Prime Number Checker
Calculation
Checks for divisibility by numbers up to the square root of the input.
Understanding Prime Numbers
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Numbers greater than 1 that are not prime are called composite numbers (e.g., 4, 6, 8, 9). The number 1 is considered neither prime nor composite. Examples of prime numbers include 2, 3, 5, 7, 11, 13, and so on.
Prime numbers have fascinated mathematicians since ancient times. Euclid's Elements (around 300 BC) contains fundamental theorems about primes, including the proof that there are infinitely many prime numbers. The Sieve of Eratosthenes, another ancient Greek contribution, provides a simple algorithm for finding all primes up to a specified limit. The study of prime numbers forms a major part of number theory.
Prime numbers are not just mathematical curiosities; they are the fundamental building blocks of integers (Fundamental Theorem of Arithmetic). They also play a crucial role in modern cryptography, particularly in public-key encryption systems like RSA, where the difficulty of factoring large numbers into their prime components underlies the security of the system. This calculator checks if a given number is prime, typically by trial division up to the square root of the number.