Let 
$$\theta(x)=\sum\_{p\leq x} \log p$$ be the Chebyshev function over primes $p$.


Computational evidence seems to suggest that $\theta(x) < x$ for every sufficiently large $x$. 


But is it true ?



Inquiry on the Chebyshev $\theta$ function
No. Littlewood proved that $\theta(x) > x + c \sqrt{x} \log \log \log x$ holds for infinitely many integers $x$, for some $c > 0$. Cf the answer to [this Mathoverflow question](https://mathoverflow.net/questions/178635/lower-bounds-on-the-error-term-of-the-prime-number-theorem), noting that $\theta(x) = \psi(x) + O(\sqrt{x})$.


