Primes

Introduction

A prime number is any natural number greater than 1, such that the only natural numbers that divide into it are itself and 1.

A number n >= 2 prime if it is only divisible by 1 and itself. A number n >= 2 which isn't prime is called composite.

Composite

A natural number that is not prime, is a composite number.

Example

9 is a composite number and not a prime number because 3 divides into 9, leaving no remainder.

Use

Example

7 is a prime number because no numbers, other than 1 and 7 divide into 7, leaving no remainder.

Introduction

Every prime of the form 4n+1 is the sum of two integral squares in exactly one way.

Use

Which of the following are prime?

0,1,2,3,4,5,6,7,8,9,10

0, and 1 not prime since not positive and greater or equal to 2

2 is prime as 1 and 2 are only factors

3 is prime as 1 and 3 are only factors. 4,6,8,10 not prime as non-trivially divisible by 2. 5, 7 prime. 9 = 3 ยท 3 not prime.