Skeel and Keiper, Example, p. 8 and Computer problem #1, p. 11

One way to approach this is using “cut and paste” -- which is okay for a “one-off” problem, but if you’re going to need to do this over and over, you’ll want to turn it into a loop!

N[Exp[Pi*Sqrt[163]],18]
N[Exp[Pi*Sqrt[163]],19]
N[Exp[Pi*Sqrt[163]],20]
N[Exp[Pi*Sqrt[163]],21]
N[Exp[Pi*Sqrt[163]],22]
N[Exp[Pi*Sqrt[163]],23]
N[Exp[Pi*Sqrt[163]],24]
N[Exp[Pi*Sqrt[163]],25]
N[Exp[Pi*Sqrt[163]],26]
N[Exp[Pi*Sqrt[163]],27]
N[Exp[Pi*Sqrt[163]],28]
N[Exp[Pi*Sqrt[163]],29]
N[Exp[Pi*Sqrt[163]],30]
N[Exp[Pi*Sqrt[163]],31]
N[Exp[Pi*Sqrt[163]],32]
N[Exp[Pi*Sqrt[163]],33]
N[Exp[Pi*Sqrt[163]],34]
N[Exp[Pi*Sqrt[163]],35]

i=21
While [i < 36, Print [{i,N[Exp[Pi*Sqrt[163]],i]}];i++]

From Appendix A.2, p. 379:

The function N returns a machine number:

c=N[Pi]

c is indeed considered a machine number:

MachineNumberQ[c]

Pi is not a machine number, however: it’s considered an “arbitrary precision” number. How can we represent Pi in a computer with a finite number of storage locations? What’s the problem?

MachineNumberQ[Pi]