What Are Prime Numbers? A Complete Beginner's Guide

A prime number is a whole number greater than 1 with exactly two divisors: 1 and itself. 2, 3, 5, 7 and 11 are prime; 4, 6, 8 and 9 are composite because they have extra divisors.

Primes are the building blocks of every integer. Here's everything a beginner needs to understand them.

The definition (and why 1 isn't prime)

A prime has exactly two distinct divisors. The number 1 has only one divisor (itself), so it fails the test — it's a 'unit', not a prime. The number 2 is the smallest prime and the only even one.

Prime vs composite

A composite number has more than two divisors, like 12 (1, 2, 3, 4, 6, 12). Check any number instantly with the Prime Number Checker.

How to test whether a number is prime

Try dividing by every integer from 2 up to the square root of the number. If none divides evenly, it's prime. You stop at the square root because any larger factor pairs with a smaller one you've already checked.

Famous primes

• Mersenne primes like 2⁷ − 1 = 127.
• Twin primes such as 11 and 13.
• The largest known primes have tens of millions of digits.

Where primes are used

Primes secure online banking (RSA), reduce hash collisions, and generate pseudo-random sequences. Their unpredictability is a feature, not a bug.