Irregularities in the distribution of primes and twin primes
Author:
Richard P. Brent
Journal:
Math. Comp. 29 (1975), 4356
MSC:
Primary 10H15; Secondary 1004
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 HardyLittlewood 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:
http://dx.doi.org/10.1090/S00255718197503692871
PII:
S 00255718(1975)03692871
Keywords:
Prime,
twin prime,
Riemann's approximation,
error bounds,
HardyLittlewood conjecture,
Brun's constant,
logarithmic integral
Article copyright:
© Copyright 1975
American Mathematical Society
