A natural number \(p\) is called prime if the only natural divisors of \(p\) are \(1\) and \(p\). Prime numbers are building blocks of all the natural numbers in the sense of the The Fundamental Theorem of Arithmetic: for a positive integer \(n\) there exists a unique prime factorization (or prime decomposition) \[n = p_1^{a_1}p_2^{a_2}...p_r^{a_r}.\] Today we will explore how unusual prime numbers are.
Essentially there is only one way to write an integer number as a product of prime numbers, where some of the prime numbers in the product can appear multiple times.