[Verse 1] Every number has a story deep inside More than meets the eye at first glance Like atoms building molecules so wide Numbers have their own atomic dance Start with any integer you find Greater than one in the number line Break it down with factors you can see There's a pattern waiting to be free [Chorus] Every number breaks down uniquely Into primes and only primes Like a molecular formula clearly Shows the elements every time Two times three times five times seven Building blocks from number heaven Fundamental theorem's the key Unique prime factorization, you and me [Verse 2] Primes are elements, pure and clean Two and three and five so bright Composites are compounds that we've seen Made of primes that multiply just right Strong induction proves they all exist Every number has its prime breakdown No exceptions on this numbered list Every integer can be written down [Chorus] Every number breaks down uniquely Into primes and only primes Like a molecular formula clearly Shows the elements every time Two times three times five times seven Building blocks from number heaven Fundamental theorem's the key Unique prime factorization, you and me [Bridge] Euclid's lemma shows us why it's true If a prime divides a product clean Then it must divide one factor through Uniqueness proved by this ancient scheme Like a periodic table made of numbers Primes are elements that never slumber Composites are the compounds that they make Arithmetic's foundation for our sake [Chorus] Every number breaks down uniquely Into primes and only primes Like a molecular formula clearly Shows the elements every time Two times three times five times seven Building blocks from number heaven Fundamental theorem's the key Unique prime factorization, you and me [Outro] Numbers are atomic, pure and true Prime factorization sees us through The fundamental theorem lights the way Mathematics' DNA on display
← Infinitude of Primes (The Inexhaustible Supply) | Fermat's Little Theorem (The Cycling of Powers) →