(If you're not interested in computer science subtleties, please ignore this node - for normal programming tasks the O(1) estimate is good).

For big numbers the algorithm is slower than O(n), while the summing all the values is O(2^n).

In computer science, if you are talking about O(f(n)), n is the input length, not the number that the input presents.

So adding two numbers with length n is O(n), multiplying two numbers naively is O(n^2), there are a few more elaborate algorithms that do it a bit faster.

Summing all numbers from 1 to $number is O(2^n), because the length of $number is what we call n.

(This calculation kinda assumes use bigint;, because otherwise on the perl vm adding and multiplying is O(1) indeed)