Prime Number Calculator

A prime number is a whole number greater than 1 that has exactly two distinct factors: 1 and itself. Examples include 2, 3, 5, 7, 11, and 13. A number with more than two factors is called a composite number.

No, 1 is not a prime number. By definition, a prime must have exactly two distinct factors, but 1 has only one factor (itself). Mathematicians exclude 1 from primes to preserve the uniqueness of the Fundamental Theorem of Arithmetic.

A composite number is any positive integer greater than 1 that is not prime — meaning it has more than two factors. For example, 12 is composite because it is divisible by 1, 2, 3, 4, 6, and 12.

The calculator uses trial division to test whether your number is divisible by any integer from 2 up to its square root. If no such divisor is found, the number is prime. If a divisor is found, all factors are listed and the number is flagged as composite.

Yes, 2 is the only even prime number. Every other even number is divisible by 2, making it composite. That makes 2 unique as the smallest and only even member of the prime numbers.

Prime numbers are the building blocks of all integers — every whole number greater than 1 can be expressed as a unique product of primes (the Fundamental Theorem of Arithmetic). They are also critical in cryptography: RSA encryption and many modern security systems rely on the difficulty of factoring large numbers into primes.

There are infinitely many prime numbers. Euclid proved this over 2,000 years ago by showing that any finite list of primes can always be used to construct a new prime not on the list. The primes become less frequent as numbers grow larger, but they never stop.

The largest known prime numbers are Mersenne primes, which have the form 2^p − 1. As of recent records, the largest known prime has tens of millions of digits and was discovered through the Great Internet Mersenne Prime Search (GIMPS) collaborative project.