246 Is As Close As We Can Prove Primes Get

Three, five, seven. Three prime numbers in a row, each one exactly two steps past the last -- the tightest a run of three primes can possibly be. Twin pairs like 11 and 13 keep showing up forever, so you would expect a run of three to turn up again somewhere too. It never does. Three, five, seven is the only one there will ever be, anywhere, and the reason fits in a single line: among any three numbers spaced two apart, one is always a multiple of three. This is the story of the one prime cluster that logic forbids outright -- and why the twin primes, the prime triplets, and the quadruplets right beside it are believed to run on without end. Chapters: 0:00 Three in a row 1:07 The search that comes up empty 2:13 The reason in one line 3:41 But the twins never stop 4:55 Which patterns are allowed 6:16 Cousins and a quadruplet 7:34 The rule behind the rule 8:52 How close we have come 10:10 Coda Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a...