Ideal Diode Equation: Current Too Large
Your value for \$I_S\$ is way too high. Where did it come from?  Note that the ideality factor is usually closer to 2 for rectifier diodes. 

Here is a typical model:-

.MODEL D1N4001 D IS=29.5E-9 RS=73.5E-3 N=1.96 CJO=34.6P VJ=0.627
+M=0.461 BV=60 IBV=10U

None of the numbers in the datasheet you linked are directly useful in determining \$I_S\$, however you could use this figure from the datasheet:



and play with different values of \$I_S\$ until you get reasonable agreement at lower current values. I say "lower current values" because real rectifier diodes have a resistive component to their \$V_F\$ which is more important at higher currents, and your ideal equation does not take that into account. Although \$I_S\$ is temperature-dependent, the figure specifies that it is measured with brief pulses of current, so we can assume that the \$T_J\$ is 25°C.