Introduction to Prime Numbers and Number Theory
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. Integers greater than 1 that are not prime are called composite numbers. The number 1 is unique—it is considered neither prime nor composite. Prime numbers are the fundamental building blocks of integers, a concept formalized by the Fundamental Theorem of Arithmetic, which states that every integer greater than 1 is either prime itself or can be represented as a unique product of prime numbers.
The study of prime numbers dates back to ancient Greek mathematicians, such as Euclid, who proved that there are infinitely many prime numbers. In modern computer science, prime numbers are of paramount importance. They form the basis of cryptography algorithms—such as RSA encryption—which secure online banking, digital signatures, and web traffic by utilizing the difficulty of factoring products of extremely large prime numbers.
This calculator provides tools to study primes. By entering an integer, the solver performs a trial division primality test, finds its divisors, locates the next and previous prime numbers, and generates lists of primes in a user-defined range using efficient sieve algorithms.