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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: cotpi 67 - Composite factorial plus one
Replies: 7   Last Post: Mar 10, 2013 4:19 PM

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Butch Malahide

Posts: 885
Registered: 6/29/05
Re: cotpi 67 - Composite factorial plus one
Posted: Mar 8, 2013 2:55 AM
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On Mar 8, 12:13 am, m...@vex.net (Mark Brader) wrote:
> > How many positive integers n are there such that n! + 1 is
> > composite?
>
> Infinitely many, or to be more specific, aleph-null.
>
> Wilson's theorem states that if p is prime, then (p-1)! + 1 is
> divisible by p.  If x > 3, then (x-1)! + 1 > x.  Therefore the
> desired property holds for all numbers n > 4 where n-1 is prime,
> and there are aleph-null of those.

Fine, but I think you mean n+1 is prime, not n-1.

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