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#1 2013-07-21 14:44:51

Stangerzv
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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 (2013-07-21 16:52:32)

 

#2 2013-07-21 14:55:54

Stangerzv
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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 (2013-07-21 19:25:13)

 

#3 2013-07-21 15:13:15

Stangerzv
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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 (2013-07-21 16:53:08)

 

#4 2013-07-21 16:06:23

bobbym
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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.
 

#5 2013-07-21 16:52:01

Stangerzv
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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.

 

#6 2013-07-21 17:01:48

Stangerzv
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Re: My New Primes with a Strange Property

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

 

#7 2013-07-21 17:08:57

Stangerzv
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Re: My New Primes with a Strange Property

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

Last edited by Stangerzv (2013-07-21 17:33:31)

 

#8 2013-07-21 17:26:52

Stangerzv
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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 (2013-07-21 17:32:35)

 

#9 2013-07-21 19:26:26

Stangerzv
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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 (2013-07-21 20:22:10)

 

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