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Dumb question

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  • David Litchfield
    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
    Message 1 of 4 , Feb 1, 2002
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      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
    • Jon Perry
      If n=pq, and x=p+q, we can say x =2sqrt(n), and x
      Message 2 of 4 , Feb 1, 2002
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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.

        >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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      • Jon Perry
        Automatic typo correction program spotted a typo in Jon Perry s email: RE:[PrimeNumbers]Dumb Question Please read: x
        Message 3 of 4 , Feb 1, 2002
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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




          Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
          The Prime Pages : http://www.primepages.org



          Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/





          Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
          The Prime Pages : http://www.primepages.org



          Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
        • 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 4 of 4 , Feb 1, 2002
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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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