OpenAI reports positive lower density of large prime gaps

For every fixed C>0, a positive lower proportion of consecutive prime gaps pₙ₊₁−pₙ exceed C log pₙ.

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Understanding the problem

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For every fixed C>0, a positive lower proportion of consecutive prime gaps pₙ₊₁−pₙ exceed C log pₙ.

Why it matters

If correct, changes the frequency known for large consecutive prime gaps, beyond existence of isolated examples.

What counts as progress

Do gaps above every fixed multiple of log p occur at positive lower density?

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