Some Results on a Conjecture of Hardy and Littlewood
30 Sep 2019
•
Axler Christian
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.(read more)