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A formula for the exact number of primes below a given bound in any arithmetic progression

Published online by Cambridge University Press:  17 April 2009

Richard H. Hudson
Richard H. Hudson
Affiliation:
Department of Mathematics and Computer Science, University of South Carolina, Columbia, South Carolina, USA.
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Abstract

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The formula of [E.] Meissel [Math. Ann. 2 (1870), 636–642] is generalized to arbitrary arithmetic progressions. Meissel's formula is applicable not only to computation of π(x) for large x (recently x = 1013), but also is a sieve technique (see MR36#2548), useful for studying the subtle effect of primes less then or equal to x1/2 on the behavior of primes less than or equal to x. The same is true of the generalized Meissel, with the added advantage that the behavior of primes less than or equal to x can be studied in arbitrary progressions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 1 , February 1977 , pp. 67 - 73
Copyright
Copyright © Australian Mathematical Society 1977

References

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