It further struck me after completing the last entry that we could apply the same condition to the distribution of the primes as the distribution of the non-trivial zeros.
For example we could pose the question: When does the frequency of occurrence of prime numbers change by just 1 which equally is the condition that the probability of a number being prime = 1.
Now the probability of a number being prime can be approximated as 1/log t. So for this to equal 1 then t = e, i.e. 1/log e = 1/1 = 1.
So once again here we can see how e is absolutely central to prime distribution.
In fact we could express 1/log e in an alternative manner which is more revealing as to its true nature.
1 = e^0 whereas e = e^1
Therefore 1/log e = e^0/log (e^1).
So the probability that a prime number = 1, really relates to the fact that the nature of a prime equally combines linear (1) and circular (0) aspects of understanding which are perfectly enshrined in the notion of e.
So e^0 = 1; log e^1 = 1.