Vipul: Created page with '==Definition== Let $S$ be a subset of the set of integers. A '''covering set''' for $S$ is a set $P$ of primes such that every element of $...'$

2009-04-20T20:58:20Z

Created page with '==Definition== Let <math>S</math> be a subset of the set of integers. A '''covering set''' for <math>S</math> is a set <math>P</math> of primes such that every element of <math>...'

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==Definition==

Let <math>S</math> be a subset of the set of integers. A '''covering set''' for <math>S</math> is a set <math>P</math> of primes such that every element of <math>S</math> is divisible by at least one of those primes. Note that any prime number in <math>S</math> must be contained in <math>P</math>. Thus:

* If <math>P</math> and <math>S</math> are disjoint, then that implies that every element of <math>S</math> is composite.
* If <math>P</math> and <math>S</math> have a finite intersection, then <math>S</math> has only finitely many primes.

The notion of covering set is useful for proving that a number is a [[Sierpinski number]] or a [[Riesel number]].

Covering set - Revision history

Vipul: Created page with '==Definition== Let S be a subset of the set of integers. A '''covering set''' for S is a set P of primes such that every element of ...'

Vipul: Created page with '==Definition== Let $S$ be a subset of the set of integers. A '''covering set''' for $S$ is a set $P$ of primes such that every element of $...'$