432^213788+13564357Lelio R Paula08/2011
7144(3^134883+2)/4831364351Lelio R Paula04/2012
7145(49^38069-46^38069)/364344Serge Batalov12/2016
7146(11^61781+2^61781)/1364338Robert Price02/2013
71476^82670+3764330Lelio R Paula07/2013
7148(3^134839+4)/3231295964328Lelio R Paula04/2012
7149(22*10^64326+161)/364327Robert Price02/2017
715011^61767-405064324Enzo Doria12/2012
71512^213645-11485364314Enzo Doria05/2015
715213^57733+1864312Lelio R Paula07/2013
71532^213621+7270764307Enzo Doria04/2016
715410^64305+13679164306Patrick De Geest05/2011
715510^64305-964305Alexander Gramolin01/2011
7156V(307652)64295Serge Batalov03/2015
71574*10^64286-8964287Robert Price08/2017
7158(2^213546-5)/222164281Lelio R Paula04/2012
71592^213438-5869564252Lelio R Paula10/2011
71602^213367-10564230Lelio R Paula08/2011
7161595^23148+23148^59564225Norbert Schneider07/2016
71623^134601+868064221Lelio R Paula05/2013
7163(26*10^64220+61)/364221Robert Price06/2017
7164500^23793+23793^50064217Norbert Schneider08/2016
7165179^28504-264216Lelio R Paula10/2017
71672^213314-45564214Yves Minet02/2012
716639^40359-3864214Norbert Schneider05/2014
71682^213292-1608564208Enzo Doria04/2013
71692^213274-7764202Lelio R Paula08/2011
717019^50203+7864198Lelio R Paula08/2013
7171(44*10^64192-233)/964193Robert Price10/2017
71722^213240-11286564192Enzo Doria06/2014
71732^213190-11239164177Enzo Doria06/2014
7174(9913*2^213184-1)/965764175Lelio R Paula04/2015
717514^55991+2764173Lelio R Paula07/2013
71762^213158-11258164167Enzo Doria06/2014
71772^213148+9164164Lelio R Paula08/2011
7178(96^32369+1)/9764163Paul Bourdelais08/2017
71806^82439+12564151Lelio R Paula07/2013
71797*2^213102+964151Lelio R Paula04/2014
7181L(306854)+F(306855)64129Henri Lifchitz01/2007
7182610^23017+23017^61064110Norbert Schneider07/2016
71832^212950-6487564105Lelio R Paula10/2011
7184(266*10^64102-17)/364104Robert Price06/2016
7185p(13679)#/2+6464097Robert Price03/2017
718619^50119+9464090Lelio R Paula08/2013
71872^212880-14764084Lelio R Paula08/2011
718811^61523-459064070Enzo Doria01/2013
71895^91663+3864070Lelio R Paula05/2013
71905^91650+5264061Lelio R Paula05/2013
71912^212770+6964051Lelio R Paula08/2011
7192(3^134227+1)/464042Paul Bourdelais11/2007
7193(2*10^64041-17)/364041Robert Price08/2014
7194(15^54449+1)/1664036Paul Bourdelais03/2010
7195(29*10^64027+91)/364028Robert Price03/2016
7196(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
719716878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
71982^212663+5364018Lelio R Paula08/2011
7199(4*10^64014+197)/364015Robert Price03/2017
720010^63986+6363987Robert Price01/2011
720110^63986-3155763986Patrick De Geest05/2013
720231487!2-2^3148763982Robert Price09/2015
7203(21*2^212522-1)/141632363971Lelio R Paula01/2014
72045^91517+9863968Lelio R Paula04/2013
7205(19*10^63960-43)/363961Robert Price10/2017
7206(62*10^63954-17)/963955Robert Price09/2015
72085^91493-4^9149363951Predrag Minovic04/2004
7207V(364793)63951Serge Batalov03/2015
721019^50004+5863943Lelio R Paula05/2013
72095*6^82172-763943Lelio R Paula09/2014
7211(56*10^63942+223)/963943Robert Price07/2016
721219^50000-2463938Lelio R Paula05/2013
7213(23*2^212374-1)/2701963928Lelio R Paula01/2014
7214(9*2^212355-1)/76163924Lelio R Paula01/2014
72162^212344-18363922Lelio R Paula08/2011
7215(58695*2^212336-1)/37963922Lelio R Paula04/2015
721710^63916+7963917Robert Price01/2011
721810^63916-7682363916Patrick De Geest05/2013
72192^212295-2563908Lelio R Paula08/2011
72212^212285-238363905Yves Minet10/2013
7220267^26336+26336^26763905Norbert Schneider09/2014
7222(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
722319^49962+6063890Lelio R Paula05/2013
72243^133906-11305663890Enzo Doria07/2014
7225(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
72263*6^82092+563881Lelio R Paula09/2014
722715441^13706+13706^1544163879Hans Havermann02/2017
72282^212154-77635163865Paul Bourdelais03/2013
722935^41359+263862Lelio R Paula05/2013
7230(61*10^63857-43)/963858Robert Price09/2015
7231(2^212131-3)/48563856Lelio R Paula04/2012
72322^212112-45999563853Enzo Doria06/2015
723315^54290+5863850Lelio R Paula05/2013
72343*2^212097-763849Lelio R Paula04/2014
723555^36683-5463842Norbert Schneider08/2014
7236(509203*2^212056-1)/363841Lelio R Paula04/2015
7237(3^133805-7)/17263839Lelio R Paula04/2012
72382^212049+14963834Lelio R Paula08/2011
72395^91318-1863829Lelio R Paula04/2013
724018468^2857+2857^1846863824Hans Havermann03/2017
7241(2^212024-5)/111163823Lelio R Paula04/2012
72422^211961+1291563807Lelio R Paula02/2013
7244(3^133707-7)/578063791Lelio R Paula04/2012
7243(44*10^63790-161)/963791Robert Price11/2017
7245747^22198+22198^74763782Norbert Schneider07/2016
72462^211800-1716963759Enzo Doria05/2013
7247(85*10^63757-1)/363759Robert Price07/2017
7248(14*10^63747-11)/363748Erik Branger09/2014
724991*19^49848+663746Curtis Bright05/2015
725018855^2402+2402^1885563741Hans Havermann03/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 19 2018 09:17 (Time in France)

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