It's well known that an infinite number of monkeys will eventually produce the works of Shakespeare. However my thesis is that this formulation is naive, and we can in fact establish a far lower bound. Proof: William Shakespeare, a monkey, produced the works of Shakespeare. Therefore the number of monkeys needed to produce the work of Shakespeare is no greater than the number of primates who lived between Altiatlasius koulchii (57 million years ago) and 1610 CE. Roughly how many monkeys is that?