The Distribution of the Primes

Abstract

Legendre was the first, as far as we know, to make any significant conjecture about the distribution of the primes. Let π(x) denote the number of primes not exceeding x. Then Legendre conjectured, somewhat tentatively, that for large x the number π(x) is given approximately by

$$ \frac{x}{{\log x - 1.08...}} $$

.