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Math Help - Number spirals

  1. #1
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    Number spirals

    Consider the following:


    81 82 83 84 85 86 87 88 89 90
    80 49 50 51 52 53 54 55 56 91
    79 48 25 26 27 28 29 30 57 92
    78 47 24 09 10 11 12 31 58 93
    77 46 23 08 01 02 13 32 59 94
    76 45 22 07 00 03 14 33 60 95
    75 44 21 06 05 04 15 34 61 96
    74 43 20 19 18 17 16 35 62 97
    73 42 41 40 39 38 37 36 63 98
    72 71 70 69 68 67 66 65 64 99

    It has several nice line patterns such as the squares of numbers, the oblong numbers, triangle numbers multiplied by 8 (e.g. 0, 8, 24, 48, 80 - incidentally when you add one to each of the foregoing numbers, you get the odd squares of numbers).

    When you extend the spiral to 168, you get eight numbers in a row that are
    prime (31, 13, 3, 5, 19, 41, 71, 109). The puzzle now is can you find a longer line of primes? How long?

    For further exploration try triangle numbers or Fibonacci numbers (for historical notes I've partially explored this over 30 years ago).
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  2. #2
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    Red faced

    I didn't follow my own advice to do a Google search (my friend found the following website). Anyways you can check out this website:

    NumberSpiral.com - Home

    Enjoy.
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  3. #3
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    One more note

    Although I have heard of Ulam's spiral, I wasn't aware of its significance until just a few days ago which is very interesting.
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  4. #4
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    Can the prime number string be lengthened by adjusting the number spiral? For example eliminating even numbers and numbers ending in 5?
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