So is the 6k±1 rule: 6k and 6k±2 are all even, 6k±3 is divisible by 3. You can extend this further: all primes greater than 5 must take one of the forms 30k±1, 30k±7, 30k±11, 30k±13. This is much less exciting, but ... suggestive. (No, not that suggestion, that one isn't actually true.)
For a certain point of view, most of math is trivial corollaries.
For a certain point of view, most of math is trivial corollaries.
(Proof: check.)