Erdős problem 287 · problems.science

Let $k\geq2$ . Is it true that, for any distinct integers $1 < n_1 < \cdots < n_k$ such that $\sum_{i=1}^k \frac{1}{n_i} = 1$ , we must have $\max(n_{i+1} - n_i) \geq 3$ ?

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

287.lean

Retained formal statement4 of 5

For all large $N$ , there exists a prime $p \in [N, 2N]$ such that $\frac{p+1}{2}$ is also prime.

This is an open conjecture. If true, it would imply erdos_287 for all but at most finitely many exceptions (see erdos_287.variants.prime_conjecture_implies).

FormalConjectures/ErdosProblems/287.leanErdos287.erdos_287.variants.prime_conjecture1 lineExact file

1True ↔ ∃ N₀, ∀ (N : ℕ), N₀ ≤ N → ∃ p, Nat.Prime p ∧ N ≤ p ∧ p ≤ 2 * N ∧ Nat.Prime ((p + 1) / 2)

OpenStatement only, no proof

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