Question

Write five pairs of prime numbers less than $20$ whose sum is divisible by $5$.(Hint: $3+7=10$)

Answer 1

Numbers divisible by $5$ are $5,10,15,20,25,30$

We need to write these as sum of $2$ prime numbers less than $20$

i.e., using $2,3,5,7,11,13,17,19$

$5=2+3$ where $2$ and $3$ are prime

$10=3+7$ where $3$ and $7$ are prime

$15=2+13$ where $2$ and $13$ are prime

$20=3+17$ where $3$ and $17$ are prime

$20=7+13$ where $7$ and $13$ are prime

So pairs are

$(2,3),(3,7),(2,13),(3,17),(7,13)$