III. Introduction to the Main Tables*.

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\The invention of new [factorization] methods may push o_ the

limits of the unknown a little farther, just as the invention of a

new astronomical instrument may push o_ a little the boundaries

of the physical universe; but the unknown regions are in-

_nite, and if we could come back a thousand years from now,

we should no doubt _nd workers in the theory of numbers announcing

in the journals new schemes and new processes for the

resolution of a given number into its factors."

D. N. Lehmer [66]

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