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Twin prime acceleration

  1. Aug 7, 2007 #1
    twin prime acceleration!!!!

    few weeks ago while i was doing my physics homework, i thought about the acceleration of prime number, so used the kinematics equations of acceleration on prime numbers. i was amazed to find that the difference of square of two prime numbers(>5) are always divisible by 24. especially if you look into twin primes then you can see a pattern (yet unknown:uhh:)
    i mean the differences are reasonable.
    how can i prove that,, or m just becoming fool? misunderstanding basic ideas? ( coz once i was glad to find that each and every numbers can be construct out of prime numbers,, which is absolute and universal truth)
    help me!!
    m lost on nothing :grumpy:

    here is the list of the few twin prime acceleration

    twin prime t. prime acceleration

    5,7 1
    11,13 2
    17,19 3
    29,31 5
    41,43 7
    59,61 10
    71,73 12
    101,103 17
    107,109 18
    137,139 23
    149,151 25
    179,181 30
    191,193 32
    197,199 33
    227,229 38
    239,241 40
    269,271 45
    281,283 47
    311,313 52
    347,349 58
    419,421 70
    431,433 72
    461,463 77
    521,523 87
    569,571 95
    599,601 100
    617,619 103
    641,643 107
    659,661 110
    809,811 135
    821,823 137
    827,829 138
    857,859 143
    881,883 147
     
  2. jcsd
  3. Aug 7, 2007 #2
    Check the sequence, http://www.research.att.com/~njas/sequences/A002822 .
    To prove it consider looking at prime numbers mod 6 and squares mod 4. There is a pattern that is readily apparant. Think about how to prove that and you are own your way to the proof you are looking for. Easy work for an student with background in algebra who is interested in numbers, because mod considerations are a basic tool of number theorists.
     
    Last edited: Aug 7, 2007
  4. Aug 7, 2007 #3
    thankx for the reply.
    by the way is it better to spend my time on that new sequence(for me) or let it go coz its already ............?

    how can i do mod consideration? i dont have any idea,( right now m taking calc III).
     
  5. Aug 7, 2007 #4

    CRGreathouse

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    Science Advisor
    Homework Helper

    You can spend time looking at this, it will help you understand better. But without a radically new idea and fast computers, you probably won't calculate further than has already been done.

    Mods are easy, you know how to do them already. It's clock math -- 11 + 3 = 2 (3 hours past 11 o'clock is 2 o'clock). That's working mod 12 -- you can freely add or subtract 12. It's usually most convenient to put them in the simplest form, that is, between 0 and one less than the modulus. (Clocks instead put the time between 1 and the modulus, which also works.)

    All primes other than 2 and 3 are equal to either 1 or 5 mod 6. (Otherwise, they'd be divisible by 2 or 3 -- and of the primes, only 2 and 3 are divisible by 2 and 3.)
     
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