In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly approximated as closely as desired by a polynomial function. Because polynomials are among the simplest functions, and because computers can directly evaluate polynomials, this theorem has both practical and theoretical relevance, especially in polynomial interpolation. The original version of this result was established by Karl Weierstrass in 1885 using the Weierstrass transform.
Marshall H. Stone considerably generalized the theorem (Stone...
Let $p$ be a prime such that $p+2$ is Also a prime.
Define
$$ f(z) = \sum_p \frac{\ln(p) \space \ln(p+2)}{p^{z/2} \space (p+2)^{z/2}} $$
For $z \neq 1 $ and $re(z) > 1$ this $f(z)$ always converges.
If there are infinitely many prime twins , and prime twins grow like $O (n * ln(n)^2 ) $ as i...
