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What is a prime number?

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Quick answer

A prime number is a whole number greater than 1 that can only be divided evenly by 1 and itself. Primes like 2, 3, 5, and 7 are the 'building blocks' of all numbers — and they quietly secure modern online encryption.

Key things to understand

  1. It has exactly two divisors: 1 and itself.
  2. 2, 3, 5, 7, 11, 13… are the first primes (2 is the only even one).
  3. Every whole number is a unique product of primes.
  4. There are infinitely many primes, proven over 2,000 years ago.
  5. Huge primes underpin internet encryption.

People also ask

Why is 1 not a prime number?
A prime must have exactly two distinct divisors; 1 has only one (itself), so by definition it's excluded.
How are primes used in encryption?
Multiplying two huge primes is easy, but factoring the result back is extremely hard — that gap secures much of online communication.
Are there infinitely many primes?
Yes. Euclid proved over two thousand years ago that the primes never run out.
Is 1 a prime number?
No. A prime has exactly two distinct factors, and 1 has only one factor.
Why are prime numbers important?
They're the building blocks of all integers and underpin encryption that keeps online data secure.
How many prime numbers are there?
Infinitely many — a fact proven by Euclid over 2,000 years ago.