Only 17% of all 64-bit Integers are products of two 32-bit integers
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Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#2I dream of a future where all 64-bit integers are products of 32-bit integers. Together, we can change math for the better.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#3> I find it interesting to consider that if you pick a value at random, it will usually fail! That is, most 64-bit integers cannot be written as the product of two 32-bit integers.
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.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#4> I find it interesting to consider that if you pick a value at random, it will usually fail! That is, most 64-bit integers cannot be written as the product of two 32-bit integers. 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" alr…
A lot of the remaining is multiples of 4, which you can either get from having a 2 in both factors or a 4 in one (multiples of 9 are similar).
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#5> I find it interesting to consider that if you pick a value at random, it will usually fail! That is, most 64-bit integers cannot be written as the product of two 32-bit integers. 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" alr…
... or just considering the even numbers almost all of them are 2 x N where N>2^32 and that gets you to within a hair of "most" and if you add in the odd thirds for which the same is true you get a bound of 2/3 - epsilon.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#6> I find it interesting to consider that if you pick a value at random, it will usually fail! That is, most 64-bit integers cannot be written as the product of two 32-bit integers. 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" alr…
All the primes above 2^32 are out, but that accounts for only two point something percent.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#7[deleted]
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#8I dream of a future where all 64-bit integers are products of 32-bit integers. Together, we can change math for the better.
I upvoted you, not because I think your joke is particularly great, but I hate that HN has this tendency to downvote comments that are clearly meant as a humorous contribution. And I get it, no-one wants HN to turn into Reddit. I also understand that not every joke lands. But I just think it's unnecessary to downvote, you could simply ignore.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#9There are about 4 billion 64 bit integers for each 32 bit integer.
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
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#10I dream of a future where all 64-bit integers are products of 32-bit integers. Together, we can change math for the better.
I upvoted you, not because I think your joke is particularly great, but I hate that HN has this tendency to downvote comments that are clearly meant as a humorous contribution. And I get it, no-one wants HN to turn into Reddit. I also understand that not every joke lands. But I just think it's unnecessary to downvote, you could simply ignore .
"Ignore" is one of those things that sounds like it's a neutral choice but really isn't in practice - it's still just saying "can only ever be positively pressured". IMO people shouldn't go as far as flag though, at the very least, and if it's already at the bottom of the sort there is no sense dumping on it further.
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.