All Questions

Under Goldbach's conjecture, let's consider once again the map $r_0\colon n\mapsto r_{0}(n)$ such that $r_{0}(n)$ is the smallest non negative integer $r$ such that both $n-r$ and $n+r$ are prime. Let'...

We all know there exists an explicit Formula for prime counting function in terms of Riemann zeros. I'm wondering if similar formula exists for $n$th prime in terms of Riemann zeros? Or any other ...

Let $\pi(x)$ be the number of primes $p$ not exceeding $x, \theta(x) = \sum_{p\leq x} \log p$ and $Li(x)$ be the logarithmic integral. Is it true that $$\pi(x)-Li(x) = \theta(x) - x + O(x^{1/2}\log^{...

Denote by $\psi(x)$ the Chebyshev psi function over prime powers. Assuming the RH, it can be shown via the Riemann explicit formula that $$\psi(x)-x \ll √x |\sum_{|\gamma| < T} \frac{1}{\rho} | +...

Given a positive integer $ n $ and assuming Goldbach's conjecture, let $r_{0}(n)$ denote the smallest non negative integer $r$ such that both $n-r$ and $n+r$ are primes. Let $k_{0}(n)$ denote 'the ...