Skip to main content
Home
plus.maths.org

Secondary menu

  • My list
  • About Plus
  • Sponsors
  • Subscribe
  • Contact Us
  • Log in
  • Main navigation

  • Home
  • Articles
  • Collections
  • Podcasts
  • Maths in a minute
  • Puzzles
  • Videos
  • Topics and tags
  • For

    • cat icon
      Curiosity
    • newspaper icon
      Media
    • graduation icon
      Education
    • briefcase icon
      Policy

      Popular topics and tags

      Shapes

      • Geometry
      • Vectors and matrices
      • Topology
      • Networks and graph theory
      • Fractals

      Numbers

      • Number theory
      • Arithmetic
      • Prime numbers
      • Fermat's last theorem
      • Cryptography

      Computing and information

      • Quantum computing
      • Complexity
      • Information theory
      • Artificial intelligence and machine learning
      • Algorithm

      Data and probability

      • Statistics
      • Probability and uncertainty
      • Randomness

      Abstract structures

      • Symmetry
      • Algebra and group theory
      • Vectors and matrices

      Physics

      • Fluid dynamics
      • Quantum physics
      • General relativity, gravity and black holes
      • Entropy and thermodynamics
      • String theory and quantum gravity

      Arts, humanities and sport

      • History and philosophy of mathematics
      • Art and Music
      • Language
      • Sport

      Logic, proof and strategy

      • Logic
      • Proof
      • Game theory

      Calculus and analysis

      • Differential equations
      • Calculus

      Towards applications

      • Mathematical modelling
      • Dynamical systems and Chaos

      Applications

      • Medicine and health
      • Epidemiology
      • Biology
      • Economics and finance
      • Engineering and architecture
      • Weather forecasting
      • Climate change

      Understanding of mathematics

      • Public understanding of mathematics
      • Education

      Get your maths quickly

      • Maths in a minute

      Main menu

    • Home
    • Articles
    • Collections
    • Podcasts
    • Maths in a minute
    • Puzzles
    • Videos
    • Topics and tags
    • Audiences

      • cat icon
        Curiosity
      • newspaper icon
        Media
      • graduation icon
        Education
      • briefcase icon
        Policy

      Secondary menu

    • My list
    • About Plus
    • Sponsors
    • Subscribe
    • Contact Us
    • Log in
    • Prime numbers

      Prime mystery

      30 June, 2014
      numbers

      What's the mystery number?

      The number N represents the first 6 digits of a special number. N consists of three prime numbers put side by side. These three prime numbers come xth, yth and zth on the list of primes, where x, y and z are themselves three consecutive primes (for example, x, y and z could be 3, 5 and 7, in which case we'd be looking at the third, fifth and seventh prime numbers). In addition, if N is split in the middle into two separate numbers, the prime factors of the left part of N add up to its right part. What is N? And what is the special number whose first 6 digits it forms?



      This puzzle was contributed by Aziz Inan, Professor of Electrical Engineering at the University of Portland. His own name, when written in capital letters, is a geometric word puzzle. Swap the vowels and turn the consonants 90 degrees and the words have switched places. "My parents didn't plan this," he says. "It's just fun."

      If you have a puzzle you think might interest Plus readers, please email us!

      Solution link
      Prime mystery: Solution
      • Log in or register to post comments

      Anonymous

      30 June 2014

      Permalink
      Comment

      314159 and pi

      • Log in or register to post comments

      Aushykoya Samuel

      8 July 2014

      In reply to 314159 and pi by Anonymous

      Permalink
      Comment

      Wow..this is cool

      • Log in or register to post comments

      Anonymous

      1 July 2014

      Permalink
      Comment

      31, 41, 59 form 11, 13, 17 th primes and pi=3.14159...

      • Log in or register to post comments

      Anonymous

      3 July 2014

      Permalink
      Comment

      pi=3.14159...

      the primes are 31, 41 and 59, which form the 11th, 13th and 17th primes.

      • Log in or register to post comments

      Anonymous

      27 November 2015

      Permalink
      Comment

      Is the question flawed? It seems to me, 3, 5 and 7 are the 3rd, 4th and 5th primes, which fits the x, y, z requirement.

      So for an answer, pi seems wrong. 31, 47 and 59 are not consecutive primes (since they missed 37, 41, 43). And, they fail the other criteria where you take the first three digits 315, sum them to get 9 which are supposed to equal the sum of the prime factors in the second three digits, 759, which is 7 plus 5 = 12, so pi fails this test as well.

      After going from 11 to 97 and looking for consecutive primes that pass the N split test, I found none. So is the question flawed, or can you clarify the "N is split in the middle into two separate numbers, the prime factors of the left part of N add up to its right part" requirement?

      • Log in or register to post comments

      Anonymous

      28 November 2015

      In reply to Prime mystery by Anonymous

      Permalink
      Comment

      Ok, it's pi. It took some head scratching but I see it fills all criteria. The prime factors of 314 are 2 and 157 which add up to 159 which is the second half of N. Great puzzle thanks.

      • Log in or register to post comments

      John76923

      25 July 2016

      In reply to Prime mystery by Anonymous

      Permalink
      Comment

      3 is the second prime, not the third.

      Although 1 is only divisible by itself and "1", seemingly meeting the definition of a prime, it is by convention excluded from the set of primes.

      I suppose this is because of all its additional special properties. If you were to count 1 as a prime factor in a greater number, how many occurrences of it would you give this factor? An infinite number would be possible.

      • Log in or register to post comments

      John Kuczaj

      13 February 2017

      In reply to Prime mystery by Anonymous

      Permalink
      Comment

      3,5 and 7 are the 2nd, 3rd and 4th primes!

      • Log in or register to post comments
      University of Cambridge logo

      Plus is part of the family of activities in the Millennium Mathematics Project.
      Copyright © 1997 - 2025. University of Cambridge. All rights reserved.

      Terms