Tinyurl-style unique code: potential algorithm to prevent collisions

Question

I have a system that requires a unique 6-digit code to represent an object, and I\'m trying to think of a good algorithm for generating them. Here are the pre-reqs:

Answer 1

Any prime number which is not a factor of the length of the sequence should be able to span the sequence without repeating. For 64000000, that means you shouldn't use 2 or 5. Of course, if you don't want them to be generated consecutively, generating them 2 or 5 apart is probably also not very good. I personally like the number 73973!

Answer 2

Don't reinvent the wheel: http://en.wikipedia.org/wiki/Universally_Unique_Identifier

Answer 3

All you need is a number that shares no factors with your key space. Easiest value is to use a prime number. You can google for large primes, or use http://primes.utm.edu/lists/small/10000.txt

Answer 4

There is another method to get a similar result (jumping over the entire set of the values without repeating, nonconsequtively), without using the primes - by using maximum length sequences, which you can generate using specially constructed shift registers.

Answer 5

My math is a bit rusty, but I think you just need to ensure that the GCF of N and 64 million is 1. I'd go with a prime number (that doesn't divide evenly into 64 million) just in case though.

Answer 6

@Nick Lewis:

Well, only if the prime number doesn't divide 64 million. So, for the questioner's purposes, numbers like 2 or 5 would probably not be advisable.