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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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 phrontisterFor P=7,

-Thanks to bobbymFor P=11,

For P=13, -Thanks to phrontister

*Last edited by Stangerzv (2023-01-31 01:02:05)*

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

For P=3

2^3 + 3^3 + 2 = 37

**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.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

Yes bobbym..both have to be primes.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

Thanks bobbym for the result for P=3

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Next one is at:

**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.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

For P = 17:

**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.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

Hi bobbym

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

For P = 7:

**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.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

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.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 266

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

Why didn't you accept?

**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.**

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