PRP Records

Probable Primes Top 10000

(173006 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 ?
6501(19*10^65572+119)/365573Robert Price02/2017
650220^50399+5165571Lelio R Paula08/2013
650311^62946-567065552Enzo Doria01/2013
65042^217742-391165547Yves Minet08/2009
6505(19*10^65545+77)/365546Robert Price08/2016
65062^217731+13165544Lelio R Paula08/2011
65072^217720-11128765541Enzo Doria05/2014
650810^65537+2765538Robert Price01/2011
650910^65537-7685965537Patrick De Geest05/2013
6510(10223*2^217676+1)/365531Lelio R Paula06/2014
6511PadovanNumber[536485]65518Eric W. Weisstein05/2009
65127*10^65492-4765493Robert Price02/2017
65132^217547-186840765489Enzo Doria04/2016
65142^217531-11176965484Enzo Doria05/2014
65157^77484-1865482Lelio R Paula06/2013
65162^217488-11328565471Enzo Doria07/2014
6517151153#/30-3065468Henri Lifchitz12/2011
65182^217466+425765464Lelio R Paula10/2011
651946396!3-8165455Robert Price09/2014
65202^217421-11318565451Enzo Doria07/2014
6521(6883*2^217440-1)/106119329589365448Lelio R Paula04/2015
65222^217408-214565447Lelio R Paula10/2011
65232^217398-1694765444Enzo Doria05/2013
65248*5^93613+365434Lelio R Paula09/2014
652511^62828-531065429Enzo Doria01/2013
652610^65426+1365427Robert Price01/2011
65272^217341-655565427Lelio R Paula10/2011
652810^65426-5484965426Patrick De Geest05/2013
6529(21*2^217363-1)/5600362666765424Lelio R Paula01/2014
653030011^14608-10865405Enzo Doria07/2012
6531(43^40031-1)/4265388Robert Price04/2014
65322^217190+9439565381Henri Lifchitz02/2005
653315^55587+4665376Lelio R Paula08/2013
65342^217088-11183365350Enzo Doria05/2014
6535(13*2^217069-1)/168294565340Lelio R Paula01/2014
6536(62*10^65331+1)/965332Serge Batalov11/2010
65372^216947-11135165308Enzo Doria05/2014
6538-E(18022)/77520184568268532294394923506835965307Thomas Ritschel02/2017
6539(13*10^65297+83)/365298Robert Price09/2016
65405^93400-865284Lelio R Paula06/2013
65412^216802-16565264Lelio R Paula08/2011
65422^216799-2863565264Lelio R Paula10/2011
65435*10^65255+5165256Robert Price01/2017
65442^216762-16765252Lelio R Paula08/2011
654511^62657-579065251Enzo Doria01/2013
65463^136756-11288065250Enzo Doria06/2014
65472^216752+2165249Lelio R Paula08/2011
654811^62651-270065245Enzo Doria12/2012
6550Pell-LucasQ(170413)/265230Eric W. Weisstein12/2006
6549gcd(V(790525),5*F(158105)*(F(158105)+1)+1)65230Serge Batalov04/2015
6551(2^216676-1017)/63765224Lelio R Paula04/2012
65522^216652-232765219Yves Minet10/2013
6553(9179*2^216648-1)/466765218Lelio R Paula04/2015
6554(5*10^65203-119)/365204Robert Price04/2016
65552^216555-11326965190Enzo Doria07/2014
6556(9513^16384+1)/265181Henri Lifchitz02/2007
65572^216474+1291565166Lelio R Paula02/2013
655819^50958-3265163Lelio R Paula08/2013
65592^216442-11213365156Enzo Doria06/2014
65602^216437-11221365155Enzo Doria06/2014
65612^216435-11276765154Enzo Doria06/2014
65622^216420+1270565149Lelio R Paula02/2013
