File:Gaps.jpg

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

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