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#1 2013-07-20 16:44:51

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

My New Primes with a Strange Property

Consider these two equation:

There are plenty of Primes of this form:

But there is no prime of this form:

If you could find a prime then you must be kool:) If you could find one, n should be greater than at least 100,000.

If you could find a counterexample then it would be a pleasure to see if you could find the twin primes of the form as follows:

Last edited by Stangerzv (2013-07-20 18:52:32)

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#2 2013-07-20 16:55:54

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

The Generalize equation can be written as follows:

I do believe it would behave more less the same for all t>1

Last edited by Stangerzv (2013-07-20 21:25:13)

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#3 2013-07-20 17:13:15

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

For t=1,

There are plenty of Prime of this form.

But for this equation:

There are only two primes for n<1,000,000 (i.e. 2 & 5)

Last edited by Stangerzv (2013-07-20 18:53:08)

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#4 2013-07-20 18:06:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,706

Re: My New Primes with a Strange Property

Hi;

P5 is not a prime. And n=2 is the only possible prime! The proof is quite easy.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#5 2013-07-20 18:52:01

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

Hi bobbym

(1+2)-1=2 and 1+2+3-1=5, sorry anyway, need to replace all s with t.

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#6 2013-07-20 19:01:48

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

Yeah..I found out the proof too:) Quite easy though!

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#7 2013-07-20 19:08:57

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

Therefore, the only twin prime for this generalize equation is (5,7).

Last edited by Stangerzv (2013-07-20 19:33:31)

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#8 2013-07-20 19:26:52

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

The proof is as follows:

Since

Then

=>

Which can be factorized as follows:

Which is a composite number.

Last edited by Stangerzv (2013-07-20 19:32:35)

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#9 2013-07-20 21:26:26

Stangerzv
Member
Registered: 2012-01-30
Posts: 173

Re: My New Primes with a Strange Property

Primes only occur at even t of the form 2^a for

where a is an integer

Last edited by Stangerzv (2013-07-20 22:22:10)

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