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### Consecutive Composite Numbers

```Date: 06/07/2005 at 14:22:39
From: mundip

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.

that you don't understand.

- Doctor Samuel, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
College Number Theory
High School Number Theory

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