Question

Write five pairs of prime numbers less than 50 but greater than 30 whose sum is divisible by 2​

Answer 1

Let’s start by writing out the numbers between 20 and 30:

21,22,23,24,25,26,27,28,29

Eliminate all the even numbers; they can’t be prime

21,23,25,27,29

Now do the same of for all multiples of 3:

23,25,29

And finally, multiples of 5:

23,29

And we are left with the two primes between 20 and 30: 23, 29.

This process is a variation of the Sieve of Eratosthenes[1], perhaps the oldest method in existence for finding prime numbers. Notice that, though we could have checked for multiples of 7, it would be redundant; this is because the largest prime less than the 30−−√ is 5, which was necessary to eliminate the 25=52 . The smallest number which requires a 7-sieve would be 49=72 .