Informal proof that for a prime p >=5, p²-1 must be a multiple of 24.

p²-1 = (p-1)(p+1)

p-1, p, p+1 are three consecutive integers. One of them must be divisible by 3 - and it can't be p, because p is prime. So either p-1 or p+1 is a multiple of 3.

Also, p is odd, so p-1 and p+1 are both even - and one or the other must be divisible by 4. One is a multiple of 2, the other of 4.

So the product of p-1 and p+1 has factors of 2, 3 and 4, and must be a multiple of 2*3*4 =24.

@whitequark

I absolutely detest SemVer because it has no way of doing graceful deprecation, which arises because it conflates implementation and interface.

A library that wants to do graceful deprecation will have three releases, A, B, and C, where B introduces a new API and C removes the old one. C is a breaking change for anything coming from A. C is a breaking change for anything using B and not moving to the new interfaces.

You really want a set of SemVers, for each interface you support. So you actually have something like:

• A: {1.0}
• B: {1.1, 2.0}
• C: {2.1}

I have never seen a system using SemVer that supports this. You can kind-of do it with UNIX SONAME and symlinks, where A has symlinks names libfoo.so.1, libfoo.so.1.1, and then B has symlinks named libfoo.so.2, libfoo.so.2.0, libfoo.so.1, libfoo.so.1.1 and libfoo.so.1.0, but I’ve never seen it done.