Graham's number (G) has
incomprehensibly many digits — but here are a few, together with the programs that computed them (for more digits, see the
Digit Files page).
The rightmost 10000 decimal digits of G:
30787260770303013096318605654995911667283941445218229402116849257446908303160862621307856182261004203129683467872420025335707165042882886038152789058317773474348899936322170937718870530216134008262310
41652609872469522381180520893701095105746695201447806881045566940953003050207963025108931458177782068496837757322945657846959175109945261571525815313383171441763572462779809715173494067855792793530636
17993752257361282030147386448940609082851119681223488381282653641293523575850556652227329985138670898557584476483711157794540071886314865346118541307684649540838335805841695412280766038020711553526827
09169587947510642507689032778267088483908774355316881338319887795056836256732704277862126880697058810276174028639378952134276596828174174610570754797760763975177038244691206302431091517315155467202072
03298057792145699917956905186596024469027274217279141430415867319657287140268008652315291316261820652195021921091461070451907392628396743433966206832681974497464193534150297618059752197469899167905539
51240749624022306775365113200227817050284227367149749179403280269907016100331717885504320865504618467657949795833488872938096176598272350673735136562412993356159242040336658602637646351364450901965169
91246803170103581306804887123251985358299162063826317014778326983245855032877628678387917200299014235470730860078246092342827582249084362130009203937656462657958086964494023780323916935845145868457435
00193087499932962375893178562196090339426243848085176276584372829470728254599948415970659821958864982353541909598033354078979538256357245359747368737720544909862394110578904843360397740815782128903796
68480534310161245447459165410165069396137727188277544585197396781572979626659473894609716957192215172421922975967039257161673139142478027719425613338419090703013839394290231456328385881249761372795027
74086096179244679618602537635821549733632038111668582649827068573480799088545586912369918198783236959935529511307212476357875208417641738390711011041222586727519228928871964307453282154261444871750080
95242123636376813961077749523532016833501424281091368978529043131788135333355110889022359477210715849496037260619984908856098462387682166967457951388588832356929998573679542011111185463440443504567679
40135676545759595889951230461872343603521793889196205026750886423489731195416265541685656346013519486952120940375141531409940727194827737444125469505369707041139086485872085962555419590302380606291371
69138722855477794398025076773239670591720768747467284465406341813803412943043609766021554233671120573908174234611757441182401340023387742371044080109403016487062327491837814787657637545981015382140877
14922326451525832690110799166775443442353837481547403100880637946597552737840758546298403351731162182383124376404468239965615920828447876334410730503146643034564958892386400206720157774336643971046097
19133977867119270761093597612697011186400883242141115735185425231753018437333602444678510859228109479432808176387274946992467944754462151350536784408285208823099795808022789783229887461982654201673541
30588210081847428327743235541621704680913967417772759547636593847461261352062528649361557993308786588372750302316984606262438168631582376854626680669440523593449818162301893013093540067002484335872199
00315863936527371581966011826743819385582719223648840620249884709395919441012031404522773151579351525369364934250530932709877378035492327740781679794020867401382441063153368792024085513096521839198783
97015952619452474978317634509661383542153408077799274104362305492058999661918974793950028080320685052798877144984365085442674905448699279843309239159997374495902995758836342736416156302674815385258930
35423500289214281922999379905539258403463179740764550809001835012576720025421347754368577841258214793482088528352847344639514454977400691547570014736262935639641159974506376325912076020850653315181912
97627524916528283327470445487220431209794181800837524288180786740953625707023916128625574340099420494628683883364612475194501407401023508584105029555399601882357799580811904419558955154139962907362641
41603259910867440214760673730270685900986998924196611409247724077899767515859936140618503569865441962523820349275896762389912155578594439247420428277018540432967913180650401616546821719644550936450059
55830907520156175779698614709767889387402006002982882878883308913088633722819728625451800838400216724842196639874673295077669833180844718217934117100532029967392340428998085682754345780727803362250745
