I speak without a mouth and write without a pen. I travel through walls but never take a step. I can be caught, but never held. I can be broken without being touched. What am I?

Silent thinker, housed in metal, counting in light and dark, orchestrating digital symphonies without a sound.

At first I was one and only one. Then I became two and grew grew. I further became three through and through. I moved to five and began to thrive. I jumped to eight and ate and ate. Unending I grew forever and never undue. What am I?

Geometric by design, a dozen sides to define.

Unlucky to ten Six may fear me Swimming swans find me prime.