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When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element methods,it is common knowledge that only a small portion of numerical eigenvalues are reliable.However,this knowledge is only qualitative rather than quantitative in the literature.Here we investigate the number of rusted" eigenvalues by the finite element approximation of 2m-th order elliptic PDE eigenvalue problems.Our two model problems are the Laplace and bi-harmonic operators.We show that the number of reliable numerical eigenvalues can be estimated in terms of the total degree of freedom N of resulting discrete systems.The result is worse than what we used to believe in that the percentage of reliable eigenvalues with a pre-set convergent rate(also in terms of N)decreases with an increased N.