[Verse 1] Euclid had a question burning in his mind Are there endless primes or just a finite kind? He said suppose we caught them all inside a cage Every prime number written on a page [Pre-Chorus] Two and three and five and seven All the primes we think we know But here's the trick that gets us closer To the truth we need to show [Chorus] Multiply them all together, add just one Watch the escape artist work, the deed is done Either it's a brand new prime we've never seen Or it's divisible by one that's been unseen No matter how tall the walls, there's always more The primes will find a way to break down every door They cannot be corralled, they're infinite and free The escape artist proves it for eternity [Verse 2] Take your list of captured primes, however long Multiply the whole collection, nothing's wrong Add a single one and see what you have made A number that escapes your prime blockade [Pre-Chorus] It can't divide by any prime you caught before The remainder's always one, that's what we know for sure So either it's prime itself or has a factor That wasn't in your list, mathematical actor [Chorus] Multiply them all together, add just one Watch the escape artist work, the deed is done Either it's a brand new prime we've never seen Or it's divisible by one that's been unseen No matter how tall the walls, there's always more The primes will find a way to break down every door They cannot be corralled, they're infinite and free The escape artist proves it for eternity [Bridge] Constructive contradiction is the key Assume the opposite and you will see The logic leads us to a clear conclusion Finite primes create their own confusion [Final Chorus] Multiply them all together, add just one Watch the escape artist work, the deed is done Every wall you build, they'll climb right over The infinitude of primes, the great discoverer They cannot be corralled, they're infinite and free The escape artist proves it for eternity [Outro] No cage can hold them all There's always one more prime to call The numbers climb over every wall Infinite primes, they never fall
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