Rational Euler-Mascheroni Constant Query

[Hans Havermann]

Back in 1997, T. Papanikolaou calculated 1000000 decimal places of this 
number and also showed that if the constant is rational, its 
denominator has at least 242080 decimal digits.

I'm trying to understand where the 242080 comes from. If we convert the 
million decimal places to continued fraction form (970031 terms) and 
find the 970031st convergent of these terms, the denominator of the 
resulting rational approximation has half a million digits, i.e., 
*half* of the decimal accuracy of the constant. Right?

So, why doesn't that show that the constant, if rational, has a 
denominator > 10^500000?