Sure. {n, n + 2, n + 4} is a 3-tuple that is not admissible: One of n, n + 2, and n + 4 will always be divisible by three, so the tuple has no chance to ever re

Sure. {n, n + 2, n + 4} is a 3-tuple that is not admissible: One of n, n + 2, and n + 4 will always be divisible by three, so the tuple has no chance to ever represent three prime numbers for one value of n. (Except for n = 3.) Conversely, {n, n + 2, n + 6} is an admissible 3-tuple. There's no fixed integer that will always divide at least one of n, n + 2, and n + 6, so we believe that there are infinitely many n for which n, n + 2, and n + 6 are all prime.