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Prime pattern

  1. Jun 28, 2006 #1
    I am curious as to whether this pattern will always hold true:

    Let's say we take the prime numbers:
    2,3,5,7,11,13,17,19,23.......primes
    and we take the square(individually) minus 1
    3,8,24,48,120,168,288,360,528....p^2 - 1

    Then starting with the third p^2 - 1 (24), all of the p^2 - 1 can be rewritten as and earlier p^2-1 times a prime # (or multiple prime #'s)

    for example: 24=8x3,48=24x2,528=48x11,...and so on.

    Is this at all interseting or just something stupid that I am missing?

    Let me know,
    Thanks
     
  2. jcsd
  3. Jun 28, 2006 #2

    Hurkyl

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    Why not just say "p²-1 times a number"?


    It's a rather trivial observation; 3 is on your list.
     
    Last edited: Jun 28, 2006
  4. Jun 28, 2006 #3
    The number 4 times out of five is a single prime #. It seemed a lot nicer when i posted it and in the first ten i checked 9 of them were single prime numbers. I have since found 3 more where the # is a multiple of 2 primes (2 and 3 in all cases). Thanks for at least looking at it Hurkyl
     
  5. Jun 29, 2006 #4

    Hurkyl

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    I suspect what you're seeing is simply a property of small numbers, rather than anything special about your construction. That's why I asked how far you looked -- I imagine when you start looking at numbers in the trillions, you won't see this sort of thing very frequently at all.
     
  6. Jun 29, 2006 #5

    matt grime

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    Since you can factor p^2-1 you should start to see that this is not likely to be a recurrent pattern (an even weaker hypothesis is for every prime p, either p-1 or p+1 to have a repeated factor). This seems highly unlikely to be true in general.
     
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