A Sonnet to Prove the Infinitude of Primes

To prove there is an infinite amount
Of primes. Assume we know all primes, assume
A largest prime, a prime that caps the count,
Then step through from that premise to its doom.

If it were true then you could multiply
That prime with every other prime and add
The unit to the product – and thereby
Obtain a number larger than we’ve had,

Which couldn’t be divided by primes known,
And thus is either product of a tandem
Of primes not known, or prime itself unknown
A paradox! quod erat demonstrandum.

This proof I wrote in rhyme with tongue in cheek
Was given by good Euclid in old Greek!