Prime numbers had been objects of fascination, for both mathematicians and artists, since the time of Euclid. This article explores the links between prime numbers and poetry. We start with a selection of poems celebrating the mathematical properties of these enigmatic and unpredictable integers and their impact on those who explore them. We then turn our attention to poetry reflecting cultural aspects associated with prime numbers, from the use of the concept of primality as a metaphor for the mysteries of life and human behavior to the inclusion of specific prime numbers in poems for the symbolic personal and cultural values these numbers acquired through history. We conclude with a sample of poems highlighting the role prime numbers and their properties play in the aesthetics of poetry, in particular their contribution to the structure of poems. We also include references to additional sources of prime number poetry, and a brief discussion on the uses of such poetry in the mathematics classroom.