Or even better: e^(tau * i) - 1 = 0

The 4/3 part of 4/3 pi * r^3 is actually a misnomer, because the sphere is in reality 2/3 of the cylinder.

We can halve 4/3 and multiply pi by 2, resulting in 2/3 * 2 * pi * r^3.
With Tau we can now gain a correct understanding of the formula by using 2/3 * tau * r^3

1339 * 2 = 2678 seconds, which is 44.63 minutes (40 minutes in round figures)

That is the theoretical longest time it takes for round trip communication with Mars.
The shortest distance is 55.7 millions kilometers, making for a smallest round trip of 372 seconds, a bit more than 6 minutes.

This will be why Earth and Mars at their furthest distance will be known as the Eternal September.