Zhang proves the first finite bound on gaps between consecutive primes that recur infinitely often.
Annals of Mathematics 179(3), 1121–1174 (2014); DOI checked against Crossref.
The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.
Zhang proves that lim inf (pₙ₊₁ − pₙ) < 7 × 10⁷, refining Goldston–Pintz–Yıldırım with a stronger Bombieri–Vinogradov estimate for moduli without large prime factors.
Passage ID: prime-gaps:entry:zhang:v1
Source item: Abstract
Source record: prime-gaps:source:zhang:v1
Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.
Problem publication v7
Source assessment
Proved
Zhang: H₁ < 7 × 10⁷
Only the exact statement and passage cited here; not an independent OpenMath assessment.
Observed Oct 21, 2026
Recorded authorship
Yitang Zhang
No AI contribution is asserted by this source record.
OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.
Bounded gaps between primes
OpenMath supplies original paraphrases and links; no proof text is republished.
Source terms ↗