Lehmer's conjecture on nonvanishing of the Ramanujan tau function

Let $\tau(n)$ be Ramanujan's tau function, the Fourier coefficients of the discriminant modular form $\Delta$, and let $p$ range over primes. Lehmer's conjecture. If $n\geq 1$, then $\tau(n)\neq 0$; equivalently, if $p$ is prime, then $\tau(p)\neq 0$. This is the same classical nonvanishing conjecture for Ramanujan's tau function stated elsewhere in the paper. It remains open.