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How may number pairs $(n - 2, n)$ are there, less than $n$, where $(n – 2)$ is prime and $n$ is composite?

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I was wondering about number pairs, that differ by 2 on the natural numbers field. They can be twin primes, twin composites, and mixed.The mixed can be 2 types, either the first is prime, the second is composite, or the first is composite, the second is prime.I am specially interested in $\pi(n-2, n)$ , where $(n – 2)$ is prime and $n$ is composite.Are there some upper limits in terms of the number of primes, or can we say something about them that has some connection with $\pi(n)$ ?


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