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RE: [PrimeNumbers] Dumb question

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  • Jon Perry
    Automatic typo correction program spotted a typo in Jon Perry s email: RE:[PrimeNumbers]Dumb Question Please read: x
    Message 1 of 4 , Feb 1 10:41 AM
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      Automatic typo correction program spotted a typo in Jon Perry's email:

      RE:[PrimeNumbers]Dumb Question

      Please read:

      x<=(n/2)+2

      for:

      x<(n/2)+2

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com


      -----Original Message-----
      From: Jon Perry [mailto:perry@...]
      Sent: 01 February 2002 18:38
      To: Prime Numbers List
      Subject: RE: [PrimeNumbers] Dumb question


      If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2.

      I don't think there is anything else we can infer.

      >I suppose it's dumb because given the sum of the two
      >factors it is trivial to work out the factors and so can't be done.

      If 20=p+q, what are p and q? And from this, what is pq?

      Jon Perry
      perry@...
      http://www.users.globalnet.co.uk/~perry
      http://www.users.globalnet.co.uk/~perry/maths
      BrainBench MVP for HTML and JavaScript
      http://www.brainbench.com


      -----Original Message-----
      From: David Litchfield [mailto:Mnemonix@...]
      Sent: 01 February 2002 18:02
      To: Prime Numbers List
      Subject: [PrimeNumbers] Dumb question


      This is probably going to sound like a really dumb question with the answer
      being a resounding no, but, is there anyway, given a number which is the
      result of multiplying two primes together, to ascertain what the sum of
      those two factors is? I suppose it's dumb because given the sum of the two
      factors it is trivial to work out the factors and so can't be done.
      TIA,
      David




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    • David Litchfield
      ... Hmm. Shame. ... Well, the reason I say it s trivial is for this. Assume the number you ve been given is say 51 and we want to work out p and q. If we knew
      Message 2 of 4 , Feb 1 10:51 AM
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        > If n=pq, and x=p+q, we can say x>=2sqrt(n), and x<(n/2)+2.
        >
        > I don't think there is anything else we can infer.

        Hmm. Shame.

        >
        > >I suppose it's dumb because given the sum of the two
        > >factors it is trivial to work out the factors and so can't be done.
        >
        > If 20=p+q, what are p and q? And from this, what is pq?

        Well, the reason I say it's trivial is for this. Assume the number you've
        been given is say 51 and we want to work out p and q.

        If we knew p + q = 20 we could say

        20 / 2 = 100

        100 - 51 = 49

        sqrt(100) = 10
        sqrt(49) = 7

        10 - 7 = 3
        10 + 7 = 17

        17 * 3 = 51

        All numbers whose factors add up to give n share the same perfect squares as
        per fermat

        e.g. p + q = 20

        3 * 17 = 51, 3 + 17 = 20, 20 / 2 = 100, 100 - 51 = 49
        5 * 15 = 75, 5 + 15 = 20, 20 / 2 = 100, 100 - 75 = 25
        7 * 13 = 91, 7 + 13 = 20, 20 / 2 = 100, 100 - 91 = 9
        9 * 11 = 99, 9 + 11 = 20, 20 / 2 = 100, 100 - 99 = 1

        Cheers,
        David Litchfield
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