# What is the intersection of the set of all prime numbers and the set of all even numbers?

2 is the only member of both the set of all prime numbers and the set of all even numbers.

### Are all prime numbers even?

Almost all prime numbers are odd. There is only one prime number that is even - the number 2. A prime number is a number with two and only two factors: 1 and itself. All even numbers greater than 2 are divisible by 2, which means they have more than two factors, so they cannot be prime numbers. All prime numbers except 2 are odd.

### Why are all prime numbers odd?

Not all prime numbers are odd. There is one prime number that is even: 2. A prime number is a number with two and only two factors: 1 (also known as unity) and itself. A composite number is a number with more than two factors. All even numbers are divisible by 2. Thus, all even numbers have 2 as a factor, which means that all even numbers greater than 2 have more than two factors…