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I propose a methodology to help find large prime numbers with a much higher probability than picking up random numbers and testing them for primality. This would help speed up prime number generators ...

I know about the importance in analytic number theory of the sutdy of series involving prime numbers or constellations of prime numbers, for example, if I am not wrong, major theorems are Mertens' ...

Let $ \mathcal{A} $ be a set of reals such that $ \sum_{a \in \mathcal{A} } \frac{1}{a} = \infty $ and $ \sum_{a \in \mathcal{A} } \frac{1}{a^2} < \infty $. For instance, $ \mathcal{A} = \mathbb{N}^...

I was inspired in the following post from this Math Overflow that was asked yerterday Asymptotic behavior of a certain sum of ratios of consecutives primes to ask about a similar question for ratios ...

Yesterday I tried to study the article [1] in wich were showed incredible expressions related to Dirichlet series. In the same way I wondered about next question. We denote for integers $m>1$ the ...

For integers $n\geq 1$ let $G_n$ be the Gregory coefficients or reciprocal logarithmic numbers, see the Wikipedia [Gregory coefficients.] (https://en.wikipedia.org/wiki/Gregory_coefficients) $${z\...