Temperature on the surface of the sun calculated with the Stefan-Boltzmann-rule

In a German Wikipedia page, the following calculation for the temperature on the surface of the Sun is made:

$sigma=5.67*10^{-8}frac{W}{m^2K^4}$ (Stefan-Boltzmann constant)

$S = 1367frac{W}{m^2}$ (solar constant)

$D = 1.496*10^{11} m$ (Earth-Sun average distance)

$R = 6.963*10^8 m$ (radius of the Sun)

$T = (frac{P}{sigma A})^frac{1}{4} = (frac{S4 pi D^2}{sigma 4pi R^2})^frac{1}{4}=(frac{SD^2}{sigma R^2})^frac{1}{4} = 5775.8 K$

(Wikipedia gives 5777K because the radius was rounded to $6.96*10^8m$)

This calculation is perfectly clear.

But in Gerthsen Kneser Vogel there is an exercise where Sherlock Holmes estimated the
temperature of the sun only knowing the root of the fraction of D and R.
Lets say, he estimated this fraction to 225, so the square root is about
15, how does he come to 6000 K ? The value $(frac{S}{sigma})^frac{1}{4}$
has about the value 400. It cannot be the approximate average temperature
on earth, which is about 300K. What do I miss ?