Could Genetic Code Be Understood Number Theoretically ?

The number of DNA triplets is 64. This inspires the idea that DNA sequence could be interpreted as an expansion of an integer using 64 as the base. Hence given DNA triplet would represent some integer in {0,1....,63} (sequences of I Ching symbols give a beautiful realization of these sequences). The observation which puts bells ringing is that the number of primes smaller than 64 is 18. Together with 0, and 1 this makes 20: the number of aminoacids!