Primality of Euclid Numbers

Open Question
Consider the Euclid numbers:

$$ $$ $$ $$ $$ $$ $$

Is there an infinite number of: in this list?
 * prime numbers
 * composite numbers

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.