Consider triples $(p,q,r)$ of prime numbers $p$, $q$ and $r$ such that $(p+1)(q+1)=(r+1)$. Here are some examples : $(2,3,11), (3,7,31)$.
How to prove there are infinitely many such triples?!
I define two integer numbers $n$ and $m$ or $(n,m)$ to be Isomorph iff $F(n)=F(m)$, where $F(n)$ is sum of divisor of $n$ (for example $(6,11), (10,17), (14, 23), (21, 31)$). If for prime numbers $p,q,r$ have: $(p+1)(q+1)=(r+1)$ so $(pq,r)$ are Isomorph and so it maybe a conjecture: there are infinitely many pairs of Isomorph numbers!