Proved. Tao and Teräväinen [TaTe25] prove unconditionally that the series, which equals $\sum_p 1/(2^p-1)$ and is thus the case of Problem 257 with the primes as the infinite set, is irrational; Pratt [Pr24] had proved it under a uniform quantitative prime tuples conjecture. The accepted claim is Tao and Teräväinen; the conditional result is Pratt.