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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Ok. If you start calling me a mathematician I'll know our friendship is off.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Mathematics is beautiful. We are lucky to be able to study it from the viewpoint of an amateur.

**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: 179

Hi bobbym

Amongst of those famous mathematicians there were amateurs like Pierre Fermat (a lawyer), Mersenne (a priest), etc. Here list of them http://en.wikipedia.org/wiki/List_of_am … ematicians

There is a mafia culture in the mathematical fields and those people tends to garbage other people ideas because they are jealous.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Q:What do men with power want?

A:More power.

It is very easy for men to become power mad. Even easier than becoming greedy. The scientific community in general had to withstand many centuries of persecution. Then they rose to the position of power where they promptly began to persecute people and differerent ideas. They began to stifle and repress new ideas that might endanger their position of power.

Anyway,

I like Fermat, Ramanujan, Lovelace and Pascal most among that list. And am saddened at the absence of the great Forman S. Acton, chemist. He is widely considered the greatest numerical analyst alive.

**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: 179

Hi bobbym

Anyway, how long do you think it would take to get 1st 100,000 digits for this prime equation? I hope it won't take too much computing time.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

Please tell me which equation you mean.

**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: 179

Hi bobbym

Equation in this thread..so far phrontister got 715 digit prime and how about 100,000 digits prime? How long would it take? And would it fry the CPU?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

Nobody even knows where it would be. I would think that it would take a very long time with a desktop,

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: 179

I am revising the equation and making it harder to get new resulting prime. I named it Perfect Twin Prime Numbers. The revised equation is given as follows:

Where all Ps are prime numbers.

Example:

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Stangerzv,

Yes...that certainly has made it more difficult to find solutions!

"569" should read "659".

I've changed my code for the original problem and have found prime solutions for Pₜ=2 and 3, but not yet for 5.

Pₜ=2: (from 1st 1000 primes) +/- = 7, 139, 199, 463, 877 and 6121

Pₜ=3: (from 1st 1000 primes) +/- = 3

I'm off to bed now, and I've given my computer the task of solving Pₜ=5 while I'm asleep.

*Last edited by phrontister (2013-05-30 23:21:43)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Woke up to this:

Pₜ=5: (from 1st 10000 primes) +/- = 17159, 32831, 62011, 70241 and 96053

Since then, this:

Pₜ=7: (from 1st 10000 primes) +/- = 81899 and 104311

Perfect Twin Prime solutions found so far (smallest):

Pₜ=2:

Pₜ=3:

Pₜ=5

Pₜ=7

Pₜ=11

Pₜ=13

Pₜ=17

Pₜ=19

*Last edited by phrontister (2013-05-30 23:22:33)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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

Hi phrontister

Thanks for finding the solutions. I am setting up a website for finding my prime numbers. Maybe in the future I could offer some prize money for the larger prime (>100,000 digits)

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

One thing that I notice about these prime pairs is that, all of their digital root for n>1 would be in pair of 2^y (y=1..3) and 1 or 7, example, (2,1), (2,7),(4,1), (4,7),(8,1), (8,7) and special case (7,7) when n is a square number (i.e n=9). This indicates that the prime distribution is not random but organized. Unless someone could find the counter examples. Perhaps for n=9, adding this into digital root system won't change anything as 9 has zero value in the decimal system and this is why the prime pairs would have the same digital roots. This applies for all n which has digital root of 9.

*Last edited by Stangerzv (2013-05-25 20:55:09)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Stangerzv,

I've done some work on what I think you're looking for, and here are pics of my findings.

I hope I've understood you correctly and that this is the info you want, but if not, please give a different example to help me understand and I'll do my best to get the info for you.

The pic with the different Pₜ values (from 2 to 13) in the left-hand column gives the results for the smallest Pₓ of each of those Pₜ values, while the other three (for Pₜ=2, Pₜ=3 and Pₜ=5) give results from the smallest Pₓ to successively-higher Pₓ values. All pics show digit roots.

I started testing for Pₜ=17, but that may have to be an overnight job while I'm asleep because after about an hour there were no results.

EDIT: The "152" in line 3 of the Sums column should read "157", which gives the digital sum 4.

*Last edited by phrontister (2013-05-30 23:23:34)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Stangerzv,

Got an overnight result for Pₜ=17:

*Last edited by phrontister (2013-05-30 23:24:14)*

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

Kool, it seems I had overlooked the primes and new pairs of digital roots, (5,7) and (4,8)

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Bobby,

Do you know of a 'proper' function in M to obtain the digital root (sum) of a number?

I couldn't find one anywhere, so I made up this one which seems to work quite well for the number sizes I've worked on:

DRoot[x_] := Total[IntegerDigits[Total[IntegerDigits[Total[IntegerDigits[Total[IntegerDigits[x]]]]]]]]

If there isn't one, could mine be squashed up somehow to eliminate the repeats?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

There are simpler alternatives.

How does this do?

NewRoot[n_] := (Mod[n, 9]) /. (0 -> 9)

I do not know how it would perform on decimals or negative integers. I tested it on 10 or 12 million from 0 to 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Perfect...thanks!

I tested it on the numbers in the hide box on my post #115.

Could you explain what it does, in particular the "/. (0 -> 9)" part?

*Last edited by phrontister (2013-05-29 16:14:41)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

That is called a replacement rule. It says turn 0 into 9. Note the syntax because these replacement rules work on anything.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Ok...thanks for that. Learnt something new. Found it under 'Rule' in the M docs.

I've included your function in my code, which is looking much better now.

Here's my new M code:

This code will expand the information given in post #111 to show primes' sums and digital roots:

*Last edited by phrontister (2013-05-29 17:42:53)*

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

Hi phrontister

Can you find the digital roots pair (1,5) & (1,7) for the twin primes?

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Hi Stangerzv,

The digital roots pair {1,5} for Pₜ=2 occurs first at:

Then at:

There are also a couple more after that, at Pₓ=70207 and Pₓ=74167. No doubt there will be more.

Still looking for {1,7}, but have to go out now for a while. Maybe there will be an answer waiting for me when I get back.

*Last edited by phrontister (2013-05-30 23:25:02)*

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

Thanks for your input.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi phrontister;

Found it under 'Rule' in the M docs.

The replacement rules are a part of the Prolog programming language and make M unique.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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