Claims

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2024_09_23_pratt: Pratt (2024, refereed 2025) proves that a uniform quantitative prime tuples conjecture implies that the sum over n of omega(n)/t^n is irrational for every integer t at least 2, the problem being the case t = 2.

2025_12_01_tao_teravainen: Tao and Teräväinen (arXiv, December 2025) prove unconditionally that the sum over n of omega(n)/2^n, which equals the sum over primes p of 1/(2^p - 1), is irrational, answering the question yes.

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