Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the greatest prime factor of $p-1$ 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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $p$ denote a prime. In this article we provide the first published lower bounds for the greatest prime factor of $p-1$ exceeding $(p-1)^{\frac12}$ in which the constants are effectively computable. As a result we prove that it is possible to calculate a value $x_0$ such that for every $x > x_0$ there is a $p < x$ with the greatest prime factor of $p-1$exceeding $x^{\frac35}$. The novelty of our approach is the avoidance of any appeal to Siegel's Theorem on primes in arithmetic progression.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 11N13

Retrieve articles in all journals with MSC (2000): 11N13

Additional Information

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

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