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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Good luck with that! I have to go out now...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

Sorry, but problems still not fixed and it looks like my connectivity will be on and off for the rest of the night.

See you later.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Hi Bobby,

Just messin' 'round with output presentation, and also included a timer, infinite looping (for looooong calcs) and a prompt for P. Here's what I've done:

*Last edited by phrontister (2013-04-28 00:51:25)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

Your machine is faster than mine. Mine took 12 seconds.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

I grease the workings of my computer with Vegemite. If you want to try that on your machine to soup it up, just make sure you don't use molasses, which has a similar appearance but will have the opposite effect.

*Last edited by phrontister (2013-04-25 00:04:35)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi phrontister;

I will try that but vegemite is hard to come by here.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Hi Bobby,

You probably already know approx how the running times of the various parts of your code compare, but I thought I'd run a 'Timing' test so I could see which area/s could do with some speeding up. I used P=13 and minimum upper limits.

0.047 seconds: p = Table[Prime[k], {k, 1, 45793}];

0.109 seconds: ans = Accumulate[Table[p[[n]]^13, {n, 1, 45793}]];

10.656 seconds: Position[MapIndexed[fubar, ans], {{True}, {True}}]

I'm not sure how to break that last one into separate times for Position and MapIndexed, but from a test I tried it seems that MapIndexed takes up most of the combined time (but I may be wrong there, because I had to split that line into two for Timing to work).

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

That is to be expected, that is where the primality testing is. But it does look like I did not choose the best way possible.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Getting sleepy...my inbuilt clock is running down. CuL8r.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

Okay, have a good night. Maybe I will have something to post when you get back.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Hi Bobby,

I just changed my code in post #53 to remove the upper limit, which will be useful for cooking my cpu during long service leave if I particularly want to solve a hard-to-get P value.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

There is some strange coincidence with these answers.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

What have you discovered?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

That all the n's are odd.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

That is an 'odd' coincidence!

Actually, I don't know how to check that. I tried printing n, but failed.

And I have to go out now...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Okay, there are even answers but the first answer is so far always odd. Have a good time.

**In mathematics, you don't understand things. You just get used to them.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 183

hi bobbym

Yeah I notice it too..can you get n to be even for Ps? It is like finding odd perfect numbers, so far all perfect numbers are even.

*Last edited by Stangerzv (2013-04-25 15:22:52)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi;

This is an even answer for n, but it is not the smallest one.

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

I changed my code to run automatically while I was out, and got the following:

All odd from P=2 to P=43.

Then 3 evens:

P=47: n=43620

P=53: n=10102

P=59: n=181138

P=61 is back to odd again, and then 3 evens:

P=67 n=25982

P=71: n=64636

P=73: n=342

There may not be an odd:even pattern.

P=79 is computing now, but is taking a long time.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Oops...for P=37, n=57126

...and P=79: n=621475

*Last edited by phrontister (2013-04-25 18:36:38)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Was that P = 37 the smallest one?

**In mathematics, you don't understand things. You just get used to them.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,854

Yes. I tested it in your program and in mine.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Okay, then that puts that conjecture to sleep.

**In mathematics, you don't understand things. You just get used to them.**

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 183

If there is no computer maybe it would take hundreds of years to verify this for sure. But now it takes less than a day:)

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 89,150

Hi Stangerzv;

I doubt that anyone would ever be attempting this without a computer.

**In mathematics, you don't understand things. You just get used to them.**

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