Prime numbers, with their unique indivisibility, form the foundation of number theory and hold key roles in cryptography and computer science, making them a fascinating and vital focus in ongoing mathematical research.
Numbers with only two factors are called prime numbers. Prime numbers are natural numbers greater than 1 that cannot be formed by multiplying two smaller natural numbers. Their only factors are 1 and the number itself. This unique property distinguishes them from composite numbers, which have more than two factors.
The common characteristic among prime numbers is their indivisibility by numbers other than 1 and themselves. This fundamental property is crucial in number theory and has applications in various fields, including cryptography. Prime numbers play a central role in algorithms that secure digital communication and data encryption.
Despite their apparent randomness, prime numbers follow certain patterns, such as the distribution described by the Prime Number Theorem. Understanding prime numbers is a profound and ongoing area of mathematical research with implications for computer science, cryptography, and the foundations of mathematics.