Functiones et Approximatio Commentarii Mathematici

Some conditional results on primes between consecutive squares

Danilo Bazzanella

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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.

Article information

Funct. Approx. Comment. Math., Volume 45, Number 2 (2011), 255-263.

First available in Project Euclid: 12 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N05: Distribution of primes

distribution of prime numbers primes between squares


Bazzanella, Danilo. Some conditional results on primes between consecutive squares. Funct. Approx. Comment. Math. 45 (2011), no. 2, 255--263. doi:10.7169/facm/1323705816.

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