IJPAM: Volume 7, No. 4 (2003)

ON THE DISTRIBUTION OF $\log(p)$

H.L. Hutson
Department of Mathematics
The US Merchant Marine Academy
Kings Point
Great Neck, NY 11024, USA
e-mail: hutsonh@usmma.edu


Abstract.A classical theorem of Franel says that the proportions of a given digit in the jth place after the decimal point in a table of log($n$), $n$=1,2,3,...are dense in a non trivial interval. We revive this result by considering the subtleties that occur when one restricts attention to a table of log($p$), $p$ prime.

Received: April 27, 2003

AMS Subject Classification: 11A41, 11K06

Key Words and Phrases: prime numbers, uniform distribution modulo 1

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 7
Issue: 4