Question

B) Prove or disprove by example or by exhaustive checking that every integer greater than 1 is either prime or sum of two primes.

Answer 1

Every integer greater than 1 is either prime or composite.

Explanation:

Let us negate this statement.

Assumption - any number greater than 1, is neither prime nor composite.

A prime number has only 2 divisors, and a composite number has at least 3.

Let a number be X such that X >1.

Now X is divisible by 1 (Any integer is divisible by 1)

And X is divisible by X (X/X = 1, if X is not zero)

So by this, we see X has at least 2 divisors, X is either prime, or composite if it has more divisors!

So our assumption is wrong, and every integer greater than 1 is either prime or composite.