Express each of the following numbers as the sum of three odd primes:

(a) 21 (b) 31

(c) 53 (d) 61

(a) 21 = 5 + 5 + 11

Clearly, 5 and 11 are prime numbers.

(b) 31 = 5 + 7 + 19

Clearly, 3, 7 and 19 are prime numbers.

(c) 53 = 5 + 17 + 31

Clearly, 5, 17 and 31 are prime numbers.

(d) 61 = 13 + 17 + 31

Clearly, 13, 17 and 31 are prime numbers.