Factor Calculator

Prime Number Calculator

Test whether any number is prime, find its nearest primes, and list all primes up to a given target.

What is a Prime Number?

A prime number is a natural number greater than 1 that has exactly 2 distinct positive factors: 1 and itself. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. The number 2 is the only even prime number — every other even number is divisible by 2 and therefore composite.

There are 25 prime numbers below 100, 168 primes below 1,000, and 78,498 primes below 1,000,000. The Prime Number Theorem states the number of primes below n approximates n / ln(n). Prime numbers are the atoms of arithmetic — the Fundamental Theorem of Arithmetic guarantees every integer greater than 1 factors uniquely into primes.

How to Test if a Number is Prime

The Sieve of Eratosthenes eliminates composite numbers step by step. Watch it identify all 25 primes below 100.

Sieve of Eratosthenes

Click Run to start the sieve.

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Prime Composite Current divisor

Frequently Asked Questions

No, 1 is not a prime number. By definition, a prime number must be greater than 1 and have exactly 2 distinct positive factors: 1 and itself. The number 1 has only 1 factor (itself), so 1 is classified as neither prime nor composite. Excluding 1 from prime numbers preserves the uniqueness of the Fundamental Theorem of Arithmetic.