The answer to the previous question is not a great estimate of the complexity of Prim's algorithm. Why not?

Finding and adding an edge is a relatively easy process, we should choose a more computationally demanding step to count:

The step where we set e to be the shortest edge between a vertex of $T$ and a vertex not in $T$ is hiding some work: this step requires a search algorithm which will be more complex the larger $T$ and $N$ are.

This estimate doesn't account for the amount of memory used.

This estimate doesn't account for the speed of the processor.