It is known that the probability in question does not tend to zero as $N\to\infty$, and it is conjectured that it tends to $1-e^{-2}\approx 0.864665$. I suggest to read the introduction of this paper by Teräväinen for an overview of this research area.

It is known that the probability in question exceeds a positive constant for $N>N_0$, and it is conjectured that it tends to $1-e^{-2}\approx 0.864665$ as $N\to\infty$. I suggest to read the introduction of this paper by Teräväinen for an overview of this research area.

It is conjectured that the probability in question tends to $1-e^{-2}\approx 0,864665$, but we are far from proving this. Read the introduction of this paper by Teräväinen for an overview of this research area.

It is known that the probability in question does not tend to zero as $N\to\infty$, and it is conjectured that it tends to $1-e^{-2}\approx 0.864665$. I suggest to read the introduction of this paper by Teräväinen for an overview of this research area.