Chinese myth suggests that a Jade Rabbit lives on the Moon, pounding away at lunar regolith to extract the elixir of life. If such an immortal rabbit were to reproduce, and its children multiply without dying, one would see the population of rabbits on the moon evolve like this - 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and so on till infinity. The Apollo mission found no such creature on the moon, however...

Two consecutive numbers when added result in the next number in the sequence above, observed first by Pingala (200 B.C.) and later, independently - in the middle ages by Leonardo of Pisa, better known as Fibonacci. 1+1 = 2, 1+2 = 3, 2+3=5, 3+5=8...thus do these breeder bunnies grow. For brevity, let us say that F(n) denotes the n'th number in this sequence and observe the table pictured above.

By themselves, these numbers are not so interesting - unless you can see an underlying pattern. Prime numbers are the atoms which help us define a unique formula for each integer (see: "The Fundamental Theorem of Arithmetic" on Wikipedia). And this is where we find a highly structured landscape, full of periods, connections and loops. Take F(33), the 33rd Fibonacci number and its formula in primes - 2 X 89 X 19801. Before we go further, keep in mind that 33 = 3 X 11.

The number 2 is actually F(3) and 89 is F(11), so we learn here that when m divides n, then F(m) definitely divides F(n). The number 19801 is in green because it appears in a formula in this sequence for the very first time. This is true for all the primes in green. In fact, you will notice that every new Fibonacci number in the sequence brings at least one new prime number with it which has not been seen before. Sometimes, and this is extremely rare, the Fibonacci number itself is that prime. Also, no two consecutive numbers have any factors in common.

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