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In[]:=
Prime[6]
Out[]=
13
where CMRB is the MRB constant,pi is the i’th prime and ch is the .
where CMRB is the MRB constant,
p
i
In[]:=
tm=Nest[Flatten[#/.{0{1,1,1},1{1,1,0}}]&,{0},10];
In[]:=
ch=FromDigits[RealDigits[FromDigits[{tm,0},2]],10];
Let p be the partial sums of the alternating Harmonic series over primes to the 10^13th prime:
In[]:=
p=TableNSum,{i,1,},Method"AlternatingSigns",WorkingPrecision30,{n,2,13};
(-1)^(i+1)
Prime[Floor[i]]
n
10
Let CMRB be the MRB constant:
∞
∑
i=1
i
(-1)
1/i
i
In[]:=
CMRB=NSum[(-1)^i-1,{i,1,Infinity},Method"AlternatingSigns",WorkingPrecision30]
1/(i)
(i)
Out[]=
0.18785964246206712024857897184
In[]:=
q=+1;
p
2
p
2
∏
i=
p
1
p
⌊i⌋
In[]:=
b=p--CMRB
p
1
p
9
q(-+(-)ch)
p
1
p
9
p
1
Out[]=
{0.07209673976214940650175485837,0.07295277329599462284881235013,0.07301110018003829179202736209,0.07301548830561549825187221943,0.07301584073079151856660077498,0.07301587023167460087096914492,0.07301587277303004072035826393,0.07301587299643149339488140551,0.07301587301637626461625166922,0.07301587301817851017013049613,0.07301587301834295310015652105,0.07301587301835807760869217212}
In[]:=
TableForm{Range[12],Abs[N[qb-,3]]},TableHeadings"x=I'th prime","absq b-",None
p
9
x
10
∑
i=1
i+1
(-1)
p
i
Out[]//TableForm=
x=I'th prime | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
absq b- x 10 ∑ i=1 i+1 (-1) p i | 0.290 | 0.0199 | 0.00150 | 0.000121 | 0.0000102 | 8.77× -7 10 | 7.65× -8 10 | 6.12× -9 10 | 1.59× -10 10 | 7.26× -10 10 | 7.78× -10 10 | 7.83× -10 10 |