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arXiv · 1806.02250

The Erdos conjecture for primitive sets

Jared Duker Lichtman·Carl Pomerance
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Abstract

A subset of the integers larger than 1 is $primitive$ if no member divides another. Erdos 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 $π(x)$ and li$(x)$.

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Jared Duker Lichtman, Carl Pomerance. 2018-06-30. The Erdos conjecture for primitive sets. https://doi.org/10.1090/bproc%2F40

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