Prime Numbers

Abstract

In this chapter, we return to a question examined in Chap. 1. It was shown there that a natural number has a unique decomposition into prime factors. Prom the standpoint of the operation of multiplying, therefore, prime numbers are the simplest elements from which we can obtain all natural numbers, similar to how we obtain them all from the number 1 using the operation of adding. From this standpoint, the interest in the collection of prime numbers is understandable. Four prime numbers are found in the first decade of natural numbers: 2, 3, 5, 7. Further, we can find prime numbers, in turn dividing each number by all previously found smaller primes to determine if it is prime. We thus find 25 prime numbers in the first century:

$$ {\text{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97}}{\text{.}} $$