Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Butch Malahide

Posts: 894
Registered: 6/29/05
Re: cotpi 67 - Composite factorial plus one
Posted: Mar 8, 2013 2:55 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.