Why does order matter?
Whether a 64-bit number can be written as the product of two 32-bit ones depends only on the prime factors of the 64-bit number - it's a property of the number itself, and apparently 17% of 64-bit numbers have this property.
Why does order matter?
Whether a 64-bit number can be written as the product of two 32-bit ones depends only on the prime factors of the 64-bit number - it's a property of the number itself, and apparently 17% of 64-bit numbers have this property.
The input space is 32 + 32 = 64 bits. The output space is 64 bits. So the best you can do is an 1-to-1 mapping.
However, since a * b = b * a, our input space has a lot of duplicate outputs. So from this alone you can conclude roughly half of the output space must be uncovered by any input pair, simply because there aren't enough input pairs.
OK - thanks. I must have misunderstood what the other poster was saying, since I thought they were objecting to the "most" characterization.
I wasn't saying it's wrong, I was saying that "most" is so easy to reach that it's a trivial and rather boring threshold.