I wasn't thinking of a formula as such. What I seem to recall is that there was some way off using knowledge derived from knowing the preceeding prime, to cut down the search space when finding the next.

I guess what comes down to is if I is prime, is there any thing in that knowledge that would help in deciding that I+2 or I+4 or I+6 etc. is or isn't prime? Is there any way of reducing the 3 .. $candidate^.5 range of divisions in order to determine it primacy or lack thereof?

I know there are some "quick" ways of determining "probable primes" eg ... though I'll admit to not understanding the formula I've seen. I thought I saw a method that used the previous known prime to achieve a similar result.

It is a unproved statement that such a formula would resolve the twin prime conjecture, although it surely sounds like that it increases the hope.

This implication can not be taken as a given, unless it is proved. We are talking about math, so be precise.