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Formulae For Primes

Published online by Cambridge University Press:  03 November 2016

R. L. Goodstein  and
C. P. Wormell
R. L. Goodstein
Affiliation:
The University, Leicester
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Extract

The criticism by T. B. M. Neil and M. Singer in The Gazette for October 1965 of C. P. Willans’ formula for the nth prime number is in my view quite unjust. Willans’ formula expresses two properties of the nth prime, namely that the number of numbers x such that 1 ≤ π(x) < n is two less than the nth prime, and that the nth prime is less than 2n. Willans gives a trigonometrical representation of π(x), the number of primes less than or equal to x. The analysis which Neil and Singer give is an exposure of the formula only in the sense that a clear proof is an exposure.

Type
Research Article
Information
The Mathematical Gazette , Volume 51 , Issue 375 , February 1967 , pp. 35 - 38
Copyright
Copyright © Mathematical Association 1967

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