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arXiv:1806.02250math.NT

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$(x)$.

arXiv comments
Theorem 1.2 was substantially improved, causing Section 4 to be completely re-written. 14 pages
Journal reference
Proceedings of the American Mathematical Society, Series B, 6 (2019), 1-14
DOI
doi:10.1090/bproc/40
Subjects
math.NTNumber Theory

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  1. Graduate Student’s Side Project Proves Prime Number Conjecture 1 comment

    • For anyone interested in a more technical summary of the some of the main ideas: Problem Statement The Erdos conjecture that all primitive sets S satisfy f(S) <= f(PRIMES), where f(S) = sum_{s} (1/(s log s)) and PRIMES is the set of all primes. Definitions Define A_q to be a…

      dragon96View on HNParent context

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