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arXiv · 1909.12625

Some Results on a Conjecture of Hardy and Littlewood

Christian Axler
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Abstract

Let $m$ and $n$ be positive integers with $m,n \geq 2$. The second Hardy-Littlewood conjecture states that the number of primes in the interval $(m,m+n]$ is always less than or equal to the number of primes in the interval $[2,n]$. Based on new explicit estimates for the prime counting function $\pi(x)$, we give some new ranges in which this conjecture holds.

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Christian Axler. 2019-09-27. Some Results on a Conjecture of Hardy and Littlewood. https://arxiv.org/abs/1909.12625

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