Frequently Asked Questions
What is a prime number? ▼
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11, 13… The number 2 is the only even prime. 1 is not considered prime by convention.
How do you check if a number is prime? ▼
To test if n is prime, check if any integer from 2 up to √n divides n evenly. If none do, n is prime. This works because if n has a factor greater than √n, it must also have one smaller than √n.
What is prime factorization? ▼
Prime factorization breaks a number down into a product of prime numbers. For example, 360 = 2³ × 3² × 5. Every integer greater than 1 has a unique prime factorization (Fundamental Theorem of Arithmetic).
What is the Sieve of Eratosthenes? ▼
An ancient algorithm for finding all primes up to a given limit. It works by iteratively marking multiples of each prime as composite, starting from 2. The tool uses this method for listing primes efficiently.
Are there infinitely many primes? ▼
Yes! Euclid proved this around 300 BC. Suppose there are finite primes — multiply them all and add 1. That number is either prime itself or has a prime factor not in the original list. Either way, a new prime exists. Contradiction.