Eternal 2014 — PCG.SE New Year’s Puzzle 2015
Python 2, 166 bytes

n=input()
d=m=y=1
M=([3]+[3,2]*3)*2
while n&gt;1721426:
 n-=1;d+=1;M[2]=y%400&lt;1or y%4&lt;1&lt;y%100
 if d&gt;M[m%12]+28:m+=1;d=1
 if m&gt;12&lt;2014&gt;y:y+=1;m=1
print'%02d/'*2%(d,m)+`y`


This cycles through every day from January 1, 1 (1721426) to the given date, incrementing the current day, month and year as it goes. The last test case takes about a second on my computer.

Output is printed in the second format:

01/01/1
31/12/999
23/15059/2014