Functiones et Approximatio Commentarii Mathematici

Some conditional results on primes between consecutive squares

Danilo Bazzanella

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Abstract

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

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

Dates
First available in Project Euclid: 12 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.facm/1323705816

Digital Object Identifier
doi:10.7169/facm/1323705816

Mathematical Reviews number (MathSciNet)
MR2895157

Zentralblatt MATH identifier
1260.11058

Subjects
Primary: 11N05: Distribution of primes

Keywords
distribution of prime numbers primes between squares

Citation

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. https://projecteuclid.org/euclid.facm/1323705816


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References

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