Dear Simon,

I send you Euler's constant to 1000000 digits. The algorithm used is
the one presented in the paper of McMillan and Brent [1] (the second
variant) accelerated by binary splitting [2], [3]. This calculation 
verified the previous 500000-digits record to 499927 digits. Using 
the 500000-digit value of gamma and a program by H.J.J. te Riele, 
CWI Amsterdam [4], I was also able to compute 470006 partial quotients
of the continued fraction of gamma. Computing the 470006-th convergent
results in the following [5]

Theorem: If Euler's constant is a rational number P/Q, for integers P, Q
	 then |Q| > 10^242080


* Acknowledgements *
The latest calculation would have been possible without the help and
motivation from H.J.J. te Riele, Richard Brent and my colleague Bruno
Haible.

Best
	Thomas Papanikolaou


References:

[1] R. P. Brent and E. M. McMillan, Some new algorithms for
    high-precision computation of Euler's constant, Math. 
    Comp. 34 (1980) 305-312.

[2] Bruno Haible, Thomas Papanikolaou, Fast multiprecision 
    evaluation of series of rational numbers, Technical 
    Report No. TI-7/97, 18.03.1997. Available via
    http://www.informatik.th-darmstadt.de/TI/Veroeffentlichung/TR/Welcome.html

[3] Jonathan M. Borwein and Peter B. Borwein, Pi and the AGM, Wiley, 1987.

[4] Richard P. Brent, Alfred J. van der Poorten and Herman J.J. te Riele,
    A comparative study of algorithms for computing continued fractions
    of algebraic numbers, pp. 37-49 in: H. Cohen (editor), Algorithmic
    Number Theory: Second International Symposium, ANTS-II, Talence,
    France, 18-23.05.1996, Springer, Berlin etc., 1996.

[5] Thomas Papanikolaou, Entwurf und Entwicklung einer objektorientierten
    Bibliothek f\"ur algorithmische Zahlentheorie, PhD Thesis, to appear.

[6] Steve Finch, http://pauillac.inria.fr/algo/bsolve/euler/euler.html

-------------------------------------------------------------------------------

Euler's constant to 1000000 digits computed on Mars 24, 1997 on a 
Sun Sparc Ultra machine with 167 Mhz and 256 MB RAM in 42 hours 27 hsec.

The algorithm was implemented using the LiDIA library for computational
number theory and it will be part of the multiprecision floating-point
arithmetic of the package in release 1.4. LiDIA is available from 

   ftp.informatik.th-darmstadt.de:/pub/TI/systems/LiDIA
   http://www.informatik.th-darmstadt.de/TI/LiDIA

LiDIA's kernel used Bruno Haible's CLN package, which is available
via anonymous FTP from 

	ma2s2.mathematik.uni-karlsruhe.de:/pub/gnu/cln.tar.z

This package contains the first implementation of a binary splitting device
for rational series.

------------------------------------------------------------------------------

Here is the output of the program:

