Irregularities in the distribution of primes and twin primes

Author:
Richard P. Brent

Journal:
Math. Comp. **29** (1975), 43-56

MSC:
Primary 10H15; Secondary 10-04

DOI:
https://doi.org/10.1090/S0025-5718-1975-0369287-1

Corrigendum:
Math. Comp. **30** (1976), 198.

MathSciNet review:
0369287

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Abstract: The maxima and minima of , and in various intervals up to are tabulated. Here and are respectively the number of primes and twin primes not exceeding is the logarithmic integral, is Riemann's approximation to , and is the Hardy-Littlewood approximation to . The computation of the sum of inverses of twin primes less than gives a probable value for Brun's constant.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0369287-1

Keywords:
Prime,
twin prime,
Riemann's approximation,
error bounds,
Hardy-Littlewood conjecture,
Brun's constant,
logarithmic integral

Article copyright:
© Copyright 1975
American Mathematical Society