Express each of the following numbers as the sum of three odd primes: (a) 21 (b) 31 (c) 53 (d) 61

A prime number is a positive integer having exactly two factors. If p is a prime, then it’s only factors are necessarily 1 and p itself.

Except 2, all other prime numbers are odd. In other words, we can say that 2 is the only even prime number.


We need to express the given numbers as the sum of odd primes. The prime numbers  between 1 and 50 are listed below:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.

So using the above any three odd primes we need to express as the sum of the given number.

(a) 21=3+7+11
(b) 31=3+11+17
(c) 53=13+17+23
(d) 61=19+29+13

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