54635303452502047026773318085940276837031308524437227254648631365299090852540852736811700598925661498015963926725007451760685374013593406210074607565408138965932473526208240166197001865513821872977219
49846316900749082737809426405608283927163655284883960382628829235989512069925942439297507498218164378334632464545517637327576552767605905826939724969245329980923380190551831802463416887618541048817756
22385553123402295796914412248364064668499259167559643046710022968172443392247921821359958689693414923690776243056770164822502041983470306716296896922618604046908954485889134827527466731552085587141664
35817616783248930807373477715001480131315872093173217027881014846523723198056977435033203823397583204572679056665163384206828154569492848663342244546199583745072045676450877888344038541732328611318923
25939242549724454004862230630447361306160309037871580058448079357952113695870525057666157284577793496116067281346768791824682195181011428216661867855439709616100093982954938824332804674688069413764541
93126560405791786371171779430458423102159623358976480405481182262288120744851408069513819124533985930930717606840321018628505400797648371363380891593720550471092872187099316006161890897978303030444170
74536501316198946986109934586683395543640840200233990670516429669348600027570319308957395061221345848777985085039705997484485916440720079353674931755601598637467305207478401560537634591003869599679216
66402485065151972178292734011493177498161942761055395341214573854386960142347615106412081678671156662702698141239492735346736586313627913641108525012050290229578455537100879820969021067093119691264011
68909948606316616230292390219529967552655598639206833081471169607143527916635260184575109114133911015135583100516372741567444562185804038832463487667167911210596640361544098108142733814394129952702989
28267705768198331834845115763234457634615885581807239488377317241718209142178274565054302349046931657016237345668584450386474453301178678720075637289970867637583657220506249130161043345591395584106522
59292055946693255710876213098711853232105196699704725638064513028255040447297723752850180331481056404968157353906178527859876031314086506853008091920000307935054937370834879297228686705737558209959799
60622710931298072888031118784826564331478394544516814980376358094827361921558071520353582645561888999676781093466973024354169692516472170626235239690360885242408899737975229765686512212364606700882735
55025280516268871774300224243017815309613987922755709702214430577903293355670516509347032488336712112602154912437814560556321802522593943710111389180996687955300606304861015768885793044484950849027511
01060298036194759637808660848638621223245386327233421961598510360706583695251304412583544807924551217328349121977645145493850412041271265386461162817130451299228861247316892869470860791609381057953424
55950474886617927058056116386911212141737555332931772421804354502689741745136461914925818460887323607368390107527538124040273298462966021077132177859353179083167201454781721677678183700692543963587784
77381821832282338662955759766576352603746962388273497026171846050804164396744639482222660472628009221300684690371447933831170282623828411960337825891780755617449686306276313945559616369461957875659406
85549606266452110502003446360786391521766128412732467550628726761482430797989282442753120277748186887250109520756590181937968438911972868200142926836525620315535316031054689168530193382247473816979430
51709072031656197695350611132139158562561824661400448048835400453257011706951826263434793588413474586938545913191359560294603491237571956426228537158608125516450896261346009079848578477972053071451865
14675412317888384738009343344165376733605639874152683883713570219486507495966616743619293364588499805610069710479310067941520844536138309110216300174376549196848839204372584196015037847845160671512017
19880115754708488393959305365055607887215999475022144221483482681447872707310013655373835777460985058660126400761294233523262553133073942052007839547749762554111899859772880815945865752809988634672233
47698047801463027893536123293125869638665593299492149114891347632146654314303272656947761889503867538372033508034358690038674211367316517236211325624799750677029423570505691130506597435265525655365427
68895266360391135992668989734244822601493574507744556050638326609473542254360350867485534248461062730568553479479128201952057764356476946631666382295000482800518276153635138000943232486790210617024259
44029209484941954536741806451930810516335749687163811882250411450158703701940568064800502257685338055303051833680912718114908175394843002680841043795561481048315835447210850384076723823375354333111031
