Given a positive integer, let’s call the difference between two consecutive potential typical primality radii of a « Goldbach gap ». There are exactly such Goldbach gaps. Let’s denote by the number of distinct Goldbach gaps, and let’s write , the -th such Goldbach gap in the increasing order. Thus and . Moreover, let’s denote by the multiplicity of . One has and . Writing , one gets . Let’s define for ranging from to so that , and if . One has . Hence , and . Therefore .