The preliminary draft states H₁ ≤ 212 and explains the analytic and exact rational calculations. Its appendix reports a formal deduction with analytic and variational hypotheses.
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The preliminary draft states H₁ ≤ 212 and explains the analytic and exact rational calculations. Its appendix reports a formal deduction with analytic and variational hypotheses.
Replaces an earlier passage. View versioned records →
Passage ID: prime-gaps:entry:212:v2
Source item: 212
Source record: prime-gaps:source:212:v2
Replaces passage: prime-gaps:entry:212: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
Historical bounds recorded in the paper
Zhang, Maynard and Stadlmann bounded-gap results.
Observed Oct 13, 2026
Bound
H₁
Source assessment
Proved
The preliminary draft proves H₁ ≤ 212
The paper’s unconditional assertion; formalization assumes analytic and variational inputs.
Observed Oct 13, 2026
Bound
H₁
Source assessment
Proved
Historical bounds recorded in the paper
Zhang, Maynard and Stadlmann bounded-gap results.
Observed Oct 13, 2026
Bound
H₁
Source assessment
Proved
Historical bounds recorded in the paper
Zhang, Maynard and Stadlmann bounded-gap results.
Observed Oct 13, 2026
Bound
H₁
Research activity
The 212 certificate is reported in the paper
The appendix credits AxiomProver with a Lean deduction that assumes five equidistribution estimates, bilinear Bombieri–Vinogradov, Harman decomposition and the variational certificate.
No exact public commit or declaration for that 212 certificate was established by this source check; it is shown as a paper-reported artifact, not a fabricated formal-code link.
History
Maynard introduces a multidimensional sieve
History
Stadlmann lowers the mathematical bound to 240
History
A preliminary draft reaches 212
History
Zhang establishes bounded gaps
Question
How small can prime gaps be?
Further reading
Read the mathematical argument; inspect its Claim for assessment and scope.
Recorded authorship
François Charton · Letong Hong · Kenny Lau · Ken Ono · Guillaume Remy · Ho Chung Siu · Ashvin A. Swaminathan · Jesse Thorner · Yunzhou Xie
François Charton, Letong Hong, Kenny Lau, Ken Ono, Guillaume Remy, Ho Chung Siu, Ashvin A. Swaminathan, Jesse Thorner, Yunzhou Xie
The nine authors supply the mathematics, building on Julia Stadlmann and earlier sieve work. AxiomProver is credited with generating a formal deduction; this is not a claim that the model independently discovered the mathematical bound.
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A new bound for small gaps between primes
Bounded gaps between primes: the 212 bound
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