# The First Two Consecutive Primes with a Difference of 100

The difference between two consecutive primes is called prime gap. Prime gaps are always even except for the prime gap between 2 (the first prime and the only even prime) and 3 (the first odd prime), which is 1.

At first, prime gaps are small. As the primes get bigger, larger prime gaps start to show up. However, that’s not always the case, as twin primes (two consecutive primes with a prime gap of 2) were found even in primes with hundreds of thousands of digits.

When does the prime gap of 10 first appear? Upon inspection of the primes table above, you would see that the answer is 139 and 149.

My question is: When does the prime gap of 100 first appear?

Solution (Click to Show)

You need to search a lot further to find the solution. The answer is 396,733 and 396,833.

Here’s another challenge for those who are interested: When does the prime gap of 1,000 first appear? (Hint: The primes contain 17 digits!)

### Posted by Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is edmarklaw@learnfunfacts.com

## 10 thoughts on “The First Two Consecutive Primes with a Difference of 100”

1. A potato PC that could run Mathematica can easily deal with it though having a CPU with a large number of cores helped a lot :)

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1. At first I thought they were 1 and 101, because I hadn’t read they were to be consecutive primes. Then, I stopped thinking…. 😉

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