Prime Number Checker

Check if any number is prime. Find prime factors, nearest primes, and generate lists of prime numbers.

Enter a Number

How to Use the Prime Number Checker

Enter any positive integer and click Check to determine if it is prime. The tool will show whether the number is prime or composite, list its prime factors if composite, and show the nearest prime numbers above and below it.

Why Prime Numbers Matter

Prime numbers are fundamental to mathematics and have critical applications in cryptography, computer science, and number theory. Modern encryption systems like RSA rely on the difficulty of factoring large numbers into their prime components. Understanding primes helps in areas from data security to algorithm optimization.

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. The first prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Is 1 a prime number?

No. By definition, a prime number must be greater than 1. The number 1 is neither prime nor composite — it is considered a unit.

Is 2 a prime number?

Yes, 2 is a prime number. It is the only even prime number, since every other even number is divisible by 2.

How do you check if a large number is prime?

For small numbers, you can check divisibility up to the square root. For very large numbers, probabilistic tests like the Miller-Rabin test are used. This calculator checks all factors up to the square root, which works well for numbers up to several million.