What are the implications of Prime Number Theorem in Cryptography?

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I know that primes and prime factorization are the basis concepts in cryptography. However, I would like to know how does the Prime Number Theorem come into picture in cryptography, since it states that the prime counting function is asymptotically equal to $\frac{n}{\ln n}$. In other words, what is the implication of knowing number of primes less than $n$, in cryptography?

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It has indirect implications on how easy it is to find the large primes needed in RSA.