Thanks to my supporters on Patreon! Get early access to videos and more: The recurrence R(n) = R(n - 1) + gcd(n, R(n - 1)) generates primes. But why? It turns out it's essentially implementing trial division in disguise. Previous video on this sequence: ---------------- Reference: Eric Rowland, A natural prime-generating recurrence, Journal of Integer Sequences 11 (2008) (13 pages). ---------------- 0:00 Generating primes 1:26 Shortcut 4:42 What if 2 n - 1 is prime? 9:31 What if 2 n - 1 isn't prime? 14:46 Trial division ---------------- Animated with Manim. Music by Callistio. Audio recorded at the Lawrence Herbert School of Communication at Hofstra University. Web site: