How many years of millisecond timestamps can be represented by 41 bits?

Question

I'm looking at the Instagram blog post about sharded ID generation. This blog post describes generating 64-bit identifiers. Their mechanism allocates 41 of the 64 bits to a millisecond timestamp, and they say:

• 41 bits for time in milliseconds (gives us 41 years of IDs with a custom epoch)

Is this a typo? I calculated that you can store 69 years of millisecond timestamps in 41 bits. Here's how:

• Max milliseconds stored in 41 bits: (2^41)-1 = 2199023255551 ms
• Divided by (1000 * 60 * 60 * 24 * 365 ) ms/year = 69 years

So, where am I wrong?

Answer 1

You're not wrong about the calculation.

(2^41)-1 ms
    == 2199023255.551 s
    == 610839.7932086 hr 
    == 25451.65805036 days 
    == 69.6828 Julian years 
    == 69.6843 Gregorian Years

Which lines up closely with your result (69 years).

However, the website you link to does say that 41 bits gives them

41 years of IDs with a custom epoch

"Epoch" in this context is probably referring to the start date. Given that that article was published "3 years ago", or in 2012, we can calculate that their epoch begins in 2012 + 41 - 69 == 1984. This date was possibly chosen as a reference.