jmc

A prime number is a number whose only divisors are $1$ and itself. If a prime were divisible by $39$, it would have to be divisible by $3$ and $13$ as well since $3$ and $13$ are factors of $39$. Thus the "prime" would have too many factors and wouldn't be a prime! Thus there are $\boxed{0}$ primes which are divisible by $39$.