The set containing all prime numbers divisible by 2 is simply {2}.
Explanation
A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Divisibility by 2 means that a number can be divided by 2 without leaving a remainder.
The number 2 is a prime number because its only divisors are 1 and 2. It is also divisible by 2. No other prime number is divisible by 2. This is because any other number divisible by 2 is, by definition, an even number greater than 2, and therefore also divisible by 1, 2, and itself, meaning it has more than two factors and therefore isn't prime.
Therefore, the only prime number divisible by 2 is 2 itself.
