Where are prime numbers used in nature?

Could you elaborate on the instances where prime numbers find their place in the intricate tapestry of nature? I'm particularly intrigued by how these mathematical wonders manifest themselves beyond the realm of abstract calculations. Are there any fascinating examples that demonstrate their integral role in the natural world, perhaps in the patterns of plant growth, the structure of animal populations, or even in the vastness of the cosmos? I'm eager to understand the profound connections between these seemingly disparate realms of mathematics and nature.