HHC 2014 Programming Contest

[David Hayden]

(09-24-2014 11:46 AM)Paul Dale Wrote:  

1. December 31st prime, assume without loss of generality that it is congruent to 1 mod 3
2. January 1st (1 day), congruent to 2 mod 3
3. December 31st (729 days), congruent to 2 mod 3
4. January 1st (1 day), congruent to 0 mod 3, cannot be prime.
   

You're counting days instead of the difference in the YYYYDDMM representation. The difference between December 31 of one year and the next is 10,000, not 729. E.g. 20141231 - 20131231.

(09-24-2014 11:46 AM)Paul Dale Wrote:  Put a leap year in the second or third year (a leap year in the first doesn't matter):

Leap years don't matter since we aren't counting days.

This changes the details of your analysis, but the results are the same: one of the days must be divisble by 3.

(09-24-2014 11:46 AM)Paul Dale Wrote:  Starting with January 1st instead of December 31st doesn't help because for January 1st to be PDP, the previous December 31st must be too.

I think it can work:

1. Jan 1.
2. Dec 31.
3. Jan 1
4. Dec 31
   

You have to include years 0 and 5 in the analysis of this pattern but you get the same result: one of the days that must be prime can't be prime.