The fact the L.C.M. is somewhere in-between serves as a first-indicator as to how many { prime numbers } there are .
And we were able to establish :
where [ pi-of-(M) ] is the { prime number counting function } .
The term on-the-very-right under the [ product sign ] is then the [ product-of-primes ] up to [ M ] .
We then use the { product-of-primes } series as the [ modulo's ] series to further identify { prime numbers } , i.e. the series :
with some success initially .
we propose the { Fung Inequality } , as follows :
as the core function in his investigations of { prime numbers } .
The f(x) fucntion is a { step function } that [ pops ] whenever the value of [ x ] hits a { prime } or a { power-of-prime } .