Hidden In The Primes

Arithmetic sequences turn up in the deepest corners of math. In 2004, Ben Green and Terence Tao proved something striking about prime numbers: within the primes you can find evenly spaced runs of any length you ask for — 3 in a row, 10 in a row, a thousand in a row.

Actually finding long ones is brutally hard. The longest such run discovered so far has 27 terms, each a prime, each the same fixed gap from the last. The proof guarantees they exist; the search for them is its own marathon.