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What is the fifth smallest prime number greater than 2000?

 Jun 15, 2024

Best Answer 

 #1
avatar+1280 
+1

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! :)

 Jun 16, 2024
 #1
avatar+1280 
+1
Best Answer

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! :)

NotThatSmart Jun 16, 2024

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