With due consideration of the high inclination ##17.2^o## of Pluto’s orbital plane to our ecliptic, the least lower bound for the minimum Earth-Pluto distance is 4.29 B km = 2.66 B miles, nearly.

I have used NASA Planetary Fact Sheet data.

Pluto : Perihelion = 4.436 billion (B) km and orbital inclination to Earth’s orbital plane = ##17.2^o##. Earth : Aphelion: 0.1521 B km.

For least possible Earth-Pluto distance,,in (E) – Sun (S) – Pluto (P) ##triangleESP##, SE = Earth aphelion, SP = Pluto perihelion and ##angleESP= max 17.2^o##

So, least ##EP = sqrt(SP^2+SE^2-2XSEXSPXcosangleESP)##. , This simplifies to 4.29 B km