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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
by HarHarVeryFunny 5mo ago
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.
- orlp 5mo agoThe 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.
- HarHarVeryFunny 5mo agoOK - thanks. I must have misunderstood what the other poster was saying, since I thought they were objecting to the "most" characterization.
- Dylan16807 5mo agoI 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.