Just posted this on the intro site, but think I should have posted here. Oops

Discussion in 'Number Theory' started by Ian M, Mar 13, 2022.

  1. Ian M

    Ian M

    Mar 13, 2022
    Likes Received:
    At 3am this morning, my mind was buzzing so in order to stop my brain wandering all over the place, I thought about a board game I like playing called Settlers of Catan.

    The game (which is very good) has 19 small hexagons that are positioned to form a larger hexagon. It got me thinking about how many smaller hexagons I would need to create an even larger hexagon. I realised that the number of smaller hexagons would always be a prime number and that:

    For any odd natural number n,
    n squared - (n squared - 1) / 4
    is always prime.

    Does anyone know if this is true? And if so, is there a proof?

    As said above, if this is totally wrong or just plain obvious, please feel to let me know!
    Ian M, Mar 13, 2022
  2. Ian M


    Jun 26, 2022
    Likes Received:
    No, it is not always prime. For example for n=11, 15 or 17 the corresponding number is not prime.

    For n=11 it is 91=7x13.
    BobLeMagnifik, Jun 26, 2022
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