[Verse 1] Every number holds a secret code within its bones A recipe written in the language of primes alone Like chemists cracking molecules down to their core We break apart integers to see what lies in store Two times three times five reveals the DNA Of thirty's hidden architecture on display [Chorus] Prime factorization, nature's preservation Every number breaks down one perfect way Like the periodic table, elements are stable Primes are the atoms that will never decay Unique decomposition, mathematical tradition Two raised to fourth times three tells the whole story [Verse 2] Strong induction proves that every number must divide Into prime components that cannot hide Start with two, assume it works for all below Then prove the next one follows suit, watch the pattern grow Either prime itself or splits in two clean parts Each piece factors further, that's where the proof starts [Chorus] Prime factorization, nature's preservation Every number breaks down one perfect way Like the periodic table, elements are stable Primes are the atoms that will never decay Unique decomposition, mathematical tradition Two raised to fourth times three tells the whole story [Bridge] But wait, what if two different paths exist? Euclid's Lemma shows that can't persist If prime divides a product, then it must Divide one factor, this we absolutely trust Contradiction proves there's only one true form Each number's signature, forever the norm [Verse 3] Twelve is two squared times three, no other way Eighteen breaks to two times three squared, clear as day Like water's H-two-O or salt's sodium chloride Each composite number has its prime recipe guide The molecular formula of the number world Where mathematical elements are precisely unfurled [Chorus] Prime factorization, nature's preservation Every number breaks down one perfect way Like the periodic table, elements are stable Primes are the atoms that will never decay Unique decomposition, mathematical tradition This is the theorem that rules all of number theory [Outro] Every integer, every count you'll ever see Has one true breakdown, guaranteed to be The fundamental theorem, carved in mathematical stone Each number's prime identity stands alone
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