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Compare the December 4 traffic statistic in these two websites:

The first one is http://stats-classic.grok.se/en/201412/MRB%20constant and the second one is the following. http://stats-classic.grok.se/en/201412/Pi

**MarvinRayBurns**- Replies: 1

Follow the frames and links at http://marvinrayburns.com/new_on_mrb.html to find out all that is known about this new constant a/k/a the M/R/B!

If you find out more and post it here I will link to it as well!

**MarvinRayBurns**- Replies: 1

I would like to announce a new unofficial record computation of the MRB constant that was finished on Sun 21 Sep 2014 18:35:06. I wonder if you can do better. It took 1 month 27 days 2 hours 45 minutes 15 seconds. I computed 3,014,991 digits of the MRB constant, (confirming my previous 2,00,000 or more digit computation was actually accurate to 2,009,993 digits), with Mathematica 10.0. I Used my version of Richard Crandall's code:

____________________________________________________________________________

(*Fastest (at MRB's end) as of 25 Jul 2014.*)

DateString[]

prec = 3000000;(*Number of required decimals.*)ClearSystemCache[];

T0 = SessionTime[];

expM[pre_] :=

Module[{a, d, s, k, bb, c, n, end, iprec, xvals, x, pc, cores = 12,

tsize = 2^7, chunksize, start = 1, ll, ctab,

pr = Floor[1.005 pre]}, chunksize = cores*tsize;

n = Floor[1.32 pr];

end = Ceiling[n/chunksize];

Print["Iterations required: ", n];

Print["end ", end];

Print[end*chunksize]; d = ChebyshevT[n, 3];

{b, c, s} = {SetPrecision[-1, 1.1*n], -d, 0};

iprec = Ceiling[pr/27];

Do[xvals = Flatten[ParallelTable[Table[ll = start + j*tsize + l;

x = N[E^(Log[ll]/(ll)), iprec];

pc = iprec;

While[pc < pr, pc = Min[3 pc, pr];

x = SetPrecision[x, pc];

y = x^ll - ll;

x = x (1 - 2 y/((ll + 1) y + 2 ll ll));];(*N[Exp[Log[ll]/ll],

pr]*)x, {l, 0, tsize - 1}], {j, 0, cores - 1},

Method -> "EvaluationsPerKernel" -> 4]];

ctab = ParallelTable[Table[c = b - c;

ll = start + l - 2;

b *= 2 (ll + n) (ll - n)/((ll + 1) (2 ll + 1));

c, {l, chunksize}], Method -> "EvaluationsPerKernel" -> 2];

s += ctab.(xvals - 1);

start += chunksize;

Print["done iter ", k*chunksize, " ", SessionTime[] - T0];, {k, 0,

end - 1}];

N[-s/d, pr]];

t2 = Timing[MRBtest2 = expM[prec];]; DateString[]

Print[MRBtest2]

MRBtest2 - MRBtest2M

_________________________________________________________________________.

I used a six core Intel(R) Core(TM) i7-3930K CPU @ 3.20 GHz 3.20 GHz with 64 GB of RAM of which only 16 GB was used.

t2 From the computation was {1.961004112059*10^6, Null}.

**MarvinRayBurns**- Replies: 0

For all real a, the partial sums s(n)= sum((-1)^k (k^(1/k) -a), k=1..n) are bounded so that their limit points form an interval [-1.+ the MRB constant +a, MRB constant] of length 1-a, where the MRB constant is limit(sum((-1)^k*(k^(1/k)), k = 1 ..2*N),N=infinity).

For all complex z, the upper limit point of sn= sum((-1)^k (k^(1/k) -z), k=1..n) is the the MRB constant.

**MarvinRayBurns**- Replies: 0

The convergents constants are discussed at https://oeis.org/wiki/Convergents_constant . Study the linked pages to see the pattern of the convergents constants that is emerging from the study.

**MarvinRayBurns**- Replies: 1

According to Mathworld a mathematical constant is any well-defined real number which is significantly interesting in some way.

Here is an article about set of new constants. https://oeis.org/wiki/Convergents_constant

**MarvinRayBurns**- Replies: 0

Here is a Demo that compares the first several digits of the MRB constant (MRB) to Pi as far as normality is concerned.

This is an attempt to compute the rationality of MRB. However, even if it computed quadrillions of digits it still would be insufficient for the task. So enjoy playing with it!

http://demonstrations.wolfram.com/HowNormalIsTheMRBConstant/

**MarvinRayBurns**- Replies: 1

The official definition of the MRB constant is found in Mathworld at http://mathworld.wolfram.com/MRBConstant.html.

For a couple of years now, you could read more about it in Wikipedia at

http://en.wikipedia.org/wiki/MRB_constant, and you still can.

However, in the Wikipedia article someone asked for a reference for the irrationality of the MRB constant. At first I thought, I could write an expert or two and they could give me a quick proof of its irrationality; however, when I wrote one of the leading experts on constants about the issue, he told me that it could take a lifetime for someone to prove, and even then the proof might not be right. Thus I figured Ive no time to waste. I started to write down some ideas that might help prove it on mapleprimes at http://www.mapleprimes.com/posts/101425-Could-The-MRB-Constant-Be-Rational.

You might not be too familiar with writing proofs, but a proof is simply an explanation of why some statement is true using only statements that are known to be absolutely true. If on the other hand you think you might be able to help me with it, please do so.

I could use all the help I can get so please consider passing this along, and I thank you in advance.

Marvin Ray Burns

**MarvinRayBurns**- Replies: 0

For example here is a very scenic route to the MRB constant: http://bit.ly/he5apv

**MarvinRayBurns**- Replies: 0

I thought you could learn from my latest tweet:

New constant found! See the whole mistake ridden process at click here .

It does use one assumption, however.

**MarvinRayBurns**- Replies: 1

It is likely that almost all mathematics has only been around at most 10,000 years.

At 25 years per generation that comes to only 400 generations of mathematicians, and that's assuming there existed mathematicians in every generation. So humanity has only had at most 400 chances to discover all there is to know about math. So the probability is approximately 1/400 that you potentially could discover something nobody else has. Compared to the lottery those are great odds!

I suggest that you spend a few minutes every day playing with math. Even if you dont discover anything really new, you will be smarter because of it.

To see what happened as I was playing with math, look up MRB constant in almost any search engine.

Marvin Ray Burns

I'm the original investigator of the MRB constant.

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