 Multiplication is by definition information conserving. We have: \(\delta(a \times b) = 0\), since \(\log (a \times b) = \log a + \log b\). Still multiplication does not preserve all information in its input: the order of the operation is lost. This is exactly what we want from an operator that characterizes an extensive measure: only the extensive qualities of the numbers are preserved. If we multiply two numbers \(3 \times 4\), then the result, 12, allows us to reconstruct the original computation, in so far as we can reduce all its components to their most elementary values: \(2 \times 2 \times 3 = 12\). This leads to the observation that some numbers act as information building blocks of other numbers, which gives us the concept of a prime number: 