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Number Theory

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What is the fifth smallest prime number greater than 100?

Jun 14, 2024

#1
+1280
+1

We can keep couting up and up until we get prime numbers.

First, we have \(101\). Notice it's only divisble by 1 and itself, so there's the first prime.

All the even numbers obviously don't work, so we skip them.

Next, we have \(103\). It also is only divisble by 1 and itself, so that's the second prime.

Third, we have 105. It's divisble by 5, so it doesn't work.

Then, we have \(107\), which is also a prime number.

\(109\) is also prime, so we count that as our fourth prime number

111 is divisble by 3 and 37, so it doesn't work.

However, \(113\) is prime, so that's the smallest.

Thanks! :)

Jun 14, 2024

#1
+1280
+1

We can keep couting up and up until we get prime numbers.

First, we have \(101\). Notice it's only divisble by 1 and itself, so there's the first prime.

All the even numbers obviously don't work, so we skip them.

Next, we have \(103\). It also is only divisble by 1 and itself, so that's the second prime.

Third, we have 105. It's divisble by 5, so it doesn't work.

Then, we have \(107\), which is also a prime number.

\(109\) is also prime, so we count that as our fourth prime number

111 is divisble by 3 and 37, so it doesn't work.

However, \(113\) is prime, so that's the smallest.