For those that have noticed how YouTube view counts freeze at 301, you'll likely enjoy this as a fun little tour through some obscure Internet history.
tl;dw - They have to scrutinise video counts, and decided on a threshold to do it. i.e. 300. However, the code was:
if (viewcount <= 300) { viewcount++; }
else {...
So, 301 got counted.
It has nothing to do with number types or data size limits or anything like that.