Mersenne semiprimes with square indices

Question

A Mersenne semiprime is a semiprime of the form $2^n-1$, it can be shown that $2^n-1$ can be a semiprime if and only if $n$ is either a prime or a square of a prime. There are plenty Mersenne semiprimes with prime indices $n$, but Mersenne semiprimes with square indices are very rare, only three are known to date: $2^4-1, 2^9-1,$ and $2^{49}-1.$ So where is the next square index $n$?