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.