The Erdős conjecture for primitive sets

Lichtman, Jared; Pomerance, Carl

doi:10.1090/bproc/40

The Erdős conjecture for primitive sets
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by Jared Duker Lichtman and Carl Pomerance HTML | PDF

Proc. Amer. Math. Soc. Ser. B 6 (2019), 1-14

Abstract:

A subset of the integers larger than 1 is primitive if no member divides another. Erdős proved in 1935 that the sum of $1/(a\log a)$ for $a$ running over a primitive set $A$ is universally bounded over all choices for $A$. In 1988 he asked if this universal bound is attained for the set of prime numbers. In this paper we make some progress on several fronts and show a connection to certain prime number “races” such as the race between $\pi (x)$ and $\mathrm {li}(x)$.

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