# Tagged Questions

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### Checking the Harald Helfgott proof of the little Goldbach conjecture without a public release of numerical checks?

A few month ago, a proof of the little/ternary Goldbach conjecture has been claimed by Harald Helfgott with three articles: Major arcs for Goldbach's theorem Minor arcs for Goldbach's theorem ...
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### How calculate $\pi$ to an accuracy of 10 decimal places?

Let $a=3.00000000001234...$ (irrational number) If $\overline{a}=3.00000000001$ (approximation $11$ places) then $|a-\overline{a}|<10^{-11}$ Note that the reciprocal is not satisfied: If ...
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### Prime numbers and limit(?)

Can someone help me to prove the following: $$\lim_{x\to\infty}(\sum_{p\leq x}\frac{1}{p}-\log(\log(x)) -C)=0$$ Where $C$ is a proper constant. Thank you...
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### gcd finding method

An integer $d$ is a $\gcd$ of two non-zero integers $a$ and $b$, if $d$ divides $a$ & $d$ divides $b$ '$c$ divides $a$ & $c$ divides $b$' implies '$c$ divides $d$' for any integer $c$. If ...
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### How to normalize these numbers for better visualization?

My dataset is like this: a1 4565380 a2 676477 a3 359939 ... b1 222431 b2 12222 ... g1 139 ... h1 134 i1 10 j1 11 and goes on.. The problem is when I ...
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### Proof that ${\left(\pi^\pi\right)}^{\pi^\pi}$ (and now $\pi^{\left(\pi^{\pi^\pi}\right)}$) is a noninteger

Conor McBride asks for a fast proof that $$x = {\left(\pi^\pi\right)}^{\pi^\pi}$$ is not an integer. It would be sufficient to calculate a very rough approximation, to a precision of less than 1, and ...
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### Efficient way for computation of derivatives of $f(x) = \zeta(1-x) + 1/x$ at integer x?

For some exercises with (divergent) summation of the Stieltjes constants I'm trying a formula, which involves derivatives of the $\zeta()$ -function at negative integers; perhaps better formulated as ...
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### Efficiently calculating the logarithmic integral with complex argument

My number theory library of choice doesn't implement the logarithmic integral for complex values. I thought that I might take a crack at coding it, but I thought I'd ask here first for algorithmic ...
I have an application that wants controllable random functions from $\mathbb{Z}^2$ and $\mathbb{Z}^3$ to $2^{32}$ , where by controllable I basically mean seedable by some parameters (say, on the ...
### Need faster division technique for $4$ digit numbers.
I have to divide $2860$ by $3186$. The question gives only $2$ minutes and that division is only half part of question. Now I can't possibly make that division in or less than $2$ minutes by applying ...