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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 summary 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.

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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.

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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 wi= th 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 command in Pari-GP and thereby double checked the first 6995 digits of a previous computation.<= /span>

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 found 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.

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10,0= 00

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

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11,0= 00

 

 

3D"TextOn 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 checked by running the same program = for fewer digits with identical resources and memory. The Convergence Accelerat= ion Series is a standard function of Pari.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12,0= 00

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

 

 

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13,0= 00

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

 

 

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14,0= 00

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

 

 

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15,000

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

 

 

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16,000

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

 

 

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17,000

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

 

 

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18,000

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

 

 

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19,000

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

 

 

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20,0= 00

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

 

 

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21,0= 00

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

 

 

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22,0= 00

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

 

 

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23,0= 00

 

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

 

 

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24,0= 00

 

These digits were extracted form the following computation of 40,00= 0 digits.

 

 

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25,0= 00

 

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

 

 

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26,0= 00

 

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

 

 

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27,0= 00

 

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

 

 

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28,0= 00

 

These digits were extracted form the following computation of 40,00= 0 digits.

 

 

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29,0= 00

 

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

 

 

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30,000<= /p>

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

 

 

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31,000<= /p>

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

 

 

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32,000<= /p>

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

 

 

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33,000<= /p>

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

 

 

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34,000<= /p>

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

 

 

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35,000<= /p>

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

 

 

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36,000<= /p>

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

 

 

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37,000<= /p>

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

 

 

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38,000<= /p>

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

 

 

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39,000<= /p>

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

 

 

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40,0= 00

On Nov 24, 2006 Marvin Ray Burns computed 40, 000 digits of the MRB Constant in 33hours and 26min via his own program in written in Mathematica 5.2.

The computation was run on a 32-bit Windows 3GH PD desktop computer using 3.25 GB of Ram.=

 

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41000

&= nbsp;

&= nbsp;

42000

&= nbsp;

&= nbsp;

43000

&= nbsp;

 

0

4060

&= nbsp;

0

4175

&= nbsp;

0

4297

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

1

4054

&= nbsp;

1

4154

&= nbsp;

1

4241

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

2

4152

&= nbsp;

2

4253

&= nbsp;

2

4349

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

3

4197

&= nbsp;

3

4304

&= nbsp;

3

4393

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

4

4080

&= nbsp;

4

4177

&= nbsp;

4

4300

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

5

3979

&= nbsp;

5

4084

&= nbsp;

5

4176

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

6

4264

&= nbsp;

6

4371

&= nbsp;

6

4473

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

7

3977

&= nbsp;

7

4074

&= nbsp;

7

4167

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

8

4101

&= nbsp;

8

4195

&= nbsp;

8

4296

 

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

 

9

4136

&= nbsp;

9

4213

&= nbsp;

9

4308

 

44000

&= nbsp;

&= nbsp;

45000

&= nbsp;

&= nbsp;

46000

&= nbsp;

&= nbsp;

47000

&= nbsp;

0

4408

&= nbsp;

0

4506

&= nbsp;

0

4598

&= nbsp;

0

4685

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

1

4347

&= nbsp;

1

4437

&= nbsp;

1

4542

&= nbsp;

1

4660

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

2

4454

&= nbsp;

2

4533

&= nbsp;

2

4641

&= nbsp;

2

4737

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

3

4502

&= nbsp;

3

4606

&= nbsp;

3

4723

&= nbsp;

3

4824

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

4

4394

&= nbsp;

4

4507

&= nbsp;

4

4602

&= nbsp;

4

4716

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

5

4267

&= nbsp;

5

4367

&= nbsp;

5

4469

&= nbsp;

5

4554

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

6

4567

&= nbsp;

6

4678

&= nbsp;

6

4770

&= nbsp;

6

4864

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

7

4255

&= nbsp;

7

4371

&= nbsp;

7

4476

&= nbsp;

7

4564

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

8

4391

&= nbsp;

8

4494

&= nbsp;

8

4585

&= nbsp;

8

4692

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

9

4415

&= nbsp;

9

4501

&= nbsp;

9

4594

&= nbsp;

9

4704

 

 

48000

&= nbsp;

&= nbsp;

49000

&= nbsp;

&= nbsp;

50000

&= nbsp;

&= nbsp;

0

4788

&= nbsp;

0

4887

&= nbsp;

0

4979

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

1

4770

&= nbsp;

1

4882

&= nbsp;

1

4971

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

2

4838

&= nbsp;

2

4935

&= nbsp;

2

5041

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

&= nbsp;

3