All I meant by "special case" was that "mod 30" isn't the whole story -- more like the most significant correction on top of what the OP said, with other smaller corrections possible, and the entire set of corrections being described by the k-tuple conjecture.
It's amazing how people can be picky and negative on HN. Someone positive would instead congratulate me for making the gist of what the prime k-tuple conjecture says about the biases easily understandable. Oh well.
So you are making comments about pure mathematics. If you want to use imprecise language and not be corrected, you should probably go write a book review or something. In math, precise language and correcting someone or forcing someone to give justification for something is expected and completely usual. It would be bizarre when talking to a mathematician about mathematics if they didn't immediately correct or demand clarification and justification when you say something vague or incorrect or unjustified.
It's amazing how people can be picky and negative on HN. Someone positive would instead congratulate me for making the gist of what the prime k-tuple conjecture says about the biases easily understandable. Oh well.