65638*3^136507-765132Lelio R Paula04/2014
6564(-lucasV(1,2,432719)-2)/(5*461)65128Mike Oakes03/2017
65652^216197-11176965082Enzo Doria05/2014
65666^83631-7965078Lelio R Paula07/2013
6567572^23601+23601^57265078Norbert Schneider08/2016
6568(3^136399-7)/54422065074Lelio R Paula04/2012
65692^216154-142165069Yves Minet01/2013
65702^216145-11266365067Enzo Doria06/2014
6571132013*10^65050+2^216091-165056Gilbert Mozzo01/2014
6572132019*10^65050+2^216091-165056Gilbert Mozzo01/2014
6573148918*10^65050+2^216091-165056Gilbert Mozzo02/2014
6574194014*10^65050+2^216091-165056Gilbert Mozzo02/2014
6575223864*10^65050+2^216091-165056Gilbert Mozzo04/2014
657882090*10^65050+2^216091-165055Gilbert Mozzo07/2012
657795133*10^65050+2^216091-165055Gilbert Mozzo12/2013
657698142*10^65050+2^216091-165055Gilbert Mozzo12/2013
6579((2^216091-1)*34009-48)/2565054Serge Batalov01/2012
65805977*10^65050+2^216091-165054Gilbert Mozzo03/2012
65817*2^216091+2^298-1365051Peter Lesala03/2007
65822^216091+2*29208-165050Makoto Morimoto10/2013
6583(10^(2*32521+1)-6*10^32521-1)/365043Robert Price02/2016
6584p(13861)#/2+25665039Robert Price05/2017
658511^62439-438065024Enzo Doria01/2013
65863^136244+265005Mike Oakes11/2009
658713^58343-5064991Lelio R Paula07/2013
6588331^25791-1000264989Enzo Doria07/2012
65892^215877+13164986Lelio R Paula08/2011
65904*5^92959+964977Lelio R Paula09/2014
65912^215789-1882564959Lelio R Paula09/2011
6592(2^215801-509203)/4132764958Lelio R Paula05/2012
6593U(315311)64954Serge Batalov03/2015
659446072!3-5904964951Robert Price12/2015
65952^215750-595564948Lelio R Paula09/2011
659613^58281+4664922Lelio R Paula07/2013
65972^215623+18364909Lelio R Paula08/2011
6598(3^136043-2^136043)/(19862279*33466579)64895Mike Oakes12/2016
65995*2^215554+364889Lelio R Paula04/2014
66002^215541-11207564885Enzo Doria06/2014
66012*10^64882-364883Dmitry Domanov11/2010
660210^64862+34233964863Patrick De Geest05/2013
660310^64862-4764862Robert Price05/2011
660419^50718-8464856Lelio R Paula08/2013
6605(3045*2^215471-1)/(17*1151*27067*173473)64853Jens K. Andersen09/2007
660710^64843+427869783964844Robert Price05/2015
660610^64843+2196764844Patrick De Geest03/2016
660810^64843-34007364843Patrick De Geest03/2016
660911^62254+7064831Lelio R Paula07/2013
66102^215351-11192564828Enzo Doria05/2014
66112^215310-11764815Lelio R Paula08/2011
6612124^30958-12364809Norbert Schneider02/2015
6613(7*10^64807+17)/364808Erik Branger03/2014
6614(7*10^(2*32400+1)-27*10^32400-7)/964801Robert Price11/2015
66152^215243-1594964795Enzo Doria04/2013
661623^47581-22^4758164793Robert Price08/2012
6617(62*10^64783-17)/964784Robert Price09/2015
66185*3^135747-464769Lelio R Paula04/2014
6619(59*10^64767-41)/964768Robert Price09/2015
6620(2^215140+3)/1964763Lelio R Paula04/2012
66212^215135-1716964763Enzo Doria05/2013
66222^215115-11127764757Enzo Doria05/2014
66239*5^92641+264755Lelio R Paula09/2014
6624(lucasV(1,2,430086)-2)/(7*1033)64731Mike Oakes03/2017
