In its simplest form, trial division operates by successively testing \(x\) for divisibility by each integer smaller than \(x\) and keeping track of the divisors which have been found thus far. As the number of divisions required by this procedure is proportional to \(x\) itself, it might at first seem that it is not a particularly onerous task to employ this method to factor numbers of moderate size using paper and pencil calculation – say \(x \lt 100000\). Note, however, that we conventionally denote natural numbers using positional notations such as binary or decimal numerals. A consequence of this is that the length of the expression which is typically supplied as an input to a numerical algorithm to represent an input \(x \in \mathbb{N}\) is proportional not to \(x\) itself, but rather to \(\log_b(x)\) where \(b \geq 2\) is the base of the notation system in   question.[4]   As a consequence it is possible to concretely inscribe positional numerals of moderate length which denote astronomically large numbers. For instance a binary numeral of 60 digits denotes a number which is larger than the estimated age of the universe in seconds and a binary numeral of 250 digits denotes a number which is larger than the estimated age of the universe in Planck   times.[5]