An integer $m$ is Fortunate if it can be written as $q-P$, where $P$ is a primorial and $q$ is the *smallest* prime greater than $P+1$. It is conjectured that Fortunate numbers are always prime.

It is easy to see that there are only finitely many possible primorials $P$ for which a given $m$ can be decomposed in the above manner (this is because $m$ must be greater than the largest prime dividing $P$).

QUESTION: Is the number of such representations of an integer $m$ uniformly bounded above?

smallestprime greater than $P+1$." For anyone who, like me two minutes ago, doesn't know what a primorial is: that's a portmanteau of "prime" and "factorial", i.e., multiply the first n primes together to get the $n^{th}$ primorial. – Todd Trimble♦ Sep 5 '12 at 3:23