# 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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