URL shortening services like tinyurl and makeashorterlink offer a redirection service based upon indexing longer URLs entered in with a character code system.
Once the number of characters have been assigned, a new digit is added with a new range of mathematical storage slots. Mathematically speaking, thought it was never one of my best subjects, these generated URLs can still stay relatively small, even if a significant number of URLs are entered into it
Using most elligible URLs from http://www.ietf.org/rfc/rfc1738.txt
a - z (26)
0 - 9 (9)
We can then calculate with the following example (not all elligible characters used, so the actual numbers are even larger):
1 digit: 35
2 digit: 1,225
3 digit: 42,875
*4 digit: 1,500,625
5 digit: 52,521,875
6 digit: 1,838,265,625
7 digit: 64,339,296,875
8 digit: 2,251,875,390,625
9 digit: 78,815,638,671,875
10 digit: 2,758,547,353,515,625
11 digit: 96,549,157,373,046,880
12 digit: 3,379,220,508,056,640,512
13 digit: 118,272,717,781,982,429,184
14 digit: 4,139,545,122,369,384,742,912
As of this writing the tinyurl service is at 4 digits, so we can assume that approximately this number of URLs have not been exceeded at the time of this writing. The other service is at 9 digits, indicating that it has been used more often, or perhaps more likely that the programmers randomized the digit outcome (78+ trillion is a lot of URLs to have generated).
