Recently I have asked two questions in MSE regarding the simultaneous solutions of the following inequalities: $$x+y>p_{\pi(x)}+p_{\pi(y)+1}\tag{1}$$$$x+y>p_{\pi(y)}+p_{\pi(x)+1}\tag{2}.$$ My earlier question regarding this inequality was answered in MSE. My next question is the following:

Let $x+y+2$ be a prime such that $x>y\ge 3$ and $x$ and $y$ both are composites. Is it true that if $(1)$ holds, then $(2)$ must hold? Are there infinitely many counterexamples to this assertion?

Can anyone tell me whether this would be a suitable question for MO?


No, this question is not suitable. In this order:

  1. It is unmotivated.

  2. It is hard to understand.

  3. It seems rather easy once deciphered.

Sorry for being a bit harsh, but IIRC you already asked several such questions (some deleted) and the same could be said for several of them. (Some also might be very hard, but then just asking some hard questions about primes is no achievement.)

  • $\begingroup$ "It seems rather easy once deciphered."-is it really that easy? If it is, please consider posting an answer to my next post to MSE (the link of the question will be given shortly). In case you don't want to write an answer, can you tell me the answer of the questions? $\endgroup$ – user 170039 Jun 5 '15 at 2:47
  • $\begingroup$ Yes, I am active on math.SE and would answer it I notice it. But for now: $125$ and $4$ should be an example where 1 holds but 2 does not. $\endgroup$ – user9072 Jun 5 '15 at 8:41

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