Calculating Euler's constant to 1000000 decimals

Time required: 42 hour 27 hsec 

Euler = 
0.5772156649015328606065120900824024310421593359399235988057672348848677267776\
646709369470632917467495146314472498070824809605040144865428362241739976449235\
362535003337429373377376739427925952582470949160087352039481656708532331517766\
115286211995015079847937450857057400299213547861466940296043254215190587755352\
673313992540129674205137541395491116851028079842348775872050384310939973613725\
530608893312676001724795378367592713515772261027349291394079843010341777177808\
815495706610750101619166334015227893586796549725203621287922655595366962817638\
879272680132431010476505963703947394957638906572967929601009015125195950922243\
501409349871228247949747195646976318506676129063811051824197444867836380861749\
455169892792301877391072945781554316005002182844096053772434203285478367015177\
394398700302370339518328690001558193988042707411542227819716523011073565833967\
348717650491941812300040654693142999297779569303100503086303418569803231083691\
640025892970890985486825777364288253954925873629596133298574739302373438847070\
370284412920166417850248733379080562754998434590761643167103146710722370021810\
745044418664759134803669025532458625442225345181387912434573501361297782278288\
148945909863846006293169471887149587525492366493520473243641097268276160877595\
088095126208404544477992299157248292516251278427659657083214610298214617951957\
959095922704208989627971255363217948873764210660607065982561990102880756125199\
137511678217643619057058440783573501580056077457934213144988500786415171615194\
565706170432450750081687052307890937046143066848179164968425491504967243121837\
838753564894950868454102340601622508515583867234944187880440940770106883795111\
307872023426395226920971608856908382511378712836820491178925944784861991185293\
910293099059255266917274468920443869711147174571574573203935209122316085086827\
558890109451681181016874975470969366671210206304827165895049327314860874940207\
006742590918248759621373842311442653135029230317517225722162832488381124589574\
386239870375766285513033143929995401853134141586212788648076110030152119657800\
681177737635016818389733896639868957932991456388644310370608078174489957958324\
579418962026049841043922507860460362527726022919682995860988339013787171422691\
788381952984456079160519727973604759102510995779133515791772251502549293246325\
028747677948421584050759929040185576459901862692677643726605711768133655908815\
548107470000623363725288949554636971433012007913085552639595497823023144039149\
740494746825947320846185246058776694882879530104063491722921858008706770690427\
926743284446968514971825678095841654491851457533196406331199373821573450874988\
325560888873528019019155089688554682592454445277281730573010806061770113637731\
824629246600812771621018677446849595142817901451119489342288344825307531187018\
609761224623176749775564124619838564014841235871772495542248201615176579940806\
296834242890572594739269638633838743805471319676429268372490760875073785283702\
304686503490512034227217436689792848629729088926789777032624623912261888765300\
577862743606094443603928097708133836934235508583941126709218734414512187803276\
150509478055466300586845563152454605315113252818891079231491311032344302450933\
450003076558648742229717700331784539150566940159988492916091140029486902088485\
381697009551566347055445221764035862939828658131238701325358800625686626926997\
767737730683226900916085104515002261071802554659284938949277595897540761559933\
782648241979506418681437881718508854080367996314239540091964388750078900000627\
997942809886372992591977765040409922037940427616817837156686530669398309165243\
227059553041766736640116792959012930537449718308004275848635083808042466735093\
559832324116969214860649892763624432958854873789701489713343538448002890466650\
902845376896223983048814062730540879591189670574938544324786914808533770264067\
758081275458731117636478787430739206642011251352727499617545053085582356683068\
322917676677041035231535032510124656386156706449847132695969330167866138333333\
441657900605867497103646895174569597181553764078377650184278345991842015995431\
449047725552306147670165993416390660912054005322158902091340802782251533852899\
511665452245869185993671220132150144801424230986254604488672569343148870491593\
044640189164502022405495386291847586293077889350643771596606909604681243702305\
465703160679992587166675247219409777980186362625633582526279422393254860132693\
530701388937436923842878938512764740856548650281563067740442203064403756826309\
102917514572234441050369317711452170888907446416048688701083862311426128441425\
960956370400619200579335034155242624026206465693543061258526583452192121497771\
878069586608516334922104836737994592594340379560002192785418379417760203365594\
673078879838084816314678241492354649148876683368407492893865281863048589820354\
