Question

how many numbers less than 20 can be written as the sum of two prime numbers?

Answer 1

Step-by-step explanation:

So 2 is the only even number less than 20 that cannot be written as a sum of 2 primes. Any odd integer that is the sum of two primes must be of the form 2+p where p is an odd prime. Hence, for p = 3, 5, 7, 11, 13, 17 we have 5, 7, 9, 13, 15, 19. Therefore, 1, 3, 11, 17 cannot be written as a sum of two primes.

Answer 2

Step-by-step explanation:

Prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17 and 19.

(i) 2+3=5 (divisible by 5)

(ii) 2+13= 15 (divisible by 5)

(iii) 3+7=10 (divisible by 5)

(iv) 3+17= 20 (divisible by 5)

(v) 7+13=20 (divisible by 5)