Use the fact that a natural number is prime if 1 it is great

Use the fact that a natural number is prime if

1. it is greater than 1 and

2. it is divisible by only itself and

A. Prove there are an infinite prime numbers

Solution

Proof :

Suppose p1 = 2 <p2 = 3 < ....pn are all prime numbers . Now , Let P = p1p2p3p4...pn+1 , p be prime number dividing P, then p cannot be any of p1 , p2 ...pn, otherwise p would divide the differences, which is impossible. thus prime numbers are infinite.