Aarav Raina

A Short-Interval Refinement of Brocard's Conjecture at Products of Consecutive Primes

Let $p < q$ be consecutive primes with $p \ge 3$. Brocard’s conjecture asserts that at least four primes lie between $p^2$ and $q^2$. We propose a more structured conjectural distribution of these primes by introducing the intermediate points $p(q - 1)$ and $pq$. Our principal co...