Problem Statement
Does the series $\sum_{n=1}^{\infty}(-1)^n\frac{n}{p_n}$ converge?
Categories:
Number Theory Primes
Progress
Major Progress
Terence Tao: Proved convergence assuming a strong form of the Hardy-Littlewood prime tuples conjecture.
Sawhney: Demonstrated absolute convergence for weighted variants with exponent $c > 2$.
Source: erdosproblems.com/15 | Last verified: January 13, 2026