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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

Did you know that for any Non-Prime that has a factor of >1, it can be produced with the below formula;

I can prove it

x = (f + L)/2

y = (f - L)/2 therefore

minus the two and it = fL which are the two factors....

And x - y = ((f + L)/2) - ((f - L)/2) = L which must be >1 to Not be, Prime or 1.

*Last edited by Primenumbers (2014-08-18 08:09:20)*

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only when

Are you saying that if x - y = 1, then x^2 - y^2 is a prime?

*Last edited by Agnishom (2014-08-18 04:37:48)*

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

Agnishom wrote:

Are you saying that if x - y = 1, then x^2 - y^2 is a prime?

No, what I am saying is only Primes and 1 can not have (x - y)>1, when

.**"Time not important. Only life important."*** - The Fifth Element 1997*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

only when (x - y) > 1

How about 8^2 - 7^2 = 15? x - y is not greater than 1 and 15 is a composite number.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

bobbym wrote:

How about 8^2 - 7^2 = 15? x - y is not greater than 1 and 15 is a composite number.

Yes, but

andWhere 15=3*5 therefore x=(5+3)/2 and y=(5-3)/2.

**"Time not important. Only life important."*** - The Fifth Element 1997*

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

I have edited formula. Thanks.

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That is a trivial result

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

Yes, but if we input the smallest values for x and y, and it results in a no.>z isn't z proven to be prime or 1...?

**"Time not important. Only life important."*** - The Fifth Element 1997*

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**marcuslee****Member**- Registered: 2014-09-04
- Posts: 12

Are you trying to say :

{

x² - y² = (x+y)(x-y)

where x, y are positive integers

and (x-y) is positive

x² - y² is therefore a composit number (non prime) with factors (x-y) and (x+y)

}

?

But are you sure every non-prime can be generated with this? How about one that is compost of an odd factor and an even factor?

For example:

70 = 10 * 7 = (x+y)(x-y)

x = ½ ( 10+7 ) = 8.5

y = ½ ( 10-7 ) = 1.5

I think you have to work with decimals in order for this to produce 'any non-prime' ...

*Last edited by marcuslee (2014-09-08 09:32:47)*

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 141

It's fine if you work with odd numbers only.

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