# Algorithm: isPrimeNumber(n)

Algorithms Math

In this post I will implement basic algorithm to detect whether a given number is a prime. In more academic terms – check a number for primality. According to Wikipedia - *a prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself*.

Naïve implementation will test whether n is a multiple of any number between 2 and n-1. Slightly more optimized version will minimize the test range up-to √n (i.e. between 2 and √n). In this post I’ll use test range between 2 and ⌊n/2⌋ due to the fact calculation of √n itself is more complex than single right shift operation.

**Complexity:** O(n/2) or just O(n).