Claims

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1980_08_01_erdos_ruzsa: Erdős and Ruzsa (J. Number Theory, 1980) state without proof that sets any m of whose elements are coprime leave at least the prime-set minimum minus o(x) integers unsifted, reducing the asymptotic question to the prime case.

1987_01_01_hildebrand: Hildebrand's Corollary 1 (Acta Arith. 1987): among sets of primes with reciprocal sum at most K, the least proportion of integers up to x divisible by none is rho(e^K) up to a power of log x; the problem's prime case.

2026_01_23_chojecki: Chojecki proves that for a reciprocal budget C at most log 2 the least proportion of unsifted integers is 1 - C + o(1), attained up to o(1) by the largest primes; a note posted to the site's thread in January 2026, credited.

2026_02_20_tao: Tao proves that a pairwise coprime set with reciprocal sum at most C leaves at least (rho(e^C) + o(1)) N integers up to N unsifted, so the prime tail is optimal up to o(N) and the problem, read up to o(N) as the site reads it, is settled; a February 2026 write-up, credited by the site.

2026_02_23_chojecki: Chojecki's write-up claiming that for every budget C above log 2 each near-minimizing pairwise coprime set is close in reciprocal sum to a tail of primes; posted to the site's thread in February 2026, reviewed by no one.

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