I have to confess that most often my eyes begin to glaze over when someone starts discussing the prime numbers. However, my ears have perked up at times over the primes--maybe first when I learned of their use by Godel and second, of their links to the Riemann zeta function and related analysis. More recently I have encountered the primes when observing the simplicity/regularity of indexed expressions in certain sequences of expressions when the index is prime in contrast to those for the non-prime indices, such as for the cyclotomic polynomials (see "A tangential note" in this MO-A) and for certain colored necklaces (see this MO-Q). In the interest of stimulating interest in or a more informed appreciation of the primes for those who are not classical number theorists, I'd like to ask

**In what scenarios do the primes occur that you find of particular interest or utility outside of pure number theory?**

Anecdote: Once long ago I was quickly passing through a wing of the Getty Art Museum, the Roman villa in the Palisades in L.A.--a wing containing medieval art with its religious motifs, at that time of little interest to me. I stopped in front of a docent who was enthusiastically informing a group of the symbology underlying a painting. She posed questions that revealed the painting subtly and cleverly indicates three events in the life of Christ in what appears on the surface to be a single moment frozen in time. I now appreciate the depth of meaning in such art.

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