Geek Date - how precise a pi do you need.

So... as we all remember, March 14th in the US is a special day, in particular just before 2 o'clock.

3.14 1:59.xxx in US notation

So, here's a question for the true geeks.

How precisely do you have to time it, so that you get a complete Pi for that date.

ie 3.14 1:59:26.xxx YYYY

so how many nths of a second (how many "xxx" digits) do you need to go to before you get the year (YYYY digits) as consecutive digits and can stop.

hint

Which interesting year appears the earliest? And, no 6535 AD is not interesting unless you know something I don't.
You could make good crackpot case for it being interesting in other calendar systems though...

Double hint: most interesting years appear in the first 10,000 digits.

Year of my birth is unusually interesting, clearly.

The earliest year of the last century is easy and also interesting.

2006 is finitely interesting.

Of the last 2005 years, which is the last to appear in the decimal expansion of this form?