In the context of Example 14.2 what is the answer if we have five numbers instead of four? (i.e., can we get four distinct prime numbers then?)
Let \(p\) and \(q\) be two prime numbers such that \(q = p + 2\). Prove that \(p^q + q^p\) is divisible by \(p + q\).
I’m thinking of two prime numbers. The first prime number squared is thirty-six more than the second prime number. What’s the second prime number?
Determine all prime numbers \(p\) such that \(p^2-6\) and \(p^2+6\) are both prime numbers.