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What is a Prime Number?

A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, a prime number has exactly two distinct positive divisors: 1 and itself.

The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47...

The number 2 is the only even prime number. All other even numbers are divisible by 2 and therefore not prime.

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Primality Testing

This tool uses trial division up to the square root of the number. For a number n, if no integer from 2 to √n divides it evenly, then n is prime. The algorithm skips even numbers and multiples of 3 for efficiency.

The Batch Check mode lets you test many numbers at once, while Find in Range uses the Sieve of Eratosthenes to efficiently find all primes within a given interval.

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Prime Number Facts

• 2 is the only even prime number
• There are infinitely many prime numbers (proved by Euclid around 300 BC)
• The largest known prime (as of 2024) has over 41 million digits
• Prime numbers are fundamental to modern cryptography (RSA, Diffie-Hellman)
• The Prime Number Theorem states that primes become less frequent as numbers grow, approximated by n/ln(n)

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