Prime Number Checker

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, 29...

No, 1 is not considered a prime number. By definition, a prime number must be greater than 1 and have exactly two distinct positive divisors (1 and itself). The number 1 only has one divisor.

Yes, 2 is the only even prime number. It's divisible only by 1 and 2. All other even numbers are divisible by 2, so they can't be prime.

Prime numbers are fundamental in mathematics and crucial for modern cryptography. RSA encryption, used to secure online transactions, relies on the difficulty of factoring large numbers into their prime components.

There are infinitely many prime numbers, as proven by Euclid around 300 BCE. No matter how large a prime you find, there's always a larger one. However, primes become increasingly rare as numbers get larger - only about 4% of numbers near one million are prime.

As of 2024, the largest known prime is 2^82,589,933 - 1, discovered in 2018. This Mersenne prime has 24,862,048 digits. New record primes are discovered through the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project.

For small numbers, check divisibility by primes up to the square root. For example, to check if 97 is prime, test primes up to √97 ≈ 9.8 (so test 2, 3, 5, 7). Since 97 isn't divisible by any of these, it's prime.

Twin primes are pairs of prime numbers that differ by 2, like (3,5), (5,7), (11,13), (17,19), and (29,31). The Twin Prime Conjecture suggests infinitely many exist, but this remains unproven despite centuries of mathematical research.

Every composite number can be expressed uniquely as a product of primes (Fundamental Theorem of Arithmetic). Prime factorization is used in simplifying fractions, finding GCD/LCM, cryptography, and solving many mathematical problems. For example, 60 = 2^2 × 3 × 5.