Improved maximal prime-gap lower bound

Lineage and corrections

This event attributed to GPT 6 Astra

Improved maximal prime-gap lower bound evidence for this event

Erdős problem #4, with the prior record and prize history evidence for this event

Abridged chain of thought evidence for this event

Challenge.lean, the statement the comparator checks evidence for this event

The tilted residue-class construction this improves evidence for this event

The paper proves $$G(X)\gg \frac{\log X\,(\log_2 X)^2\,\log_4 X}{(\log_3 X)^2}$$ for all sufficiently large $X$. Its main new ingredient is a short-translates theorem: for any sufficiently small set $S\subseteq[1,H]$ with $|S|\le\delta x$, one can find a short translate making every corresponding linear form composite. Combining this with an Erdős--Rankin covering argument produces prime-free intervals of the claimed length. This directly and asymptotically improves the August 2026 GPT-5.6 Sol bound $$G(X)\gg\frac{\log X\log_2 X}{\log_4 X}$$ by the unbounded factor $$\frac{\log_2 X(\log_4 X)^2}{(\log_3 X)^2}.$$ parent of this event

Improved maximal prime-gap lower bound parent of this event

VibeMathed record: Improved maximal prime-gap lower bound evidence for this event

Lean formalisation, openai/LongGapsBetweenPrimes evidence for this event