erdos_17.variants.upper_BES

In 1999 Blecksmith, Erdős, and Selfridge [BES99] proved the upper bound $$\pi^{\mathcal{C}}(x) \ll_A x(\log x)^{-A}$$ for every real $A > 0$. [BES99] Blecksmith, Richard and Erd\H os, Paul and Selfridge, J. L., Cluster primes. Amer. Math. Monthly (1999), 43--48.

theorem erdos_17.variants.upper_BES {A : ℝ} (hA : 0 < A) :
  (fun x ↦ (clusterPrimeCount x : ℝ)) =O[atTop] fun x ↦ x / (log x) ^ A

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