The primorial $\ p\ $# is defined as the product of the primes upto $\ p\ $ , $\ p$#$:=2\cdot 3\cdot 5\cdot 7\cdots p\ $.
Define $f(p,q)=\ q$#$/p$#$\ +\ p$# for prime numbers $\ p\le q\ $
Is $n=107$ the only positive integer for which $f(p,q)=n$ holds for two distinct pairs $(p,q)$ ?
We have $\ f(2,7)=f(5,11)\ $ and for primes $p,q\le 2\ 000$ , this is the only duplicate. Is $n=107$ the only case, and if yes, how can it be proven ?