Inquiry on the Chebyshev $\theta$ function

Question

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 ?

Answer 1

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, noting that $\theta(x) = \psi(x) + O(\sqrt{x})$.

Answer 2

In an answer to this question someone speculates that the first time this happens is "basically around the Skewes number $1.4 \times 10^{316}.$"