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Let us consider the strong twin conjecture: For all positive integer $n$ there exist a prime $p$ such that $$n+4<p<2^n2^4$$ and $p$ is a prime and $p+2$ is a prime Since the inequalities and the set o …

From this page: https://en.wikipedia.org/wiki/Chebyshev_function#Asymptotics_and_bounds A theorem due to Erhard Schmidt states that, for some explicit positive constant $K$, there are infinitely ma …

Brocard's conjecture states that: If $p_{k}$ and $p_{k+1}$ are consecutive prime numbers greater than $2$, then between $p_{k}²$ and $p_{k+1}²$ there are at least four prime numbers. I know that is st …

A positive integer $n$ is extremely abundant if either $n=10080$, or $n>10080$ and $$σ(n)/(n×log(log (n)))>σ(m)/(m×log(log (m)))$$ for all $10080≤m<n$. Here $σ(n)$ is the sum-of-divisors function a …