On the greatest prime factor of with effective constants

Author:
G. Harman

Journal:
Math. Comp. **74** (2005), 2035-2041

MSC (2000):
Primary 11N13

Published electronically:
February 16, 2005

MathSciNet review:
2164111

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote a prime. In this article we provide the first published lower bounds for the greatest prime factor of exceeding in which the constants are effectively computable. As a result we prove that it is possible to calculate a value such that for every there is a with the greatest prime factor of exceeding . The novelty of our approach is the avoidance of any appeal to Siegel's Theorem on primes in arithmetic progression.

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Additional Information

**G. Harman**

Affiliation:
Department of Mathematics, Royal Holloway University of London, Egham, Surrey TW20 0EX, United Kingdom

Email:
G.Harman@rhul.ac.uk

DOI:
https://doi.org/10.1090/S0025-5718-05-01749-7

Received by editor(s):
March 19, 2004

Received by editor(s) in revised form:
August 16, 2004

Published electronically:
February 16, 2005

Article copyright:
© Copyright 2005
American Mathematical Society