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Number theory

Erdős 218 - infinite equal prime gap

There are infintely many indices nn such that the prime gap at nn is equal to the prime gap at n+1n+1. This is equivalent to the existence of infinitely many arithmetic progressions of length 33, see erdos_141.variants.infinite_three.

No one has attempted this yet.

Formal statement

Lean type

{n | primeGap n = primeGap (n + 1)}.Infinite

What you must prove

import FormalConjectures.ErdosProblems.«218»
import TaskSupport

namespace Bounty

theorem target : fcTypeOfName% "Erdos218.erdos_218.variants.infinite_equal_prime_gap" := by
  sorry

end Bounty

Pinned source: FormalConjectures/ErdosProblems/218.lean

Source type SHA-256
sha256:e0580853f98f842ebfd4cca33ecdcb3dd6b3e76b0df71f00bc687b73e9f7f056
Task id
fc-379fc029-variants-infinite-equal-prime-gap-b79aee4163-formalized-v1
Task commitment
sha256:20e0f838a39f365afb4aa9cc9540c907b5c91619039a42a62162f18aff2b2c48

Something wrong with this formalization?

A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.