Solution for Week 2

Author: pie-flavor

Language: APL

{+/(2=+⌿0=(⍳⍵)∘.|⍳⍵)/⍳⍵}

Author Explanation

So ⍳⍵ gets us the first ⍵ integers. ∘., the outer product, is used in conjunction with the remainder operator (|) to give a big array of all possible remainders. Any elements that are equal to 0, are therefore multiples of that number. So add 0=, and now we have a big boolean array, where 1 represents an exact multiple and 0 doesn’t. +⌿ adds all these rows together, leaving us with a 1-dimensional array of the total number of factors of each number. The prime test is pretty obvious - any number with only two factors. So adding a 2= gives us a boolean array representing the indices of the prime numbers. Lastly, / against the original ⍳⍵ is used to translate this array of indexed booleans into the numbers themselves, and that’s the Sieve. Then a +/ is tacked on to sum them all together.