[xerula]

No, arbitrarily large gaps between prime numbers exist. But there are no efficient methods for locating gaps of a particular length. The largest gap for which the end primes are known, so far, is of length 337,446.

The recent work summarized on the linked page proves something else, namely that there are infinitely many pairs of prime numbers separated by only 388,284. The goal is to get that number down to two and to prove the twin prime conjecture. (In your interpretation this would be like saying every prime is within 2 of another prime, which is obviously false.)