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Author Topic: A Math... Question :)  (Read 16141 times)

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Offline Xeda112358

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Re: A Math... Question :)
« Reply #15 on: September 17, 2011, 10:27:29 pm »
Hmm, could I see the code used to test it and is there any loss of accuracy when Python works with those numbers?
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Offline sqrt(Time)

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Re: A Math... Question :)
« Reply #16 on: September 18, 2011, 02:33:51 pm »
Well, I got a slight improvement... don't know if it really counts as different from the factorial solution, though. It has 51 digits, and goes 525...[45 digits]...632. (just to not spoil it for everyone else, while letting others check if they got the same solution)

edit for typo in a digit
« Last Edit: September 18, 2011, 02:56:04 pm by sqrt(Time) »
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Offline Xeda112358

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Re: A Math... Question :)
« Reply #17 on: September 18, 2011, 02:39:07 pm »
Could you explain how you came to the result? The smallest value where a 134 digit gap or more occurs that I found (without factoring the values) was 57 digits long :/

(it should actually be a gap of more than 240)
« Last Edit: September 18, 2011, 03:35:08 pm by Xeda112358 »
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Offline sqrt(Time)

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Re: A Math... Question :)
« Reply #18 on: September 18, 2011, 02:56:48 pm »
Sent it in a PM.
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Offline AngelFish

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Re: A Math... Question :)
« Reply #19 on: September 18, 2011, 03:00:02 pm »
Quote from: Xeda112358 on September 17, 2011, 10:27:29 pm
Hmm, could I see the code used to test it and is there any loss of accuracy when Python works with those numbers?

Python has BigNum libraries, so if the program was written correctly, the answer should be correct.
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Offline Xeda112358

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Re: A Math... Question :)
« Reply #20 on: September 18, 2011, 03:20:10 pm »
Ah, okay... Still, it isn't a pretty proof :P Also, sqrt(Time) is correct! Thanks for the proof, because that helped me make sense of it :)
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Offline boot2490

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Re: A Math... Question :)
« Reply #21 on: September 18, 2011, 03:24:42 pm »
You seem to be very math savvy xeda! I mean, even your username is a reference to the Fibonacci sequence.
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Offline Xeda112358

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Re: A Math... Question :)
« Reply #22 on: September 18, 2011, 03:26:59 pm »
And my picture is a reference to Pascal's Triangle :D
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Offline boot2490

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Re: A Math... Question :)
« Reply #23 on: September 18, 2011, 03:27:58 pm »
I thought that pascal's triangle was more one dimensional? It just goes down and expands in the middle.
I suppose lots of patterns in math usually lead to curves in the end. Think of the sines and waves and all that.
« Last Edit: September 18, 2011, 03:30:12 pm by boot2490 »
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Offline Xeda112358

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Re: A Math... Question :)
« Reply #24 on: September 18, 2011, 03:37:05 pm »
Oh, the little curves are my own implementations :) It is the actual pieces that the curves "connect" to that are the pascals triangle part :) I drew it in paint, so I went down to the pixel
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Offline boot2490

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Re: A Math... Question :)
« Reply #25 on: September 18, 2011, 05:25:46 pm »
Oh, I see... yeah, i see the triangle now. Cool!
I'm gonna use my psychic skills now... You did that in windows vista!
« Last Edit: September 18, 2011, 05:28:17 pm by boot2490 »
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Offline phenomist

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Re: A Math... Question :)
« Reply #26 on: September 21, 2011, 01:06:53 am »
Wait, how would you quickly test primality for 120000-digit numbers? If we could reliably do that, then let's go get that Ti-Nspire key now.

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Offline Xeda112358

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Re: A Math... Question :)
« Reply #27 on: September 21, 2011, 04:22:41 pm »
Hehe, actually it is Windows 7 :P

@phenomist: Actually, it is relatively "easy" to check primality, it is "difficult" to factor. It was once thought that solving one would solve the other, but it has been proven that factoring and deterministic primality testing are two separate problems.

I am not too knowledgeable on the subject of the AKS deterministic primality test, but it puts Pascal's triangle to clever use and it is in fact polynomial time! The idea stems from polynomial expansion. I am sure you know how to expand (p+q)n by using Pascal's triangle (or nCr), but here is a really cool fact: Excluding the first and last element of a row in pascals triangle (so excluding the 1), all elements in row p are divisible by p if and only if p is prime. There is a neat little proof for that, but I don't have the patience to type it out :D

If you think about that, then in the expansion of (x+1)p where p is prime, all of the terms between the first and last will be divisible by p. (Wow, I think I finally understand the AKS primality test!  :w00t:) So what this means, is that if you do (x+1)p mod p, the only remaining terms are xp+1. The AKS primality test makes clever use of this :) Isn't this just lovely! Talking through this, I now actually understand the concept ! I think I could totally implement this, now!

But yeah, this doesn't help us factor numbers... hehe, yet 3:-)
« Last Edit: September 21, 2011, 04:25:08 pm by Xeda112358 »
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Offline boot2490

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Re: A Math... Question :)
« Reply #28 on: September 21, 2011, 07:02:41 pm »
I gusses vista because of the color scheme, and that 7 is harder to use so the general public can't do stuff like that.
I have been using paint since before I could read. If there is something about it, I know it.
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Offline flyingfisch

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Re: A Math... Question :)
« Reply #29 on: September 21, 2011, 07:04:16 pm »
I have too. Its so simple, yet you can get pretty good graphics out of it (pixel art)
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