Question

Write five pairs of odd primes less than $20$ whose sum is divisible by $4$.

Answer 1

The odd primes less than $20$ are $3,5,7,11,13,17,$ and $19$

$3+5=8$, which is divisible by $4$

$3+17=20$, which is divisible by $4$

$5+7=12$, which is divisible by $4$

$11+13=24$, which is divisible by $4$

Therefore, $(3,5),(3,17),(5,7),$ and $(11,13)$ are the five pairs of odd primes less than $20$ whose sum is divisible by $4$.