A scalene triangle has side lengths which are all prime numbers. What is the smallest possible perimeter it could have?
The answer is $3+5+7=15$. This is achievable since the three sides $\{3,5,7\}$ form the sides of a triangle.

To show it is best possible, note that $\{3,5,7\}$ are the three smallest odd primes; so any smaller triangle would need to have a side of length 2 . However, the two longer lengths would then be different odd primes; this would cause them to differ by at least 2 , which is impossible.