In simple terms
A prime number is a whole number greater than 1 that can be divided evenly only by 1 and by itself. Seven is prime, because no other whole number divides it without a remainder. Six is not, because 6 = 2 × 3.
Whole numbers above 1 that are not prime are called composite numbers. The first six primes are 2, 3, 5, 7, 11 and 13.
How it works
To test a small number, try dividing it by the primes below it. For example, 91 looks prime at first glance, but 91 = 7 × 13, so it is composite.
Primes are the building blocks of all whole numbers. Every whole number greater than 1 can be written as a product of primes in exactly one way, apart from the order of the factors. For example, 60 = 2 × 2 × 3 × 5. This rule is called the fundamental theorem of arithmetic.
It is also why 1 is not counted as prime. If it were, the “exactly one way” rule would fail, because you could multiply by 1 as many times as you liked. Mathematicians treat 1 as a separate kind of number, called a unit.
The primes never run out. The mathematician Euclid proved around 300 BC that there are infinitely many of them.
Why it matters
Primes help protect everyday digital life. Many encryption methods multiply two very large primes together. Working backward from the product to find the two primes would take a conventional computer an estimated billions of years for large enough numbers. That is also why researchers are building new encryption designed to resist future quantum computers.
Hunting for giant primes has become a global volunteer effort. As of 2026, the largest known prime, found in October 2024, has 41,024,320 digits.
Where you’ll see it
- School math lessons on factors, multiples and fractions.
- Online security, including the encryption that protects bank data.
- Record-setting finds by the Great Internet Mersenne Prime Search (GIMPS).
- Math puzzles and coding challenges.
Example
Because 29 is a prime number, the teacher could not split 29 students into equal groups of any size other than 1 or 29.
Often confused with
Odd numbers. Many odd numbers are not prime, such as 9 and 15. And the smallest prime, 2, is even.
Key facts
- An integer greater than one is prime if its only positive divisors are one and itself. The first six primes are 2, 3, 5, 7, 11 and 13.1
- Every positive integer greater than one can be written uniquely as a product of primes, which is the main reason 1 is not counted as prime.2
- Euclid proved that there are infinitely many primes, around 300 BC.3
- As of 2026, the largest known prime has 41,024,320 digits. It was found on 12 October 2024 through the GIMPS project.4
- Many encryption algorithms rely on how hard it is for conventional computers to find the two large prime factors of a very large number.5
Quick checkIs 1 a prime number?Show answer
No. A prime must be greater than 1; 1 is treated as a separate kind of number, a unit.
Sources
- PrimePages. Prime (The Prime Glossary). Undated (accessed 11 September 2026)
- PrimePages. Why is the number one not prime?. Undated (accessed 11 September 2026)
- PrimePages. Proofs that there are infinitely many primes. Undated (accessed 11 September 2026)
- Great Internet Mersenne Prime Search (GIMPS). List of known Mersenne prime numbers. Undated (accessed 11 September 2026)
- National Institute of Standards and Technology (NIST). What Is Post-Quantum Cryptography?. 27 February 2026 (updated) (accessed 11 September 2026)
- PrimePages. Composite (The Prime Glossary). Undated (accessed 11 September 2026)
Editorially reviewed by Specialty Digest Editorial TeamLast reviewed September 11, 2026Researched and drafted with AI assistanceReport an issue