### A Sonnet to Prove the Infinitude of Primes

**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!