erdos_244

Let $C > 1$. Does the set of integers of the form $p + \lfloor C^k \rfloor$, for some prime $p$ and $k\geq 0$, have density $>0$?

theorem erdos_244 : answer(sorry) ↔
    ∀ C > (1 : ℝ), 0 < { p + ⌊C ^ k⌋₊ | (p) (k) (_ : p.Prime) }.lowerDensity

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