Mathematicians have studied numbers throughout the years. They have found some interesting patterns in numbers, especially in Prime Numbers. A prime number is a number that has no factors other than itself and one. The first few prime numbers are 2, 3, 5, 7, 11, 13, and 19. It is conjectured that there is an infinite number of these numbers.One of the most well-known and important properties of prime numbers is that they cannot be evenly divided by any other number except for 1 and themselves.
This property is called the unique factorization theorem and it is an important concept in the study of number theory.
The importance of this theorem comes from its applications in public-key cryptography. One can easily generate a public key by multiplying two prime numbers together, but finding the private key to decrypt any message encrypted with this public key requires knowledge of those two prime numbers.