6625(5*10^64715-23)/964715Robert Price11/2014
66262^214938-178164703Yves Minet03/2013
662711^62111-42064682Enzo Doria08/2012
66285^92525+4264673Lelio R Paula06/2013
66292^214824+7189364669Enzo Doria04/2016
66302^214799-222164661Yves Minet08/2013
6631(21*2^214688+1)/29364627Lelio R Paula08/2012
663292^32907+32907^9264623Serge Batalov05/2014
66336^83013+10164597Lelio R Paula07/2013
6634p(13775)#/2+864594Robert Price01/2017
6635(7*10^64568-43)/964568Robert Price10/2014
6636Pell-LucasQ(168677)/264566Eric W. Weisstein11/2006
6637(24737*2^214476+1)/287764565Lelio R Paula06/2014
6638(47*2^214463+1)/764561Lelio R Paula04/2015
66392^214458+5461564559Lelio R Paula10/2011
6640(3^135322+7)/12291140864557Lelio R Paula04/2012
66412^214389-68311364538Paul Bourdelais03/2013
66422^214369-11124164532Enzo Doria05/2014
6643(19^50461+3^50461)/2264526Robert Price07/2013
664411^61954-366064519Enzo Doria12/2012
6645(23*2^214319-1)/2164517Lelio R Paula01/2014
6646(58695*2^214310-1)/57164516Lelio R Paula04/2015
664735^41779-3464510Norbert Schneider04/2014
664811^61939-522064503Enzo Doria01/2013
6649(2^214271+78557)/3564501Lelio R Paula05/2012
6650126^30706-12564494Norbert Schneider02/2015
6651gcd(V(1157265),5*F(231453)*(F(231453)-1)+1)64492Serge Batalov04/2015
66522^214215+1290964486Lelio R Paula10/2011
66535^92225+6664463Lelio R Paula06/2013
66542^214126-24055164459Paul Bourdelais03/2013
66558*6^82827+564453Lelio R Paula09/2014
6656(31*2^214120-1)/217048564452Lelio R Paula01/2014
6657(31*2^214088-1)/595564445Lelio R Paula01/2014
665814^56227+8964444Lelio R Paula08/2013
66612^214055-15964437Lelio R Paula08/2011
665910^64436+266764437Patrick De Geest05/2013
666065^35543-64^3554364437Robert Price08/2013
666210^64436-5364436Robert Price05/2011
6663Phi(128878,10)/3950329792764428Maksym Voznyy11/2015
66643^135027+10064425Lelio R Paula05/2013
6665(3^134972-7)/264398Lelio R Paula04/2012
66666*10^64387+764388Dmitry Domanov11/2010
66672^213864-1837764380Enzo Doria05/2013
6668(2^213821+9)/20964365Lelio R Paula04/2012
66692^213788+13564357Lelio R Paula08/2011
6670(3^134883+2)/4831364351Lelio R Paula04/2012
6671(49^38069-46^38069)/364344Serge Batalov12/2016
6672(11^61781+2^61781)/1364338Robert Price02/2013
66736^82670+3764330Lelio R Paula07/2013
6674(3^134839+4)/3231295964328Lelio R Paula04/2012
6675(22*10^64326+161)/364327Robert Price02/2017
667611^61767-405064324Enzo Doria12/2012
66772^213645-11485364314Enzo Doria05/2015
667813^57733+1864312Lelio R Paula07/2013
66792^213621+7270764307Enzo Doria04/2016
668010^64305+13679164306Patrick De Geest05/2011
668110^64305-964305Alexander Gramolin01/2011
6682V(307652)64295Serge Batalov03/2015
6683(2^213546-5)/222164281Lelio R Paula04/2012
66842^213438-5869564252Lelio R Paula10/2011
66852^213367-10564230Lelio R Paula08/2011
6686595^23148+23148^59564225Norbert Schneider07/2016
66873^134601+868064221Lelio R Paula05/2013
6688500^23793+23793^50064217Norbert Schneider08/2016
