+0

# Number Theory

-1
4
1
+153

What is the fifth smallest prime number greater than 2000?

Jun 15, 2024

#1
+1250
+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.

Thanks! :)

Jun 16, 2024

#1
+1250
+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.