Chebyshev theta function (source code)

= Chebyshev theta function
{c}
{title2=$\vartheta(x)$}

The Chebyshev theta function is one of the two <Chebyshev functions> and is the <natural logarithm> of the <primorial>:
$$
\vartheta(x)=\sum_{p\leq x}\log p
=\log\prod_{p\leq x}p,
$$
where both the sum and the product range over <prime numbers>.