Last week astronomer Phil Plait posted on his Bad Astronomy blog an article about leap day. In it he stated:
The year is not exactly 365.25 days long. Our official day is 86,400 seconds long. I won’t go into details on the length of the year itself (you can read a wee bit about it here), but the year we now use is called a Tropical Year and it is 365.242190419 days long. With malice aforethought — my calculator won’t hold that many digits — let’s round it to 365.2421904... There is no official rule for leap days with cycles bigger than 400 years. I think this is extremely ironic, because the amount we are off every 400 years is almost exactly 1/8th of a day! So after 3200 years, we’ve had 8 of those 400 year cycles...This whole 400-year thingy was started in the year 1582 by Pope Gregory XIII. That’s close enough to the year 1600 (which was a leap year!), so in my book, the year 4800 should not be a leap year.
Except that he's wrong. He was also wrong when he posted this originally four years ago. I posted a correction in the comments then, and I've done so again now, but obviously he does not read the comments. The reason he is wrong is because he's using the wrong value for the year. The document that Gregory issued establishing his calendar is called the Inter gravissimas. It clearly states that the reform is intended to fix the date of the vernal equinox, upon which Easter is based. The year defined by equinoxes is not the same as the Tropical Year mentioned above, but a slightly larger value between 365.24237 and 365.24238. This is closer to the average Gregorian year of 365.2425 days. Using the equinoctial figure, it will take about 8000 years before it's off by one day, which would be in the tenth millennium. Due to the variability of the equinoctial year, we cannot even predict its value that far in the future. The way it's trending now, I could even be much further in the future.
He is not alone. This error is often repeated by astronomers. It is sometimes traced back to John Herschel, but during the Revolution French astronomers calculated that the mean year was between 365.2422 and 365.24225 days and proposed an adjustment after 4000 years. But none of them were using the vernal equinox, as Gregory did. The correct figure may be found in Wikipedia and others. Anybody can figure it out themselves simply by taking the average between the equinoxes of any two years.