Erdős Problem #1138
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The maximal prime gap below \(x\), i.e. \(d(x) = \max_{p_n < x}(p_{n+1} - p_n)\), where \(p_n\) denotes the \(n\)-th prime.
The filter on \(\mathbb{R} \times \mathbb{R}\) corresponding to sending \(x \to \infty\) subject to \(x/2 < y < x\)
Given a pair \((x,y)\), this is the amount of primes in the interval above \(y\), of length equalling the largest prime gap before \(x\), scaled by a constant \(C\).
Attempts
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