What is the meaning of a number's "representation" on Wolfram Alpha?

Question

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?

Answer 1

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.

Answer 2

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.