My New Twin Prime Numbers

phrontister · 2013-04-24 17:07:49

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

bobbym · 2013-04-24 19:57:56

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.

phrontister · 2013-04-24 22:29:35

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)

bobbym · 2013-04-24 22:36:42

Hi;

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

phrontister · 2013-04-25 00:01:35

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)

bobbym · 2013-04-25 04:55:27

Hi phrontister;

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

phrontister · 2013-04-25 04:59:07

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).

bobbym · 2013-04-25 05:09:04

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.

phrontister · 2013-04-25 05:11:59

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

bobbym · 2013-04-25 05:19:08

Hi;

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

phrontister · 2013-04-25 13:05:23

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.

bobbym · 2013-04-25 14:19:48

Hi;

There is some strange coincidence with these answers.

phrontister · 2013-04-25 14:33:36

What have you discovered?

bobbym · 2013-04-25 14:37:02

That all the n's are odd.

phrontister · 2013-04-25 14:46:13

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...

bobbym · 2013-04-25 14:51:23

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

Stangerzv · 2013-04-25 15:21:16

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)

bobbym · 2013-04-25 15:55:17

Hi;

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

phrontister · 2013-04-25 18:32:27

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.

phrontister · 2013-04-25 18:34:59

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

...and P=79: n=621475

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

bobbym · 2013-04-25 18:38:06

Was that P = 37 the smallest one?

phrontister · 2013-04-25 18:51:32

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

bobbym · 2013-04-25 18:57:15

Okay, then that puts that conjecture to sleep.

Stangerzv · 2013-04-25 19:30:30

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:)

bobbym · 2013-04-25 22:15:27

Hi Stangerzv;

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

Math Is Fun Forum

#51 2013-04-24 17:07:49

Re: My New Twin Prime Numbers

#52 2013-04-24 19:57:56

Re: My New Twin Prime Numbers

#53 2013-04-24 22:29:35

Re: My New Twin Prime Numbers

#54 2013-04-24 22:36:42

Re: My New Twin Prime Numbers

#55 2013-04-25 00:01:35

Re: My New Twin Prime Numbers

#56 2013-04-25 04:55:27

Re: My New Twin Prime Numbers

#57 2013-04-25 04:59:07

Re: My New Twin Prime Numbers

#58 2013-04-25 05:09:04

Re: My New Twin Prime Numbers

#59 2013-04-25 05:11:59

Re: My New Twin Prime Numbers

#60 2013-04-25 05:19:08

Re: My New Twin Prime Numbers

#61 2013-04-25 13:05:23

Re: My New Twin Prime Numbers

#62 2013-04-25 14:19:48

Re: My New Twin Prime Numbers

#63 2013-04-25 14:33:36

Re: My New Twin Prime Numbers

#64 2013-04-25 14:37:02

Re: My New Twin Prime Numbers

#65 2013-04-25 14:46:13

Re: My New Twin Prime Numbers

#66 2013-04-25 14:51:23

Re: My New Twin Prime Numbers

#67 2013-04-25 15:21:16

Re: My New Twin Prime Numbers

#68 2013-04-25 15:55:17

Re: My New Twin Prime Numbers

#69 2013-04-25 18:32:27

Re: My New Twin Prime Numbers

#70 2013-04-25 18:34:59

Re: My New Twin Prime Numbers

#71 2013-04-25 18:38:06

Re: My New Twin Prime Numbers

#72 2013-04-25 18:51:32

Re: My New Twin Prime Numbers

#73 2013-04-25 18:57:15

Re: My New Twin Prime Numbers

#74 2013-04-25 19:30:30

Re: My New Twin Prime Numbers

#75 2013-04-25 22:15:27

Re: My New Twin Prime Numbers

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