818624383848175997635849075180791480634943916284705482200754945348986133827235\
730922190030740096800337666844932505567654937530318112516410552492384077645149\
842395762012781552322944928854557853820248918942441857095919558208100071578384\
039627479985817880888865716830699436060735990421068511427913169699596792300828\
988156097538338059109360341252998656790389568795673455083362907823862638563490\
747319275278740166557531190111543470018186256971261120126852923129937161403906\
965112224816615082353643982396620532633322248505191593682690715004315589871802\
783353845448309107249498057880961717996337167036554180041464667538719586948483\
331543583330641935929487420951478832347748481418149776871694413640056645156936\
116524161555734141935424721373067468333849054426626038372788217552709930958141\
026136979500786465876771608630804460749802801576962675913897794772214337515470\
829345879123898433055067223474969984942486706721502569273529585065869588997486\
535562186958043997125168976654169862653862891977542187721939605817001104236414\
158780810386172101557551923711160049880682291618097732421958328974869227183979\
190467716542668138893379296036815457939611339621922245430151580631743708405608\
536416031384982969518566952612822123716939368130321296561939718710207098007948\
833910197535104307441823448833331796978277332091143324514305086573457500687391\
475470777577559918467118308583660159437193718449039061770232536567977596744475\
747511584195746700997345002454428406585024508585646392791246119879093693072019\
804029303603738838430742162821201635386466226097198958436799430572030149638050\
832232365825557724534237187737439818333306454662906993311125973721950274646899\
065457155440303917835419756434315739034883866750542742161831050060550464223545\
708427393549359051762717479299472398908632970101905610107742690926475235740304\
630159243442464900834188630859320685522507790910195858895314328799817570981916\
829315940453005632543314488517357302698256937253469964013440871580108145287865\
790408663637945071108505104241797691911292615132010316363498086606948624407800\
668400671696221463718114777268341846646364242734053003138077349611998146861768\
585463120816316479893796426373835661893831371098328956490521148813402974238886\
863154313297876579912545424333856347200268129048994955042698088213026726358153\
248067538790323057421040330149788786752377860705468861472100992632942510887801\
970284117922402591091466584809257857192786282147667074087863519714256292427867\
028407703241437569931883243331559002433304769111009247979118006286202213707800\
621725732904735994398883139279927969397063567628116694054128859081982023838277\
035483496879734048888293016736770941584654400954862465146101353913496855912040\
236361872150992980651905861682815302875042754525860533196343259577747881343723\
939499124380614375449859068607518563142725525564259396701498041425981823785257\
682943639596562438852065654807103884546394453770191784571874101186223227802525\
194362657438242256093567692582387749116073775945140144703190224153559112506138\
178297421264982641618724606313340891926702359795802365841631755679233566210123\
133584549459059006998420067226025116774384736482438571540714626594564239112717\
078030637141692638644010057131095896063264963755295676936468941051795200061645\
202188435340473018243930514881984593076296404445687762416528716207276731860632\
540801428874571198657307471701886603687970364770854852871670003622928528837468\
246605881411754047446061676354303739923756596593696708792316774468569310838210\
783048315919643002144125970228906320317410114936648095290301171633453191792293\
924242877283787234956992923213609223494722645824375509451533552011761289751733\
951371782933287158609438662701179184155458726489825139255594379519731786744876\
992532617942338129994127939860264424519600605436818664670986594436593015437629\
148697959769499653352721002002096791043948254724411334224487005463765684086676\
215337362746159120547008629057169825735370523976123123841256434941178949861582\
859702097109703919635216812258224756271951938272828520914718237534365525402074\
620306673047695247009441381456178282666319613967359367257264603388494642489472\
448978481596715306153846712236987128231978476931105716623637326207595971180401\
514389623170601958570982381392466613527913695637655904861676205129740998314965\
597860253410129454399867288300624408440186181511750687088764671609799292017769\
624963301575829259618849485872002292248060628812177873383145882551293953651088\
191865120044923154983947731473578688973142047310945381464822632102331079439597\
462852354129575191063558792300195618131294612030157576340159785681751749842377\
882447375398247457599686770740854557432942402678193848220354096210606072192499\
082510485400318496319986322156908909761405310716511312932685349852440286448293\
470591608586995981988903959955918110764134466588145254256588153545028884739975\
324327809021522569521844145298650835512983980226238264974881811581525034599749\