This mathematical essay explores the hidden regularities of Collatz sequences which at first
sight seem rather chaotic. Their behavior is however determined by a simple threshold number
and by binary signatures which capture the percentage of down versus up movements. Their
starting elements are described by primal numbers which share properties with prime numbers.
The relationship with prime numbers and some famous theorems and unsolved problems are explored
such as Bertrand's postulate and de Polignac's second conjecture. The twin prime conjecture is
rephrased as an example of the pigeonhole principle. Graphically a Collatz sequence will be
interpreted as a walk on a fractal the Cantor set.
