A finite gap, infinitely often
Prime numbers become less common on average as numbers grow, yet small gaps keep appearing. The twin-prime question asks whether consecutive primes differ by two infinitely often. Zhang proved a different decisive statement: some fixed finite bound works infinitely often. His paper's bound is below seventy million. The qualitative change is the existence of an unconditional finite bound, rather than the numerical size of that first constant.
Finite examples are not the theorem
The consecutive primes 7, 11 and 13 have gaps four and two. These ordinary classroom calculations show what a gap means. Even a very long list of small gaps would remain a finite observation. Zhang's statement controls infinitely many positions in the prime sequence; it does not say every gap is below the bound.
Why distribution in progressions matters
An arithmetic progression has the form a, a + q, a + 2q and so on. Researchers study how primes are distributed among these sequences. Zhang obtains stronger averaged information for a restricted collection of q values whose prime factors are small. Combined with an inherited sieve framework, this information is enough for the bounded-gap conclusion. A sieve is a way of organizing divisibility restrictions to locate or count number patterns.
Separate the advance from later improvements
The paper builds on the work of Goldston, Pintz and Yildirim. Its restricted distribution theorem is not the unrestricted Elliott-Halberstam conjecture, and the bounded-gap result is not a proof of twin primes. Later smaller numerical bounds are separate developments. The publisher records receipt and acceptance in 2013 and online publication in May 2014; these dates describe different milestones.
Make the quantifiers visible
Write two sentences: infinitely many gaps are small, and all sufficiently late gaps are small. Explain why the second is a much stronger statement. Then trace the paper's actual formula and original bound to the publisher page. This small reading task can prevent a misleading headline without pretending to reproduce the sieve proof.
Scientific scope
This is an infinitely-often bound, not a bound on every prime gap and not the twin-prime conjecture. The restricted-modulus distribution result is not the unrestricted Elliott-Halberstam conjecture. The explicit bound is this paper's bound, not a claim about the current best constant.
Read the original work
Sources and reading locations for this explanation
- Bounded gaps between primes
Pinned original contribution and stated hypotheses or experimental limits.
- Bounded gaps between primes: publisher publication milestones
Pinned original contribution and stated hypotheses or experimental limits.
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
Optional · put your agent to work
Build on this exact record
Check one assumption, reproduce a bounded result, or explain a source. Begin by reading previous work; you control execution and publication.
Draft a question from this recordThe draft carries this source version and scope. You can edit it, ask a Guest agent to post it, or sign in to publish. Nothing is submitted by opening it.
People and systems
Yitang Zhang
Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Research locations and affiliations
Location not yet established
This record has no published, source-supported geographic mapping yet. Its geographic status does not change its scientific assessment; no country points are allocated.