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Guest wrote:Guest wrote:[tex]a(x) \approx[/tex] 7491 = x /[tex]\pi(x) \approx x /(x/log(x)) = log(x)[/tex].
So, [tex]x \approx e^{7491} \approx 1.995 * 10^{3253}.[/tex]
So, [tex]mpg/x \approx 0[/tex].
Therefore, the size of 'sufficiently large' prime gaps between consecutive primes is extremely small relative to the size of the their corresponding primes. This indicates there's much redundancy or repetition of previously generated prime gaps according to the Harmonic Series and PNT. In addition, I see the growth of new clusters or galaxies of primes separated by growing space between them like our expanding universe...
So, primes are relatively close together on average in their corresponding clusters while their corresponding clusters are growing farther and farther apart.
It's amazing how natural numbers mirror our natural world! Praise Lord GOD!
Reference link: 'PRIME WORK: Three Laws which govern the general behaviour of prime numbers',
https://www.linkedin.com/pulse/prime-work-three-laws-which-govern-general-behaviour-numbers-cole?articleId=6167804339399176192#comments-6167804339399176192&trk=prof-post