PRP Records

Probable Primes Top 10000

(252675 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 ?
77512^216752+2165249Lelio R Paula08/2011
77523*10^65247+1165248Robert Price11/2017
775311^62651-270065245Enzo Doria12/2012
775415130^15609-15609^1513065244Norbert Schneider07/2018
7755Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
7756gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
7757(2^216676-1017)/63765224Lelio R Paula04/2012
77582^216652-232765219Yves Minet10/2013
7759(9179*2^216648-1)/466765218Lelio R Paula04/2015
7760(5*10^65203-119)/365204Robert Price04/2016
77612^216555-11326965190Enzo Doria07/2014
7762(9513^16384+1)/265181Henri Lifchitz02/2007
77632^216474+1291565166Lelio R Paula02/2013
776419^50958-3265163Lelio R Paula08/2013
77652^216442-11213365156Enzo Doria06/2014
77662^216437-11221365155Enzo Doria06/2014
77672^216435-11276765154Enzo Doria06/2014
77682^216420+1270565149Lelio R Paula02/2013
77698*3^136507-765132Lelio R Paula04/2014
7770(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
777115132^15575-15575^1513265102Norbert Schneider07/2018
77725*10^65086-5165087Robert Price10/2017
77732^216197-11176965082Enzo Doria05/2014
77746^83631-7965078Lelio R Paula07/2013
7775572^23601+23601^57265078Norbert Schneider08/2016
7776(3^136399-7)/54422065074Lelio R Paula04/2012
77772^216154-142165069Yves Minet01/2013
77782^216145-11266365067Enzo Doria06/2014
7779(7*10^65064+53)/365065Robert Price10/2017
7780132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
7781132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
7782148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
7783194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
7784223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
778682090*10^65050+2^216091-165055Gilbert Mozzo07/2012
778795133*10^65050+2^216091-165055Gilbert Mozzo12/2013
778598142*10^65050+2^216091-165055Gilbert Mozzo12/2013
7788((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
77895977*10^65050+2^216091-165054Gilbert Mozzo03/2012
77907*2^216091+2^298-1365051Peter Lesala03/2007
77912^216091+2*29208-165050Makoto Morimoto10/2013
7792(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
7793p(13861)#/2+25665039Robert Price05/2017
7794(2^216091-2096)/(2^4*3*2918437*5220283)65036Makoto Morimoto10/2017
779511^62439-438065024Enzo Doria01/2013
77963^136244+265005Mike Oakes11/2009
779713^58343-5064991Lelio R Paula07/2013
7798331^25791-1000264989Enzo Doria07/2012
77992^215877+13164986Lelio R Paula08/2011
78004*5^92959+964977Lelio R Paula09/2014
78012^215789-1882564959Lelio R Paula09/2011
7802(2^215801-509203)/4132764958Lelio R Paula05/2012
7803U(315311)64954Serge Batalov03/2015
780446072!3-5904964951Robert Price12/2015
78052^215750-595564948Lelio R Paula09/2011
780613^58281+4664922Lelio R Paula07/2013
78072^215623+18364909Lelio R Paula08/2011
7808(46*10^64904+521)/964905Robert Price08/2017
7809(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
78105*2^215554+364889Lelio R Paula04/2014
78112^215541-11207564885Enzo Doria06/2014
78122*10^64882-364883Dmitry Domanov11/2010
781310^64862+34233964863Patrick De Geest05/2013
781410^64862-4764862Robert Price05/2011
781519^50718-8464856Lelio R Paula08/2013
7816(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
781786413!6-1264846Robert Price08/2018
781810^64843+427869783964844Robert Price05/2015
781910^64843+2196764844Patrick De Geest03/2016
782010^64843-34007364843Patrick De Geest03/2016
782111^62254+7064831Lelio R Paula07/2013
78222^215351-11192564828Enzo Doria05/2014
78232^215310-11764815Lelio R Paula08/2011
7824124^30958-12364809Norbert Schneider02/2015
7825(7*10^64807+17)/364808Erik Branger03/2014
7826(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
78272^215243-1594964795Enzo Doria04/2013
782823^47581-22^4758164793Robert Price08/2012
7829(62*10^64783-17)/964784Robert Price09/2015
78305*3^135747-464769Lelio R Paula04/2014
