Erdős problem 218 · problems.science

There are infinitely many indices $n$ such that the prime gap at $n$ is equal to the prime gap at $n+1$ . This is equivalent to the existence of infinitely many arithmetic progressions of length $3$ , see erdos_141.variants.infinite_three.

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FormalConjectures/ErdosProblems/

218.lean

Retained formal statement1 of 3

The set of indices $n$ for which a prime gap is preceded by a larger or equal prime gap has a natural density of $\frac 1 2$ .

FormalConjectures/ErdosProblems/218.leanErdos218.erdos_218.variants.ge1 lineExact file

1{n | primeGap (n + 1) ≤ primeGap n}.HasDensity (1 / 2)

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