Zeros of the Zeta Function
Mathematica 6 can efficiently find zeros of the zeta function on the critical line.
In[1]:=  |  Plot[Im[Zeta[1/2 + I t]], {t, 0, 80},
Epilog -> {PointSize[.02], Red,
Point[Table[{Im[ZetaZero[n]], 0}, {n, 20}]]}] |
Out[1]=  |  |