2 problems

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Conjecture on the nondensity of average orders of finite groups
Nondensity conjecture. Let $a\geq 0$ be a real number. Then $Im(o)$ is not dense in $[a,\infty)$ .
Conjectureopenaverage-orders finite-groupsarXiv posted 2 days ago
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Landau's average-order conjecture for Goldbach representations
Landau's average-order conjecture. The function $g(n)$ should be approximated by
Conjectureopenanalytic-number-theory average-orders goldbach-problemarXiv posted 2 days ago

Conjecture on the nondensity of average orders of finite groups