Logs over each other

Relevant wiki: Solving Logarithmic Equations

We know that: $\log_{√2}(\log_2(\log_4(x-15))) = 0$ Using the rule $\log_a 1 = 0, a > 0$ : $\log_{√2} 1 =0 \implies \log_2(\log_4(x-15)) = 1$ Using the rule $\log_a a = 1$ : $\log_4(x - 15) = 2 \rightarrow 4^2 = x - 15 \implies x = 31$ $31$ is prime and has $\boxed{2}$ factors.