Prime Number Checker
The Prime Number Checker tells you instantly whether a number is prime, lists its prime factors if it is not, and can generate every prime up to 10,000 using the Sieve of Eratosthenes.
What makes a number prime
A prime number is a whole number greater than 1 whose only divisors are 1 and itself - 2, 3, 5, 7, 11, and so on. Every other whole number is "composite" and can be written as a product of primes. The checker tests divisibility efficiently, so even large numbers return an answer in an instant.
Prime factorisation and the sieve
For a composite number, the tool breaks it into its prime factors (for example 84 = 2 × 2 × 3 × 7), which is the basis of finding LCMs, GCDs, and simplifying fractions. To list many primes at once it uses the Sieve of Eratosthenes, an ancient and remarkably fast method for finding all primes up to a limit.
Frequently Asked Questions
Is 1 a prime number?
No. By definition a prime must be greater than 1 and have exactly two divisors. 1 has only one divisor, so it is neither prime nor composite.
What is prime factorisation used for?
It underlies finding the LCM and GCD of numbers, simplifying fractions, and much of cryptography.
What is the Sieve of Eratosthenes?
It is an efficient algorithm that finds all prime numbers up to a limit by repeatedly marking off the multiples of each prime.
Is 2 really prime even though it is even?
Yes. 2 is the only even prime number, because every other even number is divisible by 2 and therefore composite.
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