If this seems counterintuitive, consider that only about a third of the two-digit numbers ({0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63, 64, 72, 81}) can be written as the product of two one-digit numbers.
Only 17% of all 64-bit Integers are products of two 32-bit integers
11–20 of 115 posts
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#12I dream of a future where all 64-bit integers are products of 32-bit integers. Together, we can change math for the better.
Why stop there? We can dream of a future where math is bent to our will [0] for the betterment of all mankind!
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#13There 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
There are about 18.446 quintillion more 64-bit integers than 32-bit integers.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#14I dream of a future where all 64-bit integers are products of 32-bit integers. Together, we can change math for the better.
1 + 1 = 3 (for sufficiently large values of 1)
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#15This feels like a underlying property that contributes to of Benford's Law[0]. That is, most numbers we measure and record are the results of various independent (addition) and dependent (multiplication) factors stacking together, and we observe this property in the distribution of them.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#16There 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
The chance of a random 64-bit integer matching some pair of 32-bit integers is a 100%, though.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#17There 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
Or, the odds of a random 64-bit integer being a 32-bit integer are the same as you or me guessing a random 32 bit integer.
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#18I dream of a future where all 64-bit integers are products of 32-bit integers. Together, we can change math for the better.
There should be a law!
Re: Only 17% of all 64-bit Integers are products of two 32-bit integers
#19There 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
There are about 18.446 quintillion more 64-bit integers than 32-bit integers.
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