Prime Numbers

Basics

Prime numbers are fundamental to mathematics, serving as the building blocks for all natural numbers. Gary Arndt explains that a prime number is a number only divisible by itself and one, making it one of the simplest yet most intriguing concepts in mathematics. Despite their simplicity, prime numbers remain central to many unsolved problems in mathematics 1.

   

History

Prime numbers have been known since antiquity, with the earliest references found in ancient Egyptian texts dating back to 1550 BC. Gary mentions that the Greek mathematician Euclid was the first to explicitly discuss prime numbers and proved that there are infinitely many of them 1.

   

Theorems

Euclid's theorem, which proves the infinitude of prime numbers, is a cornerstone of number theory. Gary illustrates this by showing that multiplying all known primes and adding one results in a new prime number. He also explains the fundamental theorem of arithmetic, which states that every number can be broken down into prime factors, highlighting the essential role of primes in mathematics 2.