I'm reading up on prime pairs, and I had a question... I can't seem to find an answer to this anywhere, and the wikipedia list of prime types is enormous! Afraid I missed it when going through it.
I know that many primes come in twin, cousin or sexy pairs (or sexy triplets, etc). Where can I find a list of primes that are NOT 2, 4, or 6 units higher/lower than another prime? :) Is it called anything specific?
Thanks!
These are just typical primes. No reason to give them a name because the majority of primes are of this "form" (and it's not so much a form as it is the absence of a form). Upper bound sieve theory shows that the number of primes up to $x$ which are twin/cousin/sexy is at most a constant times $\frac{x}{(\log x)^2}$, and it is conjectured that this is actually also the correct lower bound. Meanwhile, the number of primes up to $x$ is asymptotic to $\frac{x}{\log x}$, so the primes described in your question constitute a fraction of $1 -\frac{C}{\log x}$ of all primes. As $x$ grows very large this fraction gradually approaches 100% of primes; there is really nothing notable about these primes.