[tie_]

Isn't 4k+1/4k-1 rule trivial though?

If we take any number K=N*4 divisible by 4 and >2, that'd be an even number by definition. The two closest odd numbers on either side would be (K-3), (K-1), (K+1), (K+3). As it happens (K+3) is the same as K(-1) for the next N, and (K-3) is the same as (K+1) for the previous N. So _all_ odd numbers follow this rule.

What "4k+1 or 4k-1" says in a roundabout way is that all prime numbers (>2) are odd, which isn't much of a surprise.

[naniwaduni]

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.

(Proof: check.)

[BadOakOx]

I think this still seems trivial with a 5th grade algebra knowledge.

Additionally, for the 4k+1 / 4k-1 topic, it is just a complicated way of saying 2k+1 (as parent suggested).

[wholinator2]

Well I'm sure it looks trivial to you. But the joys of math often aren't in the difficulty but the discovery. Would your prefer it not have been stated at all, or did you just want to let us know you understood it.

As well, i think the 2k+1 thing is drastically more trivial and not at all equivalent being that all you need to know for 2k+1 is that 2k+1=odd. 4k and especially 6k take a larger generalization and different analytical method and often aren't included in the definition of the primes we learn like 2k+1 (odd) is.

[Spinnaker_]

Has anyone approached you about writing a math textbook yet? You've already got the tone perfected.