Experimental Results on Additive 2-Bases
M. L. Stein, P. R. Stein · Mathematics of Computation · 1965
Introduction.This paper describes the construction of binary additive bases for all even numbers in some finite interval 2 g 2n ^ N. The construction makes use of a simple algorithm, first introduced by the authors in an earlier paper [1].In the present paper the algorithm is applied to the sequence of primes, and several distinct "sparse" prime bases, constructed with its help, are described.As a byproduct of this work, the verification of the Goldbach conjecture has been extended up through all even numbers 2« ^ 107.tThe algorithm has also been applied to several random sequences of odd integers chosen so that their distribution is approximately that of the primes.Although the algorithm cannot, at present, be treated theoretically, even with regard to its asymptotic behavior, one may make plausible conjectures about it on the basis of various distinctive gross features; we hope to discuss this in a separate paper.