69789016999659070368756476957141995172946840582682710812079388857606780890576605973512820406609187307108483992113117957918089160673029776868734932638038255189701221105348188614158487485192009852610652
52039482322073711493410839168737854403798603368448472052729248390757866617805529414157119366603081892881936678774148231780172812693498573578327095075857659197494703919315296759666923404880302362447049
10353178090822611674695077464191287728244330583239509252549935509252616857245956574131793441675014850242595069506473839565747913651935179833453536252143003540126026771622672160419810652263169355188780
38814483140652526168785095552646051071172000997092912495443788874960628829117250630013036229349160802545946149457887142783235082924210209182589675356043086993801689249889268099510169055919951195027887
17830837018340236474548882222161573228010132974509273445945043433009010969280253527518332898844615089404248265018193851562535796399618993967905496638003222348723967018485186439059104575627262464195387
The above 10000-digit base-10 numeral converted to a 32218-bit base-2 numeral (the rightmost 10000 of these bits are rightmost bits in the base-2 numeral for G):
10111111100001010011100100110011111011011101111001110000000110001011101110111100010100010010001010110101010110010001100010011000100111001100000010001011110001000000011110100001000110111110110101001011
11100000011000111010100111000101101101100011111010111101011100100100001110000100000000100000101110001110110011100111100011100011000100010111011101101101011111110111110010001100001010111101010111100001
01001110001010111001100100010101111110001100010000111111010100001011110101011110001001100000101010101101000111110100101100011010001100100101101111000000100011011011011011111110001000100010010111110001
11101001111101101000101100100110011001001111101111110110000000100000010110010100100010110001010110001110011110110001100000111010100111101011111111110100110100011000011110101110011110110010011010111110
11001100000010100010101000011101001101001100000100011010100101010001010011010111101110101100010111100110001110010010110101011111101011100101010001111111111010111111010111000010100001100101100110101100
01110100010001011100001111011100010000111000110100010110111110011000111111101011000011100100001111100011101110101000001010001010000011110111110110101000011011101001101101101011101011001111110010001111
01101000011101100101000101000100111111001001110111110000010100111100101001011001111100101101011101000111010001001111001000111011000110111011011110111101010000000111010011011101110010100000111110011111
10111001100100111110101010101101110100011100101000010101101100111001011101100110101000001111000110001001111100010100010011010000011010111111011001000000000110101011110101010101101101100100011110100100
10111110100000000011110101100010001000010011001000011100111000110010011011001100001010001100111111100001010011110000100110001110110011111110100111101110011110111101000011001101010111110000010010010110
10101001101110111110011011010111110011011000100100110110001011100010111000010001101000000000011110110001111000101100001101111111101111101110001101110100111110010100101001101010101001010110111000110001
00000110100010010100010110011010000000001111001100101100000100000100000111010100000010110100000101100111111011011101000001011011100011100100010011001111110000011101001101011001110000100111110001010110
01110001001001110111111011010010011011101001100011101001110011110100101110011000010010010001011011101001111101011100101101100010100100010100110011010001110101111010101110101010101101011010001010110100
01000011000001001110001100011110111010000000000010000011101111010011001100010111010111000001011111000101111100010111010101011001011001110000011011000110100001111110101100000110110010101100000110011010
00110010011010011011010100010101010100100000010001011100100011100101010100110010000110001001110000000101010011111111001011011100000101111100010010101100000101010010110110100010101011010101100101110100
11111011100000000110110101110110010110110000111110110000001000010011010010010110110110100101110101111001011001001110001100110011110011100000110011100100011011000101011011101000101011100000101011110101
11011101100110110001000011110111110111011011111000110011011000001100001101010100111001010010100101001010101010010110110110101011001000100011111010011110101101110010111001011000000010100001001110011111
01110111101110011110110001100110000110110010101110010010000110010011100000000000001101101001011100011001000101010001110111000001001000100001010100110001010111111111010110110001001111011111111001110000
