# Is there a set of 2015 consecutive positive integers containing exactly 15 prime numbers?

Check out this intriguing Math Olympiad Number Theory question: Is there a set of 2015 consecutive positive integers containing exactly 15 prime numbers?

For instance, the number of primes in the set {1,2,3,…,2014,2015} is 305. This can be computed by entering $\pi (2015)$ in WolframAlpha.

The solution to this problem can be obtained at: http://www.fen.bilkent.edu.tr/~cvmath/Problem/problem.htm (February 2015 Problem of the Month)

To learn more about techniques for Math Olympiad style questions (including Number Theory and more), check out this book Mathematical Olympiad Treasures by noted author Titu Andreescu. Truly a treasure trove of useful tips and techniques.   ## Author: mathtuition88

https://mathtuition88.com/

## 5 thoughts on “Is there a set of 2015 consecutive positive integers containing exactly 15 prime numbers?”

1. abyssbrain says:

Ha! I should have known that the solution would be easy (since it’s a math olympiad question). When I first read the problem, I immediately thought of some complicated concepts…

Liked by 1 person

1. mathtuition88 says:

Haha, thanks for your comments! The generalized Riemann Hypothesis is not required for solving this question 😉

Liked by 1 person

1. abyssbrain says:

Oh well, sometimes the more concepts we know, the more we complicate things. 🙂

Liked by 1 person

2. ivasallay says:

Congratulations again for solving this one!

Liked by 1 person

1. mathtuition88 says:

Thanks!

Liked by 1 person

This site uses Akismet to reduce spam. Learn how your comment data is processed.