File:Gaps.jpg

Summary
The plot showing the dependence of the histogram $$h_N(g)$$ on g at $$ N=2^{20}, 2^{22}, \ldots, 2^{44}$$. There is a logarithmical scale on the y-axis , while on the x-axis there is a linear scale. The values of $$h_N(g)$$ obtained from the computer search are represented by small circles. The points oscillate with main period 6. Let us mention local spikes at $$g=30 ( = 2 \cdot 3 \cdot 5), 60, \dots$$. Especially well profound are spikes at $$g=210=2\cdot 3\cdot 5\cdot 7$$, and for $$ N=2^{40},~N=2^{42}, ~N=2^{44}$$ also at its multiplicity g=420 (second harmonic).