Here are two pieces of information that the atomic number of carbon being 6 tells us:

1. Number of Protons: The atomic number directly corresponds to the number of protons in an atom's nucleus. Therefore, a carbon atom has 6 protons.

2. Identity: Each element is defined by its unique number of protons. Since carbon's atomic number is 6, we know that any atom with 6 protons is a carbon atom.