Prime Number Calculator

Formula used

A number n is prime if no integer from 2 to √n divides it exactly

How to use this calculator

1. Enter a whole number of 2 or more.
2. The result tells you whether it is prime and, if not, how it factorises.
3. The nearest primes either side are useful when you need a prime close to a target value.

Example calculation

What does this result mean?

Primes are the building blocks of arithmetic: every integer above 1 factorises into primes in exactly one way, which is the fundamental theorem of arithmetic. Testing only up to the square root is sufficient because factors come in pairs — if n has a factor above √n, it must also have a matching one below.

Frequently asked questions

Is 1 a prime number?

No. Primes are defined as having exactly two distinct divisors, and 1 has only one. Excluding it also keeps prime factorisation unique.

Is 2 really prime?

Yes, and it is the only even prime, because every other even number is divisible by 2.

Why do primes matter outside mathematics?

Public-key cryptography relies on the fact that multiplying two large primes is easy while factoring the product back is computationally hard.

Related calculators

• GCD & LCM CalculatorGreatest common divisor and lowest common multiple of any set of integers.
• Square Root & Root CalculatorSquare roots, cube roots and any nth root, plus squares.
• Random Number GeneratorRandom integers in any range, with optional uniqueness.