14
$\begingroup$

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?

  • 0
    @Kobi: You've got me there. I retract my statement :)2011-01-19

2 Answers 2

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.

  • 0
    @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 $10$.2011-01-18
1

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.

  • 0
    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.2013-10-09