TheMRBconstantlayscenteredinaverysmallneighboroodofcwhereFloor2
2
12
c
-Pi+199=
3
12
.

2and
2
12
areFibonaccinumbers,​​
3
12
+1isaCarmichaelnumber(pseudoprime)andtheHardy-Ramanujannumber(thesmallestnumberexpressibleasthesumoftwocubesintwodistinctways)and199isthe11thLucasnumber,definedinthis
link
.
Let m = the MRB constant.
In[]:=
m=NSum[
n
(-1)
(
Log[n]/n
E
-1),{n,1,Infinity}]
Out[]=
0.18786
In[]:=
Floor
2
2
12
m+
1
710^3
-Pi+199
3
12
Out[]=
1727
1728
In[]:=
Floor
2
2
12
m
-Pi+199
3
12
Out[]=
1
In[]:=
Floor
2
2
12
m-
1
810^3
-Pi+199
3
12
Out[]=
1729
1728