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Erdős problem 15 · Conjectures.io
Number theory
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Erdős problem 15
Is it true that ∑n=1∞(−1)npnn converges,
where pn is the sequence of primes?
Note: In the problem statement, pn is the n-th prime, indexed such that p1=2,p2=3,….
We 0-index here to reflect how Nat.nth works.
Withdrawn 5 Aug 2026
SOURCE_MISMATCH + EXPLOITABLE (the informal problem asks for real convergence; Lean states Summable over ℚ, so failure of ℚ-summability does not establish real divergence; the counterexample exploited this domain mismatch)
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.
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