Quotes About Factorization

Primes are the important main ingredient of numbers, for every number is either a prime or a product of primes.

Fundamental to understanding the arithmetic of Rd is the following question: which ordinary prime numbers p are irreducible elements of Rd and which ones factorize as products of irreducible elements in Rd? We will see shortly that if a prime number does factorize in Rd, it must be expressible as the product of precisely two irreducible factors.

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.

Primes are the atoms of the number system: every whole number is a product of primes.