6.3, due on October 20

1. (Difficult) One thing I was wondering about is how splitting up a composite modulus into it's primes helps us better understand Miller-Rabin better (as is done on p. 180).  I think there's things with splitting up moduli that I don't understand yet.  Does this all relate to the Chinese Remainder Theorem?
2. (Reflective) This section on primality testing actually seemed pretty approachable.  I did not take the time to understand everything (not that I necessarily could understand everything by reading), but the approach seemed comprehensible.  It seemed more conversational, and less formal (proof-y?) than other things we've looked at.  Is there sufficient information in this section to prove the ideas talked about, or are more details required?