What a prime gap is
A prime gap is the difference between one prime and the next prime after it. If the primes are 11 and 13, the gap is 2. If the primes are 23 and 29, the gap is 6. Prime-gap language focuses on spacing between consecutive primes.
Why this distinction helps
This page is a clarification bridge. It explains the difference between talking about the distance between consecutive primes and talking about particular pairs of primes that fit a named pattern. That distinction makes several other pages on the site easier to read correctly.
What a prime pair is in this site's context
A prime pair is a pair of primes being discussed as a recognizable pattern. On this site, the most important example is a twin-prime pair: two primes that differ by 2. In that sense, a prime pair is about a named relationship, while a prime gap is about a measured spacing value.
Why twin primes are a special case rather than the whole story
Twin primes are one especially famous prime-pair pattern, but prime-gap language is broader. Every pair of consecutive primes has a gap, but not every pair belongs to a named pattern people focus on. That is why the twin-prime story sits inside the larger study of prime gaps rather than replacing it.
A concrete comparison
Consider the primes 11, 13, 17, and 19. The pair (11, 13) is a twin-prime pair, and so is (17, 19). The gap from 13 to 17 is 4, but that gap is not itself a twin-prime pair. This is a good example of why gap language and pair language should not be collapsed into one thing. One is a spacing measurement, the other is a pattern name attached to a pair.
Why people blur these ideas together
The confusion is understandable because twin primes are literally the gap-2 case. So one page may talk about pairs and another about gaps while pointing to the same examples. But once you move into bounded gaps, Analysis summaries, or broader spacing questions, the distinction becomes important. Gap language supports the larger distribution story, while pair language highlights named special configurations inside it.
Why this helps with bounded gaps and Analysis
Bounded-gap theorems say that some small prime gap recurs infinitely often, but they do not name one exact prime-pair pattern such as twin primes. The Analysis page also makes more sense when you keep this distinction clear: some tabs summarize spacing, while others help you interpret recurring pair structure. This page exists so those shifts in language feel intentional rather than confusing.
Where to go next
Use these links to keep reading or jump back into the live number views.
Read the broader gap page
Use the prime-gaps page when you want the full spacing story rather than only the distinction itself.
Return to the twin-prime pattern
The twin-primes page shows the named pair pattern that motivates this whole comparison.
Compare the bounded-gap result
This page helps you see why bounded-gap progress is close to, but not the same as, a twin-prime proof.
Use the Analysis Guide
The guide explains how the site's analysis views shift between structural and spacing questions.