00101010100010101110100011110001011111100011011111100011100111000000111101001011011011100011111000110000101010001000110100110000100001111001110001101000011100011000011110001001001000100110011001100100
00010010100010111000011110011101001000000110100001011100010111001010001100001000110110001110100101000110111010011101000000001011101001101010111000111011111001010111001000101000100010000111101111111001
10100011100110000100001001011001011101011100000010001111000011010011110010010101110001011110001011101000010011010101010001000010100101101011000010111001111100001010101110100000001001111100111010101010
00110001100100010101110100001000000011110100111110010010000100010001010001101010101011011011010001111010100001001110100100001100110000101110110110111111100101110011101010011111011011001011101001010111
01000111110001001001001100100010100001000010100100011000000000000101100101000100100111000010010111010111010000110101000010011011001011011110110001011010001010010010011100110010011010100101010000111010
11111010000010111100101000100111011101111101001110100000001001110010001110011110101100101110101111001100100011010100101001011010011011101000110001111001111001000000000011111111001111111101111100010100
00010101000000000010101010111101101101011000100101101000011001011000000110000010011000110110001001010100100001010001110111100000001100111010001011111111110011000000111110010010111000110001011011010011
10010000110001011110011110111001000100100010111100100011101000111111100011011110001100110101010100000001100100010100111101001110100001001010100101110010000110001111100001100010001011001100111110011100
11000000111101011011111001110100110101011011100111101110100011111010100001111000111000001001000000101011110110100001111111000011110100010001011011101010010101100000100011111101100000101011001011101001
00000101111011000000100100111011011111010001110100011110111110101000110010101100000111000011000001001011001110011010011010110010101010110111011100011101110001100001100000100011000111111101110101111010
01000001111110001010000001001110110001000101111000110011001001101011000010101010110001011110100100100011101000110110111100010000010100010111011111111100100111010001101100110110100110010010111111100001
01010000111000001101011101010011110101111110101001110110111011110001100111110011110001100110001010111111111100101011110100010110011110110110010000101001001000001100010100111000100010101011101111111101
01010001010000100110111111001010011010100111110001100110100100101010010101101011111110111011110000010010110111010001011011010111110111101000110000011010011001111101101000101110010011011000000100100011
10110000010101101010100010101010110011001101010011000111100110011100110101100001000111011111101000100000011100001100001000111111111110100110101101000001110111000111000111100000111110100010001111101000
00001011001110100100001010100111000101111111001000101011000110011010011100100001010110011110001011111101100000000101001000001100100010110001001101111101010011010101110001010001110100100011011000100001
11111000101011100111001100110001001110011100101001110010111111001001101101011011101110100110000100001101010010010000000011100100010001101010001001100011110111010100011101110110000110010011100010101110
11010100110000011101111010100111100101101011101001101000001000011001101101101001100100100000010100101000101110010010110110011100110000100111100101010100110001101010011001001001000111011110011101010000
01010001100100111011111111010100011001110000010100010001110110000101110101110111110110111001010011011000100111111111000101001000001100010111011011000001000101000010111010000100000001011111110001111001
00100001000111101011000001110111000010010001010001111010100101100111100101111000001001111111101100100010000001111111010011111111001100001001000010011001110011000100001000000100000111111101110110100011
10010011101110001110110100011000101000110011011010110100110101100011101100101001010000101011011011010100011011011101001101111011001000011011010010011111101010010000000111010001011001010100111011100010
10100011010110000110111010101101000101111101011100001010110001011100010001110111001100001100100010001001001101001010111011100010010010000010111101010011011100100001100001110110000000100000101010110110
10001001111000101100000011110110101000011011101110000111010111101010001010000011001100001000010110001000010101100100010110001101000001110001101111001001010101001010010100000000011100001100100010111101
01011010000011101111110111101011000000110000000111011111000110001110101010100001110111100011111010111111111101011000101100100010100000010001010111101010101101010001000110010011101100000010010010101111
