OPENHARDnumber theoryprimes
Is it true that $\sum_{n=1}^{\infty}(-1)^n\frac{n}{p_n}$ converges, where $p_n$ is the sequence of primes?
Notes: Tao proved convergence assuming a strong form of the Hardy-Littlewood prime tuples conjecture. Zhang's work on bounded gaps implies a related series does not converge.
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