Prime Number Checker

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. In other words, it can only be divided evenly by 1 and itself.

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

The number 1 is not considered prime. The number 2 is the only even prime number.

Interesting Facts

• There are infinitely many prime numbers (Euclid's theorem)
• 2 is the only even prime number
• All primes greater than 3 can be written as 6k±1
• The largest known prime (as of 2024) has over 24 million digits
• Prime numbers are fundamental to cryptography and computer security

Applications

• Cryptography: RSA encryption uses large prime numbers
• Hash tables: Prime-sized tables reduce collisions
• Random numbers: Linear congruential generators
• Number theory: Fundamental building blocks

Famous Primes

• Mersenne primes: Form 2^p - 1
• Twin primes: Pairs differing by 2 (e.g., 11 and 13)
• Sophie Germain primes: p where 2p+1 is also prime
• Fermat primes: Form 2^(2^n) + 1