The basic definition
If one prime is followed by the next prime, the difference between them is a prime gap. For example, the gap between 11 and 13 is 2, while the gap between 23 and 29 is 6. Later on, the gap between 89 and 97 is 8. Prime gaps measure spacing rather than primality itself, so they are one of the cleanest ways to talk about how primes are distributed along the number line. They let you ask not just whether primes exist, but how tightly or loosely they cluster as you move through larger ranges.
Small gaps and large gaps tell different stories
A small gap shows that two consecutive primes land unusually close together. A larger gap shows a longer stretch of composite numbers between one prime and the next. Both are important. A gap of 2 gives you twin primes, a gap of 4 or 6 still shows close clustering, and larger gaps remind you that prime spacing becomes increasingly uneven as numbers grow. Looking at both small and large gaps helps prevent the false idea that primes either stay close forever or spread out smoothly in a simple pattern.
Twin primes are the gap-2 case
Twin primes are the smallest nontrivial example of a prime-gap pattern. When two consecutive odd primes differ by 2, they form a twin-prime pair. Examples include (11, 13), (17, 19), and (29, 31). That is why studying prime gaps naturally leads to the twin prime conjecture: the conjecture is asking whether this smallest recurring odd-prime gap appears infinitely many times.
Why gaps tend to grow on average
As numbers get larger, primes become less frequent on average, so larger gaps become more common. This does not mean small gaps disappear forever. It means the overall spacing picture becomes more uneven. You should expect more room between many consecutive primes at large scales, while still allowing special close pairs to keep appearing here and there. On this site, that distinction matters because visible examples in a finite range are observations, not proofs about what must happen forever. The average trend toward larger gaps is real, but the local behavior remains jagged rather than smooth.
Why bounded gaps matter
A bounded-gap theorem says that some fixed finite prime gap occurs infinitely often. That is a powerful statement because it proves recurring close proximity between primes at arbitrarily large scales. Zhang's result and the work that followed show that primes do not drift apart without ever coming close again. But bounded gaps still do not settle the special gap-2 case. The theorem-level fact is that some bounded gap repeats infinitely often; the unproved conjectural claim is that the exact gap 2 also repeats infinitely often.
How this site lets you inspect gaps
Analysis is the best place to study gap structure directly because it summarizes repeated spacing across a chosen range. Explorer helps when you want exact examples and exact neighboring primes, while the Lab helps when you want to see clusters and separation before reading structured summaries. The twin-primes page, the Zhang page, and the conjecture page then connect those visible gap patterns back to the broader mathematical story.