Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

When searching a number on Wolfram Alpha, one of the results is its representation.
For example, for 8549:

8549 has the representation 8549 = $5·2^6·3^3-91$.

Similarly for 75290:

75290 has the representation 75290 = $3·2^9·7^2+26$.

What is the significance of these representations?

share|improve this question
2  
Hum, it shows the numbers as sums or differences of products of small primes. It is curious. –  Willie Wong Jan 18 '11 at 14:39
1  
Have you tried to ask Wolfram Alpha? If not, you could send an e-mail to this adress: info@wolframalpha.com or start a discussion at their forum: community.wolframalpha.com –  Max Muller Jan 18 '11 at 19:37
    
My guess is that it is the "shortest" way of expressing this number. Note that it doesn't do it for primes. –  Noon Silk Jan 18 '11 at 23:18
    
Very well. I've submitted a question to their forum, I hope to get results. I wanted to give Math.SE the first chance of ansering the question. It is possible that line is just a filler... –  Kobi Jan 19 '11 at 5:12
    
@Noon Silk - Well, isn't the "shortest" way simply writing the number? 8549 is quite short. And 83×103 (prime factors) is also shorter than that representation. –  Kobi Jan 19 '11 at 5:17

2 Answers 2

What it seems to do is, when $n$ is your number, that it maximizes the number of prime factors of $q$ within the range $q \in (n-100,n+100)$. And then sets $n=q+(n-q)$. Doing this it can easily find that 513 is for example $513=2^9+1$. However for the numbers you gave it is not really interesting.

share|improve this answer
2  
@user3123: is this a guess, or is this referred to in some documentation? (In particular, why $(n-100,n+100)$?) And what is the criterion for making the result "noteworthy" enough to be displayed? Note that for many large numbers the properties section lists no such representations. –  Willie Wong Jan 18 '11 at 14:43
    
@Willie It is a guess and the $\pm100$ comes because I tried like 50 numbers and what it added was always below $100$ but sometimes near to $100$. Also I see that my initial guess is at least not fully correct. Consider that $9660=3*2^7*5^2+60$ but Wolfram writes it as $9660=7^4*2^2+56$. Using only $6$ factors instead of the optimal $10$. –  Listing Jan 18 '11 at 17:18

I think it is just a curious fact to know and tell. They seem to be a product of small primes plus or minus a small correction. For 2010, besides the "obvious" 2010=2^11-38 it also finds that 2010 divides 29^6-1.

share|improve this answer
    
I would argue it isn't a curious fact at all. I'd say that without any noticeable pattern, it's no more or less interesting than any other random expression that equates to the same value. –  Michael J Swart Oct 9 '13 at 19:44

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.