  It is tacitly accepted that, for practical basis sets consisting of N
functions, solution of the two-electron Coulomb problem in quantum mechanics
requires storage of O(N^4) integrals in the small N limit. For localized
functions, in the large N limit, or for planewaves, due to closure, the storage
can be reduced to O(N^2) integrals. Here, it is shown that the storage can be
further reduced to O(N^{2/3}) for separable basis functions. A practical
algorithm, that uses standard one-dimensional Gaussian-quadrature sums, is
demonstrated. The resulting algorithm allows for the simultaneous storage, or
fast reconstruction, of any two-electron coulomb integral required for a
many-electron calculation, on each and every processor of massively parallel
computers even if such processors have very limited memory and disk space. For
example, for calculations involving a basis of 9171 planewaves, the memory
required to effectively store all coulomb integrals decreases from 2.8Gbytes to
less than 2.4 Mbytes.
