prime factors of numbers formed by primorials Let $p,q$ be primes with $p \leq q$. The product $2\cdot3\cdot\dots\cdot p$ is denoted with $p\#$, the
 product $2\cdot3\cdot\dots\cdot q$ is denoted with $q\#$ (primorials). 
Now $z(p,q)$ is defined by $z(p,q) = p\#+q\#/p\#$
For example $z(11,17) = 2\cdot3\cdot5\cdot7\cdot11 + 13\cdot17$
What can be said about the prime factors of $z(p,q)$ besides the simple fact that
 they must be greater than $q$?

The number $z(p,q)$ is coprime to any of these primes.  
It is more likely to be prime, especially for small values, but not necessarily so.  For example, $z(7,11) = 13*17$ is the smallest composite example, but one fairly easily finds composites (like $z(11,13)$, $z(5,19)$, $z(3,11)$, $z(13,19)$, $(13,23)$, and $z(13,37)$ to $z(13,59)$ inclusive.  For $z(17,p)$, it is composite for all $p$ between $23$ and $113$ inclusive, only $19$ and $127$ yielded primes.
There is nothing exciting, like proper powers, for valeues of $q<120$.
There does not seem to be any particular pattern to the primes.  Some are small, and some are fairly large. 
