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I want to ask "is the probability of N being prime smaller than the probability of M being prime, if N and M are randomly chosen, and M < N?"

Having tried to do some research, as a non-trained mathematician, I find many people ask "what is the probability that a randomly chosen number N is prime".

The responses fall into 2 groups:

  1. A random integer chosen in the range K, has a probability of being prime that falls towards 0 as K increases.

  2. The Prime Number Theorem approximates the probability of N being prime as $\frac{1}{log(N)}$ so the bigger N, the smaller the probability.

I can't seem to reconcile these two statements. What am I missing?

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  • $\begingroup$ Second statement is more precise than first one, stating how fast probability of being prime falls towards $0$. $\endgroup$ – Atbey Jun 13 '18 at 14:01
  • $\begingroup$ thanks, that makes sense $\endgroup$ – Tariq Rashid Jun 13 '18 at 14:53

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