While I find the 17% number interesting to think about, "most" is far less interesting. Multiplication doesn't care about order so you're instantly cutting 2^64 possibilities down to about 2^63. That's a hair's breadth away from "most" already, and considering even a tiny amount of overlapping results gets you there.
What gets interesting is actually trying to quantify the overlapping results.
{255 through 226 not used} 15 \* 15 = 225
{224 through 211 not used} 15 \* 14 = 14 \* 15 = 210
{197 through 209 not used} 15 \* 13 = 13 \* 15 = 195
14 \* 14 = 196
{183 through 194 not used} 14 \* 13 = 13 \* 14 = 182
Toy example. Of course with 32-bit factors you skip way more 64-bit numbers.The chance of a random 64 bit integer being a 32 bit integer is 0.0000000233 %
The chance of a random 64 bit integer being a product of two 32 bit integers is 17%
Nice
pants2•57m ago
kleiba2•30m ago
zamadatix•25m ago
My current comment itself, for instance, also doesn't really add anything to the discussion about the article and I'd have no expectation people leave it from going negative. Maybe the will, maybe they won't, but there is no reason to expect they should in principle of me loving tangents :D.
jihadjihad•22m ago
0: https://en.wikipedia.org/wiki/Indiana_pi_bill
dvh•15m ago