Daniel,
just a remark - you can achieve the same by simply plotting the PrimePi-function:
Plot[PrimePi[x], {x, 0, 200}]
If you do it your way you probably might consider the option InterpolationOrder:
ListLinePlot[Table[{Prime[n], n}, {n, 46}],
PlotStyle -> PointSize[Medium], InterpolationOrder -> 0]
