Primality of Euclid Numbers

Open Question
Consider the Euclid numbers:

Is there an infinite number of:
 * prime numbers
 * composite numbers

in this list?

It is known that $E_1$ to $E_5$ are all prime, and so is $E_{11}$.

The next such prime is $E_{75}$.

However, whether the Euclid primes go on for ever is unknown.

Neither is it known whether the non-prime Euclid numbers is infinite.