I've thought of the following algorithm to find the entire list of prime numbers:
Take a prime number $p$ to your list.
$1.$ Multiply all the numbers in your list and call the number you get $P$.
$2.$ Add the new primes that divide $P+1$ to your list.
Repeat ad infinitum.
The question is:
For which $p$ (if any) will this algorithm create a list of all the prime numbers?