A prime number has exactly two positive factors: 1 and itself. Prime numbers are the indivisible building blocks used in factorization and many areas of mathematics.
The definition
Seven is prime because its only positive divisors are 1 and 7. Twelve is not prime because it also has 2, 3, 4, and 6 as factors. The definition uses positive whole-number divisors.
A practical test
To test n, you only need to try possible divisors up to √n. If none divides evenly, n is prime. Testing 97 only needs candidates through 9.8, so checking 2, 3, 5, and 7 is enough.
Why one is not prime
The number 1 has exactly one positive factor, not two. Treating it as prime would break the uniqueness of prime factorization, so modern definitions classify it as neither prime nor composite.
Use a verified result
For large values, use a tested implementation rather than relying on a quick visual pattern. A number page should show the classification and factor evidence so the result can be checked.
Sources
The figures and rules in this guide are checked against:
- Prime Number — Wolfram MathWorld
- Why is the number one not prime? — PrimePages (University of Tennessee at Martin)
- Finding primes and proving primality: trial division — PrimePages (University of Tennessee at Martin)
- Prime number — Encyclopaedia Britannica