This is the table of 144 numbers that Emily, and millions like her, are drilled on every week at school. The numbers have been colour-coded to their lowest prime factor according to Emily’s scheme.
Each number is repeated 2.5 times on average and some numbers appear 6 times. The table only contains the safe, friendly and boring numbers.
Here is another table of 144 numbers with each appearing only once.
We can see the odd numbers, even numbers and multiples of three more clearly than before – and now we also have all the interesting oddish numbers.
In both tables, only the primes in the top row need distinct colour-coding to highlight the other numbers in the table where that prime is the lowest factor. The tables have a square format and so, by definition, the highest number in the bottom-right corner is the square of the number in the top-right corner. The fact that this is true for both tables tells us something about the relationship between addition and multiplication.