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#1 2013-04-16 22:14:39

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

My New Twin Prime Numbers

Consider this equation

Where all Pi are the consecutive primes, Pt is the Prime-th Power, n is the n-th of the Prime number, P1=2, and Ps is the resulting Prime.

Example for smallest solution for each Prime-th Power.

For P=2,

For P=3,

-Thanks to bobbym:)

For P=5,

-Thanks to phrontister

For P=7,

-Thanks to bobbym

For P=11,


For P=13,
-Thanks to phrontister

Last edited by Stangerzv (2013-04-24 00:34:05)

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#2 2013-04-19 04:18:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

For P=3

2^3 + 3^3 + 2 = 37


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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#3 2013-04-19 04:34:11

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Dear bobbym

P=3 has no twin prime solution because

and 33=3x11 which is not a prime

Last edited by Stangerzv (2013-04-19 04:34:49)

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#4 2013-04-19 04:35:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

Oh, it has to both of them? I did not understand the question, sorry for the false positive.


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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#5 2013-04-19 04:38:46

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Yes bobbym..both have to be primes.

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#6 2013-04-19 04:44:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

For P = 3, how is this?

2^3 + 3^3 + 5^3 ± 3 = {157, 163}


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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#7 2013-04-19 04:49:22

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Thanks bobbym for the result for P=3

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#8 2013-04-19 04:54:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Next one is at:


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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#9 2013-04-19 05:06:38

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

I think there are few more solutions for P=3, have you tried P=7 and I think there would be no solution at lower amount or no solution at all.

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#10 2013-04-19 05:09:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

There are 5 solutions for P = 3 using the first 1000 primes.

I will check for P = 7:

No solutions up to n = 2000.


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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#11 2013-04-19 05:18:28

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

I do believe that if there is a solution it should occur at lower primes, as the prime number getting larger, it would be hard  or impossible to find.

Last edited by Stangerzv (2013-04-19 05:19:11)

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#12 2013-04-19 05:20:32

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Yes, the primes get rarer as the numbers get larger.

I have searched all the way up to the 2000th prime for P = 7 and found none.


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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#13 2013-04-19 13:49:39

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Hi bobbym

What program do you use to calculate them? On the other hands, can you get any solution for P>11? I think there could be no more solution, if there is one, it would be very large.

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#14 2013-04-19 14:14:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

I am using mathematica right now for this:

For P=11


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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#15 2013-04-19 18:00:48

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

I see, for P=11, I got the result already but not 13 and above.

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#16 2013-04-19 20:31:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

For P = 13 , I could not find any and I went up to the 4000th prime.


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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#17 2013-04-21 23:56:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

For P = 17:


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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#18 2013-04-22 02:42:35

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Hi bobbym

Thanks..It is really kool to know there is a solution for P=17.

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#19 2013-04-22 04:46:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

For P = 7:


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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#20 2013-04-22 11:12:33

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Hi bobbym

It seems there must be a solution for P=13 otherwise it would look strange. Otherwise there would be a gap for sure. By the way, thanks for calculate the primes. If you could tell me how to do it with the mathematica, maybe I would do some calculation myself for bigger P and finding the solution for P=13.

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#21 2013-04-22 12:01:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

I am looking for one but so far there is none among the first 20000 primes.

The code I have developed is highly inefficient, it only has the virtue of being quick to discover. I would need to clean it up some because right now it takes a lot of human intervention.

Also, I have an idea to speed it up greatly.


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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#22 2013-04-22 13:27:39

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

Basically, If there is no solution for P=13, it would be mind boggling to proof it so but if there is a solution, it would be very big. I am currently working on my equations and primes numbers, there are many more equations but I need someone to help me with the coding. There is someone suggesting me to use grid computing and the problem is that, I am not a programmer and I have left programming more than 10 years ago. Maybe I could apply for a research grant to study these prime numbers and work with collaborators.

Last edited by Stangerzv (2013-04-22 13:29:16)

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#23 2013-04-22 16:56:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Grid computing? Where are you going to get all the computers from?

The P = 13 will fall as soon as I bring more computers into the problem.


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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#24 2013-04-22 17:53:07

Stangerzv
Member
Registered: 2012-01-30
Posts: 179

Re: My New Twin Prime Numbers

A university here did invite me to use their first grid computing to run my prime number equations.

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#25 2013-04-22 20:07:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,264

Re: My New Twin Prime Numbers

Hi;

Why didn't you accept?


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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