Help me find the exact conjecture statement. What I roughly remember is that it stated that the difference between primorial $n\#$ (product of first $n$ primes) and "some" larger number than the primorial (the number being well defined in the statement) is always a prime.
I simply cannot recall or find the exact statement... Does anyone know?
Edit: Thanks iadvd for help, let me just exact statement i had in mind for clarity:
Fortune's Conjecture: For any integer $n>0$, the difference between the primorial $\#n$ and the smallest prime $p > n\#+1$ is always a prime.
I think you are defining the Fortunate numbers. Just an excerpt from Wikipedia: a Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m > 1 such that $p_n\# + m$ is a prime number, where the primorial $p_n\#$ is the product of the first $n$ prime numbers.
There are a lot of variations of this conjecture. For instance you can find some other questions at MSE regarding the topic here and here.