All integers are of the form \(4k\), \(4k+1\), \(4k+2\) or \(4k+3\). If a number if greater than 1 and is of the form \(4k\) or \(4k+2\), then it's divisible by 2:
$$2|4k \\ 2|(4k+2)$$
This means primes can only be of the form \(4k+1\) or \(4k+3\).
All integers are of the form \(4k\), \(4k+1\), \(4k+2\) or \(4k+3\). If a number if greater than 1 and is of the form \(4k\) or \(4k+2\), then it's divisible by 2:
This means primes can only be of the form \(4k+1\) or \(4k+3\).