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## 25169Re: Multiplying Primes and Numbers in General

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• Jun 4, 2013
--- In primenumbers@yahoogroups.com, "G Fischer" <golfbum71@...> wrote:
>
> Hit send again and realized I misspoke below for the 6N+1 multiplied by 6N-1
> numbers...
> c = 6ab + a - b
> This formula will show differently since a and b can be different... when
> the numbers are interchanged.
>
> As an example: 59*67 = 3953
> The formula for c in this case is: c = 6ab + a - b
> a = 10
> b = 11
> c = 659
> c = 6*10*11 - 10 + 11
> c = 660 + 1
> c = 661
>
> and flopped:
> a = 11, b = 10, c = 659
> c = 6*10*11 - 11 + 10
> c = 660 - 1
> c = 659
>
> Perhaps a rule for whichever number is 6N-1 is added and 6N+1 is subtracted?

It's not complicated at all, Geoff, it's just high-school algebra.

Let the 2 numbers be x=6*a+a1 and y=6*b+b1, where a1 and b1 are each either +1 or -1.
Then x*y = (6*a+a1)*(6*b+b1) = 6*c+c1,
where c = 6*a*b+a1+b1,
and c1 = a1*b1 (= +1 or -1).

Mike
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