### 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 n_{k}, the smallest natural number that is the product of k such primes. In this paper we derive asymptotic bounds for n_{k}.

Original language | English |
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Pages (from-to) | 39-43 |

Number of pages | 5 |

Journal | Journal of Number Theory |

Volume | 61 |

Issue number | 1 |

DOIs | |

Publication status | Published - Nov 1996 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Erdös, P., & Evans, A. B. (1996). Sets of prime numbers satisfying a divisibility condition.

*Journal of Number Theory*,*61*(1), 39-43. https://doi.org/10.1006/jnth.1996.0135