Finding primes

Number Theory Level pending

Let \(P(N)\) be the probability that a randomly chosen integer, \(N\), is prime. If \(P(N) = x/(6\ln N)\) Then find the value of \(x\) where \(x\) is an integer.

Note: Assume that \(N\) is very large, and ignore terms in your answer that are of subleading order in \(N\). Also, make the assumption that the probability that \(N\) is divisible by a prime \(p\) is exactly \(1/p\) (which is essentially true, for a large enough sample size of numbers).

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