There is a magic number, 6 digits long, that when you add, multiply, subtract and divide all or parts of it, it does amazing stuff. What is this number?

It is difficult to know quite what you are looking for with that description.
The 6-digit cyclic number 142,857 is quite unusual in that:

142,857 x 2 = 285,714
142,857 x 3 = 428,571
142,857 x 4 = 571,428
142,857 x 5 = 714,285
142,857 x 6 = 857,142
142,857 x 7 = 999,999

Also 142 + 857 = 999.
The square of 142,857 = 20,408,122,449 and...
20,408 + 122,449 = 142,857.

All these facts relate to it being the recurring part of 1/7 as a decimal.

https://en.wikipedia.org/wiki/142,857
http://www.decisionsciencenews.com/2013/07/10/numbers-worth-knowing-142857/