Et al,
This was gathered and cross checked with many sources including
the "Cunningham Project" and "The Book of Numbers." The next biggy is
to find a factor for F14! You'll be famous. Bob.
The complete factorization (that is all numbers below are prime) of the Mersenne
Number, M16384 = 2^2^14 -1, is (2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)
(2^16+1)(2^32+1)(2^64+1)(2^128+1) ... (2^8192+1). For n >1, factors of the Fermat
Numbers, see above Fn = 2^2^n +1, are of the form k*2^(n+2)+1, k and n are listed
below.
1
* 3 1/2, 0
* 5 1/2, 1
* 17 1, 2
* 257 8, 3
* 65537 1024, 4
* 641 5, 5
* 6700417 52347, 5
* 274177 1071, 6
* 67280421310721 262814145745, 6
* 59649589127497217 116503103764643, 7
* 5704689200685129054721 11141971095088142685, 7
* 1238926361552897 1209889023954, 7
* 93461639715357977769163558199606896584051237541638188580280321 k1, 8
* 2424833 1184, 9
* 7455602825647884208337395736200454918783366342657 k2, 9
*
741640062627530801524787141901937474059940781097519023905821316144415759504705008092818711693940737
3640431067210880961102244011816628378312190597, 9
* 45592577 11131, 10
* 6487031809 1583748, 10
* 4659775785220018543264560743076778192897
1137640582563481089664199400165229051, 10
*
130439874405488189727484768796509903946608530841611892186895295776832416251471863574140227977573104895898783928842923844831149032913798729088601617946094119449010595906710130531906171018354491609619193912488538116080712299672322806217820753127014424577
k3, 10
* 319489 39, 11
* 974849 119, 11
* 167988556341760475137 10253207784531279, 11
* 3560841906445833920513 434673084282938711, 11
*
173462447179147555430258970864309778377421844723664084649347019061363579192879108857591038330408837177983810868451546421940712978306134189864280826014542758708589243873685563973118948869399158545506611147420216132557017260564139394366945793220968665108959685482705388072645828554151936401912464931182546092879815733057795573358504982279280090942872567591518912118622751714319229788100979251036035496917279912663527358783236647193154777091427745377038294584918917590325110939381322486044298573971650711059244462177542540706913047034664643603491382441723306598834177
k4, 11
* 114689 7, 12
* 26017793 1588, 12
* 63766529 3892, 12
* 190274191361 11613415, 12
* 1256132134125569 76668221077, 12
*
22964766349327374158394934836882729742175302138572222575931764391308418951609613238265928038086431231577633045391531446045019455657263788959152095959500781101126096495656976145338084323609391242570049591461461009320782551308966824222425528731569111534949127744166427236012769418206949701929914631287953679124328078403443589001544785043209243005176672365124985675566011296182335806426461484656070802115048389659355236182068241950344201999449825647341556766313684295383743697537161298411893329950259437024572510849559797869011132011530806731079473144998988576165709735222707748481535236825623944595112533741234160090993221997405711848497115626313770615846340179366098118224044157942824481075801501388316794925034549722720218237177989415153573141944390933701532957472310726727304029461192020120667119324409064623758146438555005036265643143116137400042228823945740010105764278856096541459650682547836386210032027169896230115182649724551245475912070548418459211407403006769164719869749959222439806164715470175945861462895201453214517960762686355562039296307129357252744645128034273466002900209575716007479669129661683944031076099220826572016496603734398963042158832323677881589363722322001921
k5, 12
* 2710954639361 , 13
* 2663848877152141313 20323554055421, 13
* 3603109844542291969 k6, 13
* 319546020820551643220672513 609485665932753836099, 13
085598646391108374644303012131413429026919971035433354887348460526052637339779893596577990604338746439034989482359859049218824929660605100389117582120258754885519585052756213421228476386163579247803563282797040796563182422179053643781126922224573279622191423434519766560284182096695775395546669938172224483146065671751172183802129699735864452522949541852035854734337212733863157970031522224970363941209099492883375677993153879701370104382744193538256866738152347531687172837600368048294017541419726117718075789013050850345112624534555442408294353749793855633691943625289107274389682170660447227313276738663511996400570534245795710526003680482940175414197261177180757890130508503451126245345554424082943537497938556336919436252891072743896821706604472273132767386635119964005705342457957105203914402638889064382864987765343240332925550930017192143468703628304999985059646548483174531283778430609542492596982480577439271834619001055573127856149148864086871500376740364063751382639185497819747745182296552276746469170774785782604677338131683907661063093685741813111168096285019490413360405743657216638079314312116402208231577452892864068637225098923843745344623028789302932162492480208641935248356456665670403223570826634794415639916008502232879355149141446622157183268341260950665476845850593126292672285108878441780792980388482307573523134562093836301424627508716369085840033461866887115332318895350164453904905814652265080420821887685219123844711548769045865550497148053267518010393454599197212179695074532337789302978167311885477351034369276695555903508469835699226729783467220331817193877838037391325441214124437761325588307736204392003146324955282946037566720377428535873984161942480391232235552342417767374816991000869484836290575215308122955018045746181817711627310799156802391342105071232818542487058624364738664571689440091738762084841466580622837649665236973955435397857047079178180594902440772876565000572481849846211069652060751185774024009365138945603106474516407517745647362202417311788078570407327504354214205833093962744390398169280548154410644653348284377669010847519020174418760825327811005167556562948062313033701884413100193693299508399443471053029166862979957167301699984250269120539301715344338235087511897935382431598981843297334574405613888369527192904706877952795982116537855531866828436532661097125619376423033805285066214685326018568501334396163929771111985638342657
k7, 13.
begin:vcard
n:Wilson v;Robert G.
tel;cell:316-393-6353
tel;fax:316-262-7221
tel;home:316-788-8757
tel;work:316-264-6353
x-mozilla-html:FALSE
org:Kansas Paint & Color Co., Inc.
adr:;;132 N. Mosley;Wichita;KS;67202-2898;
version:2.1
email;internet:[EMAIL PROTECTED]
title:President
fn:Robert G. Wilson v
end:vcard
