Question

(a) The sum of three prime numbers is an even number. Prove that one of the three numbers must be 2. [b] The sum of three prime numbers is 30. Write all such triplets of prime numbers. hint: all the prime number will be less than 30​ i need a clear explaination

Answer 1

Answer:

(A) We know that except 2 all are odd prime numbers.

so if you add two odd primes or any two odds we get an even.

Moreover, even + even is also an even.

so when we add the above sum with 2 we get an even number.

Hence proved...

(B) so the triplets of prime which give sum 30 are as follows:

1. 23, 2, 5

2. 11, 2, 17