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The Goldbach conjecture states that every even integer ≥ 4 can be written as a sum of two prime numbers. It is known to be true up to 4 × 1011. In this paper, new experiments on a Cray C916 supercomputer and on an SGI compute server with 18 R10000 CPUs are described, which extend this bound to 1014. Two consequences are that (1) under the assumption of the Generalized Riemann hypothesis, every odd...
In a recent article [6] a new method was proposed for computing internal eigenvalues of symmetric matrices. In the present paper we extend these ideas to non-hermitian eigenvalue problems and apply them to a practical example from the field of magnetohydrodynamics (MHD). The method is very suitable for an efficient parallel implementation. We give some results for the time-consuming kernels of the...
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