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on the number of carmichael numbers up to $\lowercase{x}$

Published online by Cambridge University Press:  23 September 2005

glyn harman
glyn harman
Affiliation:
department of mathematics, royal holloway, university of london, egham, tw20 0ex, united kingdomg.harman@rhul.ac.uk
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Abstract

it is shown that, for all large $x$, there are more than $x^{0.33}$ carmichael numbers up to $x$, improving on the ground-breaking work of alford, granville and pomerance, who were the first to demonstrate that there are infinitely many such numbers. the same basic construction as that employed by these authors is used, but a slight modification enables a stronger result on primes in arithmetic progressions based on a sieve method to be employed.

Keywords

11n13 (primary)11n36 (secondary)
Type
papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 5 , October 2005 , pp. 641 - 650
Copyright
the london mathematical society 2005

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