Here are the steps to solve this problem:
1) Mercury is the closest planet to the Sun.
2) Neptune is the farthest planet from the Sun.
3) To calculate the distance between them, we would need the actual distances of each planet from the Sun in astronomical units (AU). Without those values, there is no numerical calculation we can perform.
The statement gives us the relative positions of Mercury and Neptune compared to the Sun, but not enough quantitative information to calculate a numerical distance between the two planets.