[Verse 1]
A prime is special, greater than one
Divisible by itself and one, that's all it's done
Two, three, five, seven, eleven in the line
These building blocks are truly divine
But what about the numbers in between?
There's something magical we haven't seen
[Chorus]
Every number breaks apart
Into primes, that's just the start
Unique factorization, it's the fundamental way
Two to the third times five times seven
Makes two-eighty, mathematical heaven
The atoms of numbers, they never decay
[Verse 2]
Take any number bigger than one
If it's prime already, then we are done
If it's composite, split it in two
Each piece breaks down, that's what they do
Strong induction proves they all fall
Into prime pieces, one and all
[Chorus]
Every number breaks apart
Into primes, that's just the start
Unique factorization, it's the fundamental way
Two to the third times five times seven
Makes two-eighty, mathematical heaven
The atoms of numbers, they never decay
[Bridge]
But wait, there's more to this story told
Uniqueness makes this theorem bold
Euclid's Lemma shows the way
If p divides a times b today
Then p divides a or p divides b
This uniqueness sets the integers free
[Verse 3]
In other worlds where numbers play
Like Z root minus five they say
This magic fails, the atoms split
Unique factoring doesn't fit
But here in our integer home
Each number has one way alone
[Chorus]
Every number breaks apart
Into primes, that's just the start
Unique factorization, it's the fundamental way
Two to the third times five times seven
Makes two-eighty, mathematical heaven
The atoms of numbers, they never decay
[Outro]
Primes are atoms, numbers are molecules
Following arithmetic's golden rules
One structure only, that's the key
The Fundamental Theorem sets us free