7831(59*10^64767-41)/964768Robert Price09/2015
7833(2^215140+3)/1964763Lelio R Paula04/2012
78322^215135-1716964763Enzo Doria05/2013
78342^215115-11127764757Enzo Doria05/2014
78359*5^92641+264755Lelio R Paula09/2014
7836(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
78375791^17200+17200^579164720Norbert Schneider12/2018
7838(5*10^64715-23)/964715Robert Price11/2014
78392^214938-178164703Yves Minet03/2013
784011^62111-42064682Enzo Doria08/2012
78415^92525+4264673Lelio R Paula06/2013
78422^214824+7189364669Enzo Doria04/2016
78432^214799-222164661Yves Minet08/2013
78445939^17128+17128^593964637Norbert Schneider10/2018
7845(21*2^214688+1)/29364627Lelio R Paula08/2012
784692^32907+32907^9264623Serge Batalov05/2014
7847(89*10^64608-539)/964609Robert Price11/2017
78486^83013+10164597Lelio R Paula07/2013
7849p(13775)#/2+864594Robert Price01/2017
7850(7*10^64568-43)/964568Robert Price10/2014
7851Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
7852(24737*2^214476+1)/287764565Lelio R Paula06/2014
7853(47*2^214463+1)/764561Lelio R Paula04/2015
78542^214458+5461564559Lelio R Paula10/2011
7855(3^135322+7)/12291140864557Lelio R Paula04/2012
78562^214389-68311364538Paul Bourdelais03/2013
7857(76*10^64534+113)/964535Robert Price11/2017
78582^214369-11124164532Enzo Doria05/2014
7859(19^50461+3^50461)/2264526Robert Price07/2013
786011^61954-366064519Enzo Doria12/2012
7861(23*2^214319-1)/2164517Lelio R Paula01/2014
7862(58695*2^214310-1)/57164516Lelio R Paula04/2015
78632^214300-454764511Yves Minet03/2019
786435^41779-3464510Norbert Schneider04/2014
7865(159^29303+1)/16064506Eric Chen12/2017
7866(89*10^64504-179)/964505Robert Price11/2017
786711^61939-522064503Enzo Doria01/2013
7868(2^214271+78557)/3564501Lelio R Paula05/2012
7869L(308604)+P(308604)64495Robert Price12/2017
7870126^30706-12564494Norbert Schneider02/2015
7871gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
78722^214215+1290964486Lelio R Paula10/2011
78735^92225+6664463Lelio R Paula06/2013
78742^214126-24055164459Paul Bourdelais03/2013
78758*6^82827+564453Lelio R Paula09/2014
7876(31*2^214120-1)/217048564452Lelio R Paula01/2014
7877(31*2^214088-1)/595564445Lelio R Paula01/2014
787814^56227+8964444Lelio R Paula08/2013
78812^214055-15964437Lelio R Paula08/2011
787910^64436+266764437Patrick De Geest05/2013
788065^35543-64^3554364437Robert Price08/2013
788210^64436-5364436Robert Price05/2011
7883(3^135043-lucasV(1,3,135043)+1)/364432Paul Vanderveen11/2017
7884Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
78853^135027+10064425Lelio R Paula05/2013
7886(3^134972-7)/264398Lelio R Paula04/2012
78876*10^64387+764388Dmitry Domanov11/2010
78882^213864-1837764380Enzo Doria05/2013
7889(2^213821+9)/20964365Lelio R Paula04/2012
78902^213788+13564357Lelio R Paula08/2011
7891(3^134883+2)/4831364351Lelio R Paula04/2012
7892(49^38069-46^38069)/364344Serge Batalov12/2016
7893(11^61781+2^61781)/1364338Robert Price02/2013
78946^82670+3764330Lelio R Paula07/2013
7895(3^134839+4)/3231295964328Lelio R Paula04/2012
7896(22*10^64326+161)/364327Robert Price02/2017
789711^61767-405064324Enzo Doria12/2012
78982^213645-11485364314Enzo Doria05/2015
789913^57733+1864312Lelio R Paula07/2013
79002^213621+7270764307Enzo Doria04/2016
790110^64305+13679164306Patrick De Geest05/2011
790210^64305-964305Alexander Gramolin01/2011
7903V(307652)64295Serge Batalov03/2015
79044*10^64286-8964287Robert Price08/2017
7905(2^213546-5)/222164281Lelio R Paula04/2012
79062^213438-5869564252Lelio R Paula10/2011
79072^213367-10564230Lelio R Paula08/2011
7908595^23148+23148^59564225Norbert Schneider07/2016
79093^134601+868064221Lelio R Paula05/2013
7910(26*10^64220+61)/364221Robert Price06/2017
7911500^23793+23793^50064217Norbert Schneider08/2016
7912179^28504-264216Lelio R Paula10/2017
79132^213314-45564214Yves Minet02/2012
791439^40359-3864214Norbert Schneider05/2014
79152^213292-1608564208Enzo Doria04/2013
7916(72524!5+1)/2564203Joe McLean10/2018
