Math Is Fun Forum

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Did you know this about any Non-Prime?

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

only when (x - y) can be> 1

I can prove it

x = (f + L)/2
y = (f - L)/2 therefore

   and

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)

---

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Did you know this about any Non-Prime?

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)

---

'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.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Did you know this about any Non-Prime?

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Did you know this about any Non-Prime?

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.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Did you know this about any Non-Prime?

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

Yes, but

   and   

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

---

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

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Did you know this about any Non-Prime?

I have edited formula. Thanks.

---

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Did you know this about any Non-Prime?

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.

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Did you know this about any Non-Prime?

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

marcuslee

Member

Registered: 2014-09-04

Posts: 12

Re: Did you know this about any Non-Prime?

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)

Primenumbers

Member

Registered: 2013-01-22

Posts: 149

Re: Did you know this about any Non-Prime?

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

---

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