Primes in Short Intervals.

Glyn Harman

Displaying similar documents to “Primes in Short Intervals.”

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Prime numbers in short intervals

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Prime numbers of the form p = m²+n²+1 in short intervals

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The localisation of primes in arithmetic progressions of irrational modulus

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A new method for counting primes in a Beatty sequence is proposed, and it is shown that an asymptotic formula can be obtained for the number of such primes in a short interval.

Primes in tuples IV: Density of small gaps between consecutive primes

Daniel Alan Goldston, János Pintz, Cem Yalçın Yıldırım (2013)

Acta Arithmetica

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We prove that given any small but fixed η > 0, a positive proportion of all gaps between consecutive primes are smaller than η times the average gap. We show some unconditional and conditional quantitative results in this vein. In the results the dependence on η is given explicitly, providing a new quantitative way, in addition to that of the first paper in this series, of measuring the effect of the knowledge on the level of distribution of primes.