79172^213274-7764202Lelio R Paula08/2011
791819^50203+7864198Lelio R Paula08/2013
7919(44*10^64192-233)/964193Robert Price10/2017
79202^213240-11286564192Enzo Doria06/2014
79212^213190-11239164177Enzo Doria06/2014
7922(9913*2^213184-1)/965764175Lelio R Paula04/2015
792314^55991+2764173Lelio R Paula07/2013
79242^213158-11258164167Enzo Doria06/2014
79252^213148+9164164Lelio R Paula08/2011
7926(96^32369+1)/9764163Paul Bourdelais08/2017
79286^82439+12564151Lelio R Paula07/2013
79277*2^213102+964151Lelio R Paula04/2014
7929L(306854)+F(306855)64129Henri Lifchitz01/2007
7930610^23017+23017^61064110Norbert Schneider07/2016
79312^212950-6487564105Lelio R Paula10/2011
7932(266*10^64102-17)/364104Robert Price06/2016
7933p(13679)#/2+6464097Robert Price03/2017
793419^50119+9464090Lelio R Paula08/2013
79352^212880-14764084Lelio R Paula08/2011
793611^61523-459064070Enzo Doria01/2013
79375^91663+3864070Lelio R Paula05/2013
79385^91650+5264061Lelio R Paula05/2013
79392^212770+6964051Lelio R Paula08/2011
7940(3^134227+1)/464042Paul Bourdelais11/2007
7941(2*10^64041-17)/364041Robert Price08/2014
7942(15^54449+1)/1664036Paul Bourdelais03/2010
7943(29*10^64027+91)/364028Robert Price03/2016
7944(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
794516878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
79462^212663+5364018Lelio R Paula08/2011
7947(4*10^64014+197)/364015Robert Price03/2017
794885402!6-364014Robert Price08/2018
7949(140^29819+1)/14163994Richard Fischer05/2018
795010^63986+6363987Robert Price01/2011
795110^63986-3155763986Patrick De Geest05/2013
795231487!2-2^3148763982Robert Price09/2015
7953(21*2^212522-1)/141632363971Lelio R Paula01/2014
79545^91517+9863968Lelio R Paula04/2013
7955(19*10^63960-43)/363961Robert Price10/2017
7956(62*10^63954-17)/963955Robert Price09/2015
79585^91493-4^9149363951Predrag Minovic04/2004
7957V(364793)63951Serge Batalov03/2015
795919^50004+5863943Lelio R Paula05/2013
79615*6^82172-763943Lelio R Paula09/2014
7960(56*10^63942+223)/963943Robert Price07/2016
796219^50000-2463938Lelio R Paula05/2013
7963(23*2^212374-1)/2701963928Lelio R Paula01/2014
7964(9*2^212355-1)/76163924Lelio R Paula01/2014
79662^212344-18363922Lelio R Paula08/2011
7965(58695*2^212336-1)/37963922Lelio R Paula04/2015
796710^63916+7963917Robert Price01/2011
796810^63916-7682363916Patrick De Geest05/2013
79692^212295-2563908Lelio R Paula08/2011
79702^212285-238363905Yves Minet10/2013
7971267^26336+26336^26763905Norbert Schneider09/2014
7972(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
797319^49962+6063890Lelio R Paula05/2013
79743^133906-11305663890Enzo Doria07/2014
7975(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
79763*6^82092+563881Lelio R Paula09/2014
797715441^13706+13706^1544163879Hans Havermann02/2017
79782^212154-77635163865Paul Bourdelais03/2013
797935^41359+263862Lelio R Paula05/2013
7980(61*10^63857-43)/963858Robert Price09/2015
7981(2^212131-3)/48563856Lelio R Paula04/2012
79822^212112-45999563853Enzo Doria06/2015
798315^54290+5863850Lelio R Paula05/2013
79843*2^212097-763849Lelio R Paula04/2014
798555^36683-5463842Norbert Schneider08/2014
7986(509203*2^212056-1)/363841Lelio R Paula04/2015
7987(3^133805-7)/17263839Lelio R Paula04/2012
79882^212049+14963834Lelio R Paula08/2011
79895^91318-1863829Lelio R Paula04/2013
799018468^2857+2857^1846863824Hans Havermann03/2017
7991(2^212024-5)/111163823Lelio R Paula04/2012
79922^211961+1291563807Lelio R Paula02/2013
7993(3^133707-7)/578063791Lelio R Paula04/2012
7994(44*10^63790-161)/963791Robert Price11/2017
7995747^22198+22198^74763782Norbert Schneider07/2016
79972^211800-1716963759Enzo Doria05/2013
7996(85*10^63757-1)/363759Robert Price07/2017
799885089!6-863757Robert Price08/2018
7999(14*10^63747-11)/363748Erik Branger09/2014
800091*19^49848+663746Curtis Bright05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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