Diagonalization of 40000x40000 real symmetric matrix

[Simplemind]

Dear LAPACK experts,

Would it be possible to diagonalize a 40.000x40.000 real symmetric matrix or is this size too large? Years ago I read 20.000^2 was about the limit. I hope this may have increased.
Could you give a time estimate on a 3GHz quadcore or a machine of your choice?

I apologize, if my question is naive. It would be the first time I diagonalize large matrices...

All the best,
simplemind