Decimal Expansions:

Decimal Expansions

We will use around 5MB of data to prove the MRB Constant is very normal.

For each expansion of said decimal places there = is a summery of how many times each digit is used.

5,00= 0

In September of 1999, Marvin Ray Burns computed the first 5,000 dig= its of the MRB Constant on a 350 MHz Pentium II with 64 Mb of ram.

.

0.187859642462067120248517934054273230055903094900138786= 17200468408947723

15646602137032966544331074969038423458562580190612313700= 94759226630438929

34889618412083733662608161360273812637937343528321255276= 39621714893217020

76282062171516715408412680448363541671998519768025275989= 38993914457983505

56135096485210712078444230958681294976885269495642042555= 86483670441042527

95247106066609263397483410311578167864166891546003422225= 88380025455396892

94711421221891050983287122773080200364452153905363950553= 32203470627551159

81282803951021926491467317629351619065981601866424582495= 06972033819929584

20935515162514399357600764593291281451709082424915883204= 16906640933443591

48067055646928067870070281150093806069381393859533606579= 87405562062348704

32936073781956460310476395066489306136064552806751519350= 82808373767192968

66398103094949637496277383049846324563479311575300289212= 52329181619562697

36970748657654760711780171957873683009659022606687536563= 05516567361288150

20143875613668655221067430537059103973575619148909369077= 79832035511933624

04637253494105428363699717024418551654837279358822008134= 48096105880203064

78196195969537562878348123349763858630101407272529230147= 23333362509185840

24803704048881967676760119858111679169352796852044160027= 08613722868894510

15102919988536905728659287086875425492533794395347589703= 56331344038263888

79866561959807335147399025657781331722610761279758527227= 42777308985774922

30597096257256271883675575297887925361687673940354321451= 36277254922931312

62764357321446216187786377154205423128223446295396532903= 32217147982028075

98422106556489004853685870708326887487737763504768916098= 31855362816671591

08412193420164386000258508426556435006954832830120546193= 20515593504002350

83512613359217408970073297842771289673651619602250771173= 88084262325697885

46537869046222708567487474709306935732666859085616282375= 38655124329756474

64914619179575869342996208149878536663170197264534260468= 37801075905514867

87190395783150604524441907570445113820585333984692194828= 79476486575931785

95816527492977822095977440911371434216929624593175324537= 34012995939950049

17912983680848547143925846704238528608320053664510586678= 15119645967607919

64317343076715344983004971288694016566004270621110790531= 64721504556329943

88400521115239016877311545696102836920503689610880603160= 36603828965332393

83524154510137534165673472607464891120088099838152046695= 41502637703557328

35929966306427173051589721163519991611359546703154087252= 87243998197872502

74679738863889705686743537785798105855619249218571694913= 56734627040774914

48799682065482817465880642236348160780950777057939313495= 82980660282527212

84916888092303252902700599177550596158359199931908693930= 39736611646514858

21997292533710676873868623504791587973796826984787808222= 34106187896746674

50680064404065553875213281494980700209858132220620109011= 26590344971741080

10632475647128346095492843700651474502182261204156439303= 08859826426256828

12609249113673396723593371453421690256014005016946998387= 59073429203617293

01531400405936246406781400779475613077369732409923529464= 79458077816460769

62408645956660841411263999885757394293152262838987984363= 50719371486573491

96202542844351041147284197381493380706622257319102148158= 57450428867284772

50434386718443149128948635448929492143259660847149600072= 53406621538756134

13252542741301581824766364321115068094774514063091609280= 29719327606796946

86092636208176344227297754632673716111030222001949845540= 72338596799729567

45318490433826332931888160330054013690316104309973777863= 93439313562149654

99699373142058190653346615738352222808713909343313252383= 60305287172314811

15102970585628129955899183038107196630813270167049861768= 31683295290537987

60030666570203435884960342104811488681216083611944605571= 91397329297068323

26450945715371702023251751982208521511884275346588918121= 72660333192804801

17475904613189844972072206824891915393325800262462721617= 64244687477896097

64906070479605351740205227992021112876539835381740117955= 26700337583139607

88477267092157001428248335741882127065588260757223843468= 36425460624376294

97255720844291090101469203229763400883134038164037291131= 13149598830486629

44964532193113574956453912385456662881566099860325447839= 86287801475697722

81911518615208276282401455651794253838186194793399401497= 59987240427388505

64411437560795202115791025539876536653932315849200653295= 70705591855222675

42845736812670699565824674762111599567798871089943129103= 40144254976593713

52169077892867695205556979383621955999138096214465028267= 84457775198333561

87449579988435319909055045642406109160942975136747726225= 13506116867915294

53643717739913922126483778806203872768088381032267284933= 08593907877273472

82725262001885607446549531438327158297381955786656871622= 81676008390755269

47433774805427170933889797531701890689551439394048455382= 98301981692536597

97476778546865045859640238175930139996122667668117389670= 50203329234908051

36900674702817092565211984795692028584777685609789206862= 14307401593342577

72629101667523494055741002072868985014792774291066431369= 41528199585609819

76523216255318623764260591320667123942398310748008900676= 97570607132333012

49195951646813480370178134651913158679=

6,00= 0

These digits were extracted form the following computation of 11,000 digits.

.

7,00= 0

First co= mputed on June 10-11, 2003 over a period, of 10 hours, on a 450mh P3 with an available 512mb RAM: The firs= t (to the right of the decimal point) 6,995 accurate digits of the value given by the series with an even upper sum:

digit

# of times used=

0

711

1

687

2

707

3

689

4

665

5

706

6

744

7

683

8

676

9

727

8,000

Using a Sony Vaio P4= 2.66 GHz laptop computer with 960 MB of available RAM, on 2:04 PM 3/25/2004,

Marvin Ray Burns computed 8000 digits of the MRB constant shown below.

He used the sumalt c= ommand in Pari-GP and thereby double checked the first= 6995 digits of a previous computation.

He computed 5000 digits in 1999 (all were found = to be correct), and 6000 digits in 2000 (5995 were found to be correct),

and 7000 digits in 2003 (6995 were fo= und to be correct).

The method which PARI presently uses is based on= an amalgamation of ideas of F. Villegas, D. Zagier= and H. Cohen.

digit

# of times used=

0

817

&nbs= p; 1

796

2

812

3

809

4

765

5

804

6

840

7

776

8

755

9

826

PARI/GP is free software, under the terms of the = GNU General Public License, published by the Free Software Foundation.

9,00= 0

These digits were extracted form the following computation of 11,000 digits.

.

10,0= 00

These digits were extracted form the following computation of 11,000 digits.

.

11,0= 00

On March 01, 2006 with a 3GH PD with 2GBRAM available, Marvin Ray Burns, using= the Convergence Acceleration of Alternating Series of Henri Cohen, Fernando Rodriguez Villegas, and Don Zagier, computed the first 11,000 digits of the MRB Constant. The first 10,000 digits were check= ed by running the same program for fewer digits with identical resources and memory. The Convergence Acceleration Series is a standard function of Pari.

12,0= 00

These digits were extracted form the following computation of 40,000 digits.

digit	# of times used=
0	711
1	687
2	707
3	689
4	665
5	706
6	744
7	683
8	676
9	727

digit	# of times used=
0	817
&nbs= p; 1	796
2	812
3	809
4	765
5	804
6	840
7	776
8	755
9	826