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Very fast, very good, you win the small prize of one star.
* The prize was mentioned in the initial post asking the question, but you have to use the "quote" button (or "edit" button if you are a mod) to see it. 

28 Sep 2008, 12:51 

Hmm, does it work in phinary (base φ)?


28 Sep 2008, 13:07 

revolution wrote: The prize was mentioned in the initial post asking the question, but you have to use the "quote" button (or "edit" button if you are a mod) to see it. _________________ Previously known as The_Grey_Beast 

29 Sep 2008, 16:57 

Show either of the following (only one can be true):


16 Oct 2008, 16:30 

EDIT2: I'll stand with what I first said
From wiki's page on pandigital nubmers: Quote:
Loco, heres a quote from some other website, Quote:
The added together thing is only to test for division by 3 and 9 Thus, any number using 09 only once is divisible by 3 and not prime. Last edited by windwakr on 16 Oct 2008, 19:46; edited 8 times in total 

16 Oct 2008, 18:48 

Are you honestly convinced of that? How is possible that you are not convinced about 0.(9) = 1 then?
31 is prime, a Mersenne prime, but the sum of both digits is 4, a composite number, so why summing from 0 to 9 is enough proof of the non existence of a base 10 pandigital with non redundant digits prime number? 

16 Oct 2008, 19:09 

Great! Seems that you won the small price then, congratulations
Here I found the proof http://technocosm.org/chaos/divisibility.html wrote: Divisibility by 3 

16 Oct 2008, 19:28 

That page lacks the explanation for the rule for divisibility by 11, but it can be done with the very same trick. For example:
1000*a+100*b+10*c+d=1001*a+99*b+11*c+(dc+ba) The number that consists of even count of 9 digits (let's call it "form *") is divisible by 11, because it is 9*11+9*11*100+etc. The number that is equal to an odd power of 10 plus 1, is equal to 11 plus number, which is "form *" multiplied by 10. For instance 1001=99*10+11. 

16 Oct 2008, 20:41 

So far no one has been able to prove that a 10 digit pandigital number cannot be prime, and no one has provided a counter example. The competition is still open.
Proof that a two or three digit number (from LocoDelAssembly) is divisible by three has not been shown to extend to 10 digits. Perhaps induction might help here? 

16 Oct 2008, 23:25 

You looking for something like this?
Quote:


17 Oct 2008, 00:29 

windwakr: If you keep up with that sort of posting then you might just win the prize.
Can you complete the proof? BTW: I would have also accepted a small program that generates all the permutations and tests each for primality. Of course, we only need to do one trial division by three and check the remainder is zero. Quite trivial really. 

17 Oct 2008, 00:51 

Quote:
is that what you want? 

17 Oct 2008, 01:00 

windwakr wins the prize:
* Congratulations! The prize of one star was listed in the very first posting that stated the problem (you have to see the hidden text with either the quote button or the copy and paste method), I hope you are happy with the prize and may it always bring you joy and happiness forever and ever. 

17 Oct 2008, 01:18 

Wow, I can't believe that was right! Woooo, a star.....I'm gonna put it in my sig.
How do I make a link to a specific post in a thread? 

17 Oct 2008, 01:25 

windwakr wrote: How do I make a link to a specific post in a thread?


17 Oct 2008, 05:43 

revolution: I believe windwakr really provided the proof (even though not his own) in his first post. It is based on wellknown facts and complete in just one sentence.
Also how to proceed with induction is obvious from the thing that LocoDelAssembly provided, in math books this kind of showing the proof is also often and recognized. Don't exagerrate with formalism  when you go into some serious mathematics with it, it's gonna kill you. 

17 Oct 2008, 07:40 

Tomasz Grysztar wrote: revolution: I believe windwakr really provided the proof (even though not his own) in his first post. It is based on wellknown facts and complete in just one sentence. Tomasz Grysztar wrote: Don't exagerrate with formalism  when you go into some serious mathematics with it, it's gonna kill you. Actually I think you are correct,. You could easily kill me with some formal mathematics, I'm still just learning this stuff and never had any formal training. Maybe later I'll get around to solving the Riemann Hypothesis. 

17 Oct 2008, 09:18 

lol this stuff kills me im only half way through year 11 math a  but at least im finding it easy


17 Oct 2008, 14:10 

revolution wrote: BTW: I would have also accepted a small program that generates all the permutations and tests each for primality. 32. Find the sum of all numbers that can be written as pandigital products. 38. What is the largest 1 to 9 pandigital that can be formed by multiplying a fixed number by 1, 2, 3, ... ? 41. What is the largest ndigit pandigital prime that exists? 43. Find the sum of all pandigital numbers with an unusual substring divisibility property. 104. Finding Fibonacci numbers for which the first and last nine digits are pandigital. 170. Find the largest 0 to 9 pandigital that can be formed by concatenating products. It appears I have solved some of them (including #41), so I have some BCD code floating around with pandigital algorithms...(can't remember where though). Of the people using Assembler to solve the problems I've dropped to 6th place and I haven't solved a problem in 859 days, lol. 

17 Oct 2008, 14:59 

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