What is a prime number?
A prime is a natural number greater than 1 whose only divisors are 1 and itself. The first few are 2, 3, 5, 7, 11 and 13. Two is the only even prime, because every other even number is divisible by 2 and therefore composite.
Prime number checker
Whether a number is prime, and how many divisors it has.
1
Prime (1 = yes)
How this is calculated
- Number of divisors
- 2
- Prime (1 = yes)
- 1
Page updated 20/08/2026
Frequently asked questions
Why is 1 not a prime number?
It is a choice of definition with a practical reason. The fundamental theorem of arithmetic says every number factors into primes in exactly one way. If 1 counted as prime there would be infinitely many factorisations, since you could multiply by ones indefinitely. Excluding 1 keeps the theorem true.
How do you test whether a number is prime?
You only need to test divisibility by primes up to the square root of the number. For 97 the root is about 9.8, so testing 2, 3, 5 and 7 suffices — none divides it, so 97 is prime. Going further is pointless: a larger divisor would require a smaller partner, which you would already have found.
How many primes are there?
Infinitely many — Euclid proved it more than two thousand years ago. The proof is short: if the primes were finite, you could multiply them all together and add one, producing a number divisible by none of them. Primes thin out as numbers grow, but they never run out.