[Verse 1] Imagine you've collected every prime you know Two, three, five, seven, let the listing grow Eleven, thirteen, seventeen in line Think you've caught them all? Here's Euclid's design [Chorus] Multiply them all together, add just one The number that emerges can't be done By any prime you thought you had contained The infinite spring can never be drained Constructive contradiction shows the way New primes are born from every finite tray [Verse 2] Take your prison of primes, however vast Multiply every prisoner, from first to last Add one to that product, what do you find? A rebel that slips through your perfect bind [Chorus] Multiply them all together, add just one The number that emerges can't be done By any prime you thought you had contained The infinite spring can never be drained Constructive contradiction shows the way New primes are born from every finite tray [Bridge] Either it's prime itself, expanding your cage Or factors reveal new primes on the page Every finite net has holes to explore The primes keep flowing, an endless shore [Verse 3] No collection, however grand or wide Can hold all primes locked safe inside Euclid's proof builds what seems absurd Then shows that truth through reasoning assured [Chorus] Multiply them all together, add just one The number that emerges can't be done By any prime you thought you had contained The infinite spring can never be drained Constructive contradiction shows the way New primes are born from every finite tray [Outro] The well runs deeper than you'll ever know Prime numbers in eternal overflow
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