Sets of prime numbers satisfying a divisibility condition

P. Erdős, Anthony B. Evans

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We study sets P of k primes that satisfy the condition gcd(Π A - Π B, Π P) = 1 whenever A and B are disjoint non-empty subsets of P. It is known that such sets of primes exist for all positive integers k. It is of interest to know the asymptotic behavior of nk, the smallest natural number that is the product of k such primes. In this paper we derive asymptotic bounds for nk.

Original languageEnglish
Pages (from-to)39-43
Number of pages5
JournalJournal of Number Theory
Volume61
Issue number1
DOIs
Publication statusPublished - Nov 1996

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Divisibility
Prime number
Natural number
Disjoint
Asymptotic Behavior
Integer
Subset

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Sets of prime numbers satisfying a divisibility condition. / Erdős, P.; Evans, Anthony B.

In: Journal of Number Theory, Vol. 61, No. 1, 11.1996, p. 39-43.

Research output: Contribution to journalArticle

Erdős, P. ; Evans, Anthony B. / Sets of prime numbers satisfying a divisibility condition. In: Journal of Number Theory. 1996 ; Vol. 61, No. 1. pp. 39-43.
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