I was 10 when I went to the cinema watch this movie for the first time, and to this day it still is the deepest movie I've ever seen. I had the book at my home but I lost it while moving out and unfortunately never got to read it (yet). The plot is awesome and it's based on true science - the factorization into primes, for instance, that the aliens use to communicate with us, was actually tried out (see http://en.wikipedia.org/wiki/Arecibo_message) and you can learn more about it in a fascinating paper called "A Tale of Two Sieves" by mathematician Carl Pomerance:
"The cardinality of 1679 was chosen because it is a semiprime (the product of two prime numbers), to be arranged rectangularly as 73 rows by 23 columns".
: Thanks for the suggestion, regarding the DNA - I saw a similar theory in Through the Wormhole I think (or was it NOVA ScienceNOW?) S02E09 or S03E02 but I Googled a bit and I think they haven't found an intelligent slope in our DNA plotting, the frequency seems to be near-randomic.