### 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 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

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

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

Research output: Contribution to journal › Article

*Journal of Number Theory*, vol. 61, no. 1, pp. 39-43. https://doi.org/10.1006/jnth.1996.0135

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TY - JOUR

T1 - Sets of prime numbers satisfying a divisibility condition

AU - Erdős, P.

AU - Evans, Anthony B.

PY - 1996/11

Y1 - 1996/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030295876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030295876&partnerID=8YFLogxK

U2 - 10.1006/jnth.1996.0135

DO - 10.1006/jnth.1996.0135

M3 - Article

VL - 61

SP - 39

EP - 43

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -