Well that's essentially what I have done, except the unique hash is just a single integer and the hash function is f(x,y) = x + y.

Such a trivial hash function would normally be unacceptable due to the prevalence of hash collisions but avoids them by x and y being (multiples of) prime numbers.

it works anyway

**You were lucky**. The' x+y is unique if x,y E prime numbers' is a fallacy that is disprovable by the presence of multiple prime pairs. [1]

I just created a simple "x,y" hash myself.

[1] came across this in a PhD thesis once. It was the cornerstone of his algorithm. He failed. [2]

[2] 5+13 == 7+11.

I agree

,

*but*, is there not a condition you could place on the primes to guarantee it?

My initial 'hunch' was that that condition would be

p1>n AND p2 > n

I have absolutely no idea how to prove that however.

Thinking about it however

would

p1 > p2 x n AND p2 > n

not guarantee it?

Again, no idea how to prove, just a hunch

Can

*you dis*prove it?

so if, say, n = 10, I would choose primes 11 and 113...

i.e. 11 > 10 and 113 > 10* 11.

what moves (values of m1 and m2) would cause a hash collision i.e. such that

m1 * p1 = m2 * p2

where

m1 <= 10

m2 <= 10

p1 = 11

p2 = 113

?

How to prove there are no such values of m1 and m2?

If I place that condition do they even need to be prime?