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Re: $10K Mathematica Machine
Other programs do some things faster than Mathematica (correct me someone if I'm wrong). Me personally, and I do some Number Theory, is to get a combo of Mathematica for the GUI and a highly efficient number cruncher to do some of the more CPU intensive work. Example: calculate RSA code for two 512-digit primes. I used PARI to do some of the Number Theory calculations, loaded the results into Mathematica and used Mathematica's nice PowerMod function to do the rest.