International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 15, Pages 789-798
On the existence of a non-zero lower bound for the number of
Goldbach partitions of an even integer
Institut für Mathematik, Universität Potsdam, Potsdam D-14415, Germany
Received 15 March 2002
Copyright © 2004 Simon Davis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Goldbach partitions of an even number, given by the sums of
two prime addends, form the nonempty set for all integers
with . It will be shown how to
determine by the method of induction the existence of a non-zero
lower bound for the number of Goldbach partitions of all even
integers greater than or equal to 4. The proof depends on contour
arguments for complex functions in the unit disk.