# Show that if all three of p, p + 2 and p + 4 are prime, then p = 3.

## Solution

n We apply the Division algorithm to p and 3 and find that p has a remainder of either 0, 1 or 2, after division by 3.

In the first case, we necessarily have p = 3.

In the second, it follows that p + 2 is divisible by 3 and hence equal to 3, contradicting the fact that p is prime.

In the third case, we have that p + 4 is divisible by and hence equal to 3, again a contradiction.