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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,238

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 181

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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