x/ln x.........is a good........"ball park figure"...............as "Music of the Primes" put it........but is locally irregular.....................x/log of pi of x...........................................is more accurate.....................

Locally irregular..............cycles........................................

How many primes are there? - The Prime Pages

https://primes.utm.edu/howmany.html

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The prime number theorem tells us the number of primes less than n is about ... So even though pi(x) is "locally" irregular, there is a definite trend to its values.

Prime Numbers and Twin Primes - National Curve Bank

web.calstatela.edu/curvebank/prime/prime.htm

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Math in the news: Are there an infinite number of pairs of "twin primes? ... prime number theorem that there are about n/(log n)² twin primes less than ... On the left, the number of primes between 0 and 100 would appear to be "locally" irregular.

[PDF]Prime Number Theory and the Distribution of the Primes

vknight.org/Computing_for_mathematics/Assessment/.../lunn2013-2014.pdf

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A prime number is defined to be a positive number greater than 1 that