A well-known conjecture about the distribution of primes asserts that between two consecutive squares there is always at least one prime number. The proof of this conjecture is quite out of reach at present, even under the assumption of the Riemann Hypothesis. The aim of this paper is to provide the upper bounds for the exceptional set for this conjecture under the assumption of some heuristic hypotheses.
"Some conditional results on primes between consecutive squares." Funct. Approx. Comment. Math. 45 (2) 255 - 263, December 2011. https://doi.org/10.7169/facm/1323705816