Asymptotic Formula for Totient Sum Over Shifted Primes with \(6/π^2\) Constant — E8 Intelligence Research

FINDING: Asymptotic formula for sum of Euler totient over shifted primes reveals a constant term involving \(6/π^2\) and a \(loglog x\) growth. | MATH: \(∑p ≤ x φ([x/p]) = 6/π^2 x loglog x + c_0 x + O( x (log x)⁻¹ )\); constant \(6/π^2 ≈ 0.607927\) (reciprocal of \(ζ(2)\)). | CONNECTION: The constant \(6/π^2\) is the density of squarefree integers, linked to the hexagonal lattice packing density in 2D (circle packing ratio \(π/(2√3) ≈ 0.9069\) is distinct, but \(6/π^2\) appears in lattice point counting for coprime pairs). No direct golden ratio or base-60 link. | DEPTH: 6 — solid analytic number theory result with a clean constant, but not a paradigm shift. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com