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.

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5 Responses to 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

  2. ivasallay says:

    Congratulations again for solving this one!

    Liked by 1 person

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