Proof that there are infinitely many prime numbers.

Assume that there are a fixed number of prime numbers. P1, P2, P3, ... Pn

Let h = (P1•P2•P3 ... Pn)+1

This means h is not divisible by any prime number. (you will get 1 as remainder)

This gives an absurd result as all number greater than 1 are divisible by a prime number.

Hence, the initial assumption is false. This means there are infinitely many prime numbers.

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Proving for all n<1, n is divisible by a prime number.

Let r be the smallest divisor of n, where r is not 1.

If r is not a prime number, then there exists a v which is a divisor of r, where 1
v is a divisor of r => v is divisor of n

This gives an absurd result as we took r as the smallest divisor of n.

Therefore r is a prime.

For the future.

I am going to be very busy with my academics this year, so all my future blog posts may be in point form for a certain period of time.