Consecutive Composite Numbers

Date: 06/07/2005 at 14:22:39
From: mundip
Subject: about consecutive composite integers

Hi -

I want to know if m > 0 (an integer) is given, then is it possible to
find m consecutive composite integers?

For example, 

  if m = 2 the numbers could be 8,9; 9,10; 14,15; 15,16; ...
  if m = 3 the numbers could be 8,9,10; 14,15,16; ...
  if m = 4 the numbers could be 24,25,26,27; 25,26,27,28; ...

and so on.  Is this possible for any value of m?

Date: 06/13/2005 at 10:11:34
From: Doctor Samuel
Subject: Re: about consecutive composite integers

Hi Mundip,

Given any integer m > 0, 

     (m + 1)! + 2, (m + 1)! + 3, ..., (m + 1)! + m + 1

is a sequence of m consecutive composite integers, so arbitrarily long
sequences of such integers exist. 

Don't hesitate to write again if there's anything about this answer
that you don't understand.

- Doctor Samuel, The Math Forum
  http://mathforum.org/dr.math/