66892^213314-45564214Yves Minet02/2012
669039^40359-3864214Norbert Schneider05/2014
66912^213292-1608564208Enzo Doria04/2013
66922^213274-7764202Lelio R Paula08/2011
669319^50203+7864198Lelio R Paula08/2013
66942^213240-11286564192Enzo Doria06/2014
66952^213190-11239164177Enzo Doria06/2014
6696(9913*2^213184-1)/965764175Lelio R Paula04/2015
669714^55991+2764173Lelio R Paula07/2013
66982^213158-11258164167Enzo Doria06/2014
66992^213148+9164164Lelio R Paula08/2011
67016^82439+12564151Lelio R Paula07/2013
67007*2^213102+964151Lelio R Paula04/2014
6702L(306854)+F(306855)64129Henri Lifchitz01/2007
6703610^23017+23017^61064110Norbert Schneider07/2016
67042^212950-6487564105Lelio R Paula10/2011
6705(266*10^64102-17)/364104Robert Price06/2016
6706p(13679)#/2+6464097Robert Price03/2017
670719^50119+9464090Lelio R Paula08/2013
67082^212880-14764084Lelio R Paula08/2011
670911^61523-459064070Enzo Doria01/2013
67105^91663+3864070Lelio R Paula05/2013
67115^91650+5264061Lelio R Paula05/2013
67122^212770+6964051Lelio R Paula08/2011
6713(3^134227+1)/464042Paul Bourdelais11/2007
6714(2*10^64041-17)/364041Robert Price08/2014
6715(15^54449+1)/1664036Paul Bourdelais03/2010
6716(29*10^64027+91)/364028Robert Price03/2016
6717(lucasV(1,2,425405)+2)/(17*89)64027Mike Oakes03/2017
671816878!+16878#-164022D. Gazzoni Filho & Lucas Teixeira05/2005
67192^212663+5364018Lelio R Paula08/2011
6720(4*10^64014+197)/364015Robert Price03/2017
672110^63986+6363987Robert Price01/2011
672210^63986-3155763986Patrick De Geest05/2013
672331487!2-2^3148763982Robert Price09/2015
6724(21*2^212522-1)/141632363971Lelio R Paula01/2014
67255^91517+9863968Lelio R Paula04/2013
6726(62*10^63954-17)/963955Robert Price09/2015
67285^91493-4^9149363951Predrag Minovic04/2004
6727V(364793)63951Serge Batalov03/2015
673019^50004+5863943Lelio R Paula05/2013
67295*6^82172-763943Lelio R Paula09/2014
6731(56*10^63942+223)/963943Robert Price07/2016
673219^50000-2463938Lelio R Paula05/2013
6733(23*2^212374-1)/2701963928Lelio R Paula01/2014
6734(9*2^212355-1)/76163924Lelio R Paula01/2014
67362^212344-18363922Lelio R Paula08/2011
6735(58695*2^212336-1)/37963922Lelio R Paula04/2015
673710^63916+7963917Robert Price01/2011
673810^63916-7682363916Patrick De Geest05/2013
67392^212295-2563908Lelio R Paula08/2011
67402^212285-238363905Yves Minet10/2013
6741267^26336+26336^26763905Norbert Schneider09/2014
6742(-lucasV(1,2,424552)-2)/160163899Mike Oakes03/2017
674419^49962+6063890Lelio R Paula05/2013
67433^133906-11305663890Enzo Doria07/2014
6745(lucasV(1,2,424451)+2)/363886Mike Oakes03/2017
67463*6^82092+563881Lelio R Paula09/2014
674715441^13706+13706^1544163879Hans Havermann02/2017
67482^212154-77635163865Paul Bourdelais03/2013
674935^41359+263862Lelio R Paula05/2013
6750(61*10^63857-43)/963858Robert Price09/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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