I assume the articles didn't bother to state that because it isn't particularly relavent to what they are discussing and they probably consider it obvious. (:

Of course the bounds are not accurate to a "distance" of around 1 or 2! No such bound can ever be more accurate than the "after P try P+2" idea (or else it would be incorrect) or even equally as accurate (or else it would be exact and constitute a closed formula for computing primes).

Ah! Perhaps you aren't aware that...

No matter how large of numbers you deal with, you can find (P such that) P and P+2 that are both prime and you can find arbitrarily large D such that (there is a P where) P and P+D are adjacent primes (as I recall, the proofs of these aren't even very complicated, involving N! with +1 and/or -1 inserted here and there).

That is, even extremely large adjacent primes can be as close together as 2 or very far apart. The theorems you've been reading put bounds on how big you have to make P before you can get D to be a desired size.

(updated)

                - tye

In reply to Re^4: Finding the next larger prime. (conclusions) by tye
in thread Finding the next larger prime. by BrowserUk

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