The newly released LAPACK Working Note #206 gives yet another reason why generating good pseudorandom numbers matters:

In May 2007, a large high performance computer manufacturer ran a twenty-hour long High Performance Linpack benchmark. The run fails with the following output:

|| A x - b ||_oo / ( eps * ||A||_1 * N ) = 9.22e+94 ...... FAILED

What happened was that the benchmark's matrix generator uses a lame linear congruential pseudorandom number generator, which causes generated matrices to have repeated columns for certain unfortunate choices of matrix dimension. This of course makes one wonder why the generator doesn't just make a matrix which is known to be invertible, say, by generating a sufficiently nonzero diagonal matrix and hitting it on both sides with orthogonal transforms until the zeros are filled in. Regardless, the bug meant 20 hours of very expensive, intensely power-consuming supercomputer time were wasted on computing the wrong answer to a problem which at such sizes very few people need to solve. So, random numbers do matter ;-)