Sets of prime numbers satisfying a divisibility condition

Paul Erdös, Anthony B. Evans

Research output: Contribution to journalArticle

1 Citation (Scopus)


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
Issue number1
Publication statusPublished - Nov 1996

ASJC Scopus subject areas

  • Algebra and Number Theory

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