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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 131

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)*

'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: 131

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: 131

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.

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**Primenumbers****Member**- Registered: 2013-01-22
- Posts: 131

I have edited formula. Thanks.

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

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That is a trivial result

'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: 131

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: 131

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

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

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