Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T19:05:41.900Z Has data issue: false hasContentIssue false

On the Product of the Primes not Exceeding n

Published online by Cambridge University Press:  20 November 2018

Leo Moser*
Affiliation:
University of Alberta
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

One of the most elegant results of the elementary theory of the distribution of primes is that

1

where the product runs over primes. A very simple proof of (1) has recently been given by Erdös and Kalmar [1], [2].

Type
Notes on Number Theory I
Copyright
Copyright © Canadian Mathematical Society 1959

References

1. Trost, E., Primzahlen, (Basel, 1953), 57.Google Scholar
2. Hardy, G.H. and Wright, E.M., The Theory of Numbers, 3rd ed. (Oxford, 1954), Chap XXII.Google Scholar
3. Rosser, J.B., Explicit bounds for some functions of prime numbers, Amer. J. Math. 63 (1941), 211-232.Google Scholar