Number Theory

We don't have to consider any numbers ending with 5 or even, since we know they are composite numbers. 

,

So now, we go through a list. 

 

First, start with 2001. We have $2001=3*667$, and it has 8 factors, so it is composite. 

2003 is prime, as it is only divisible by 1 and itself. 

 

We have $2007=3*669$, so 2007 is composite. 

 

$2009 = 7*287$, so 2009 is composite. 

 

$2011$ is prime. 

 

$2013=671*3$, so 2013 is composite.

 

$2017 \text{and} 2027$ are prime, but everything in between is composite. 

 

$2029$ is prime, so that's our final answer. 

 

So 2029 is our answer. 

 

Thanks! :)