## Tuesday, January 17, 2012

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.