  Let $\zeta(s)$ be the Riemann zeta function. We prove the statement in the
title, which improves a recent result of Rivoal and Zudilin by lowering $69$ to
$35$. We also prove that at least one of $\beta(2),\beta(4),\ldots,\beta(10)$
is irrational, where $\beta(s) = L(s,\chi_4)$ and $\chi_4$ is the Dirichlet
character with conductor $4$.
