How was the date of December 4, 292,277,026,596 calculated for the overflow of the 64 bit signed unix timestamp?

I've tried to calculate the date myself using the maximum 64-bit signed integer but always end up with another date that's a few million years different. I've tried using sidereal years and leap years but I always get results that are at least a few million years off.

Here is what I've tried thus far:

dateA = 1970 + (9223372036854775807/31556926.08)

dateB = 1970 + (9223372036854775807/31536000) + (((9223372036854775807/31536000)/4)/365)

Both return the wrong answer. Can anyone guide me in the right direction?

Solution

You need to account for the years that are leap years. A year is a leap year if:

it is evenly divisible by 4;
unless it is evenly divisible by 100;
or if it's evenly divisible by 400.

As a rough estimate for the year, calculating 1970 + 0x7fffffffffffffff // 86400 // (365 + 1/4 - 1/100 + 1/400) gives an answer of 292277026596. I'll leave the derivation of the exact day as an exercise for the reader.

I used Python 3 for this calculation which gives real results for integer divides. Adjust accordingly for Python 2.