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25157Re: Multiplying Primes and Numbers in General

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  • mikeoakes2
    Jun 4, 2013
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      --- In primenumbers@yahoogroups.com, "golfbum71" <golfbum71@...> wrote:
      >
      > I'm trying to find more resources to help verify something I've noticed. You guys are all math geniuses (okay most of you are...but I won't say who...) and I'm hoping someone can point me in the right direction.
      >
      > When multiplying two prime numbers...that can be expressed (we'll assume two 6N-1 numbers...) as (6a-1)(6b-1) = 6c-1. I've recently noticed that in this case, c can be expressed as: 6ab - b + a. (when there is one 6N+1 number, c = 6ab + a - b, and when there are two 6N+1 numbers, c = 6ab + a + b)
      >
      > I'm guessing this thought isn't original and probably several thousand years old...I just don't know where to look.
      >
      > By the way. this expression can be taken further for the multiplication of any two numbers if expressed from 6N-2 to 6N+3.

      Hi Geoff,

      I'm afraid there are so many errors in your algebra that it's hard to know where to start...

      It's always a good idea to double-check before posting, by putting in at least one set of values.
      Let's take the primes 5 and 11, so a=1, b=2.
      The product is 55.
      Is this of the form 6c-1, with c=6ab - b + a?
      I don't think so !

      Anyway, a formula of that kind can't be right, as interchanging a and b gives a different answer, but multiplication is commutative.

      Another general point: I should have thought that whether or not the numbers are /prime/ must be irrelevant in equations of the kind you are considering, no?
      Try some non-prime numbers.

      Best regards - and better luck next time !

      Mike
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