Answers to “Nerdy fun with dates and primes”

Answers to the questions in "Nerdy fun with dates and primes":

1. What was the last date to be a prime number in both notations?
   2010-08-09, which translates to 20100809 and 2010221
   (the only such date in 2010)
2. What will be the next date that is a prime number in both notations?
   2012-03-23, which translates to  20120323 and 2012083
   (the only such date in 2012)
3. What is the most recent past year with more than one date which is prime in both notations?
   2008 had 3 such dates: 2008-01-03, 2008-10-03, and 2008-10-23.
4. What is the nearest future year with more than one date which is prime in both notations?
   2013 will have 3 such dates: 2013-08-29, 2013-11-03, and 2013-11-09

Nerdy fun with dates and primes – Updated

Programmers have a couple of common methods of turning dates into integers for ease of sorting and comparison. Using my own terminology, let's call these YMD-notation (for Year-Month-Day) and YJ-notation (for Year-Julian date).

YMD-notation

yyyymmdd -- the four-digit year, followed by the two-digit month, then the two-digit day of the month, using leading zeros where necessary. Thus, 3/17/2009 would be the number 20090317 -- the 17th day of the third month of the year 2009.

YJ-notation

yyyyjjj -- the four-digit year, followed by the three-digit day of the year, again using leading zeros. Thus, 1/2/2001 would be 2009002 -- the second day of the year 2009; 2/1/1998 would be 1998032 -- the 32nd day of the year 1998.

Obviously, when you turn a date into an integer, it might be prime. The following dates in 2011 are prime in one notation or the other:

You might notice that no date in 2011 is prime in both YMD-notation and YJ-notation. That gives rise to the following questions.

1. What was the last date to be a prime number in both notations?
2. What will be the next date that is a prime number in both notations?
3. What is the most recent past year with more than one date which is prime in both notations?
4. What is the nearest future year with more than one date which is prime in both notations?

Answers in a later post! Update: Answers have been posted.