11010101110001001101111110101111100000000011010100111110101100001100101110111111010111001000000110101100101000001110111111000110110110101000100111000001001111100000011101001010000010001011011110000101
11010011110011000011110011100001101110010011001001101000100001111011111000111100100101010100001110000010101111010101001100000110111101101110001101010111110111111100111001111010101011001100111001001111
00111110110001101001110101010001110110011000100101101010100011100001110001010011101000001101111110100001000000000000111001010111010001100101010101011110000000101101000100010101001010001100101100101111
11100010001111100100110110010001100100000110111010100111100001000011001001011100000001111110111110010100011011000011101000111111111011010110010000101000111010111101001001000000100100001111001011110001
11001101001111101100100010110011001000101011111001000010110001001100001000000010000001111000110001110100010101101010111110010000001011110010000111010001110001111000111001000101111110100011011010011100
10010011111011101001000001010101001111011011001101110110011001010111011100110100100110011011111000011011110010111100010000111101101010001110010101000000010100100101010000101110100010111001011010010110
10111011010110110011011111000011100010111111101011101000101011011000101111010001010111000000001001101111101101011010010110011000010001110111000000100010110111111110111010010010101000001000000000111100
00100110110001110001100010111010010101000010111010000100100111100100001100011001101011010000110010001111100110101110011110011101111010100011100001101001000101000001110011110100101000010010011111001101
10101001110011110000011100110110011111100101001110101110000100100100101110001000001111001101111000111001001011001001111100011110101010111111111000010001000010011000110010100000100011101111001100111001
01011110111101111111110001101110001100101111000100000110010001100100001011001000111010101110111000000110011111100000100000000110011110011110100111111110100100111010101110001001101101111000010000111011
10111100001110100010000100001010110110010111101110011101000001100110000010001011010010111101111101101100100110001001110000001000111010000110110010011101100110010011101010110001100110100101100010100000
10101101111100101001110101111111101011000010101111000101110100000010100011011001000100100011101101111011010100010001010011011011011001001110111010010001011001010011001111010001011001000101000100000110
00000001010111110101110101010111011110000100111110000000100100100011010000001010010100011101101000100111010110000100011110010000111010111001011001111111100111000011000011100111101101101101000011000011
00100110001110001101100001001001111000010101111110001000010100110101111010111111001010010000100110000100001100011101100101101010111101010001001101000000000011111010111001110100001101111110010100110111
10010100001000010100111111010101001001101111111111101001101010000001100001010010011001000101101010110110000011111110110000101111110010010001110100011011001111010110001001010100010010100101100111101101
10010100100001011011100010101010001010100101010010000010001010001111101101011100001111010100001100111101010000101111000010110010000111110111110000000000001101000011111111100011101011010101110010000000
10100101011011100100111000010001001110110000111111100101100000110011001101101110111010101010111101000001100101000001111110101111010111111000111000101011010001011111001100010011001001000101101000100011
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010111101100111011
ANSI C program for the d rightmost decimal digits of any exponential tower of 3s whose height is greater than d (such as Graham's number G):
#include "stdio.h"
#include "gmp.h"
void
tower_digits (mpz_t x, unsigned long d)
{
unsigned long n;
mpz_t base, mod;
mpz_init_set_ui (base, 3L);
mpz_init_set_ui (mod, 1L);
for (n = 0; n < d; n++)
{
mpz_mul_ui (mod, mod, 10L);
mpz_powm (x, base, x, mod);
}
mpz_clear (base);
mpz_clear (mod);
}
int
main ()
{
mpz_t x;
mpz_init_set_ui (x, 3L);
/*compute 10000 digits*/
tower_digits (x, 10000L);
gmp_printf ("%Zd\n", x);
mpz_clear (x);
return 0;
}
For 10000 digits, this program (compiled by MinGW32-GCC and run as a Win7 background task) required about 30 hours with a 2.6 GHz Pentium E5300 CPU.
An equivalent Python program (not run to completion -- too slow):
def tower_digits(d):
m = 1
x = 3
for n in range(d):
m = 10*m
x = pow(3, x, m)
#compute 10000 digits
print tower_digits(10000)
With t equal to the output of the above C program, the Python command
print bin(t)
converts t, as a 10000-digit base-10 numeral, to a 32218-bit base-2 numeral.:
NB: The rightmost 10000 of these bits are rightmost bits in the base-2 representation of G.