MathOverflow

Pomerance in A Note on the Least Prime in an Arithmetic Progression states under $GRH$ Chowla shows we have $$P(K)\ll k^{2+\epsilon}$$ where $$P(k)=\max_{l\in\{1,\dots,p-1\}:(k,l)=1}p(k,l)$$ where $p(k,l)$ is the smallest prime satisfying $l\bmod k$...

The function g(N) for counting the prime pairs in an even integer N can be implemented as:
Question: Is there a separate algorithm, that uses an apparently different logic, but still achieves the same count of prime pairs in N?

In a paper published in 1971, R. Crocker proved that there are infinitely many positive odd numbers not of the form $p+2^a+2^b$ with $p$ prime and $a,b\in\mathbb Z^+=\{1,2,3,\ldots\}$. The proof makes use of Fermat numbers and covers of $\mathbb Z$ by...

Let $G$ be a connected Lie group. Let $\Gamma$ a lattice in $G$ not necessarily uniform (cocompact). Is it true that $\Gamma$ is finitely generated?