Editing APL (programming language) (section)

==== Prime numbers ====
The following expression finds all [[prime number]]s from 1 to R. In both time and space, the calculation complexity is <math>O(R^2)\,\!</math> (in [[Big O notation]]).

<syntaxhighlight lang="apl">
(~R∊R∘.×R)/R←1↓⍳R
</syntaxhighlight>

Executed from right to left, this means:
* ''[[Iota]]'' <code>⍳</code> creates a vector containing [[integer]]s from <code>1</code> to <code>R</code> (if <code>R= 6</code> at the start of the program, <code>⍳R</code> is <code>1 2 3 4 5 6</code>)
* ''Drop'' first element of this vector (<code>↓</code> function), i.e., <code>1</code>. So <code>1↓⍳R</code> is <code>2 3 4 5 6</code>
* ''Set'' <code>R</code> to the new vector (<code>←</code>, ''assignment'' primitive), i.e., <code>2 3 4 5 6</code>
* The <code>/</code> ''replicate'' operator is dyadic (binary) and the interpreter first evaluates its left argument (fully in parentheses):
* Generate ''[[outer product]]'' of <code>R</code> multiplied by <code>R</code>, i.e., a matrix that is the ''[[multiplication table]]'' of R by R (<code>°.×</code> operator), i.e.,

{| class="wikitable" style="text-align:right;"
|-
| 4
| 6
| 8
| 10
| 12
|-
| 6
| 9
| 12
| 15
| 18
|-
| 8
| 12
| 16
| 20
| 24
|-
| 10
| 15
| 20
| 25
| 30
|-
| 12
| 18
| 24
| 30
| 36
|}
* Build a vector the same length as <code>R</code> with <code>1</code> in each place where the corresponding number in <code>R</code> is in the outer product matrix (<code>∈</code>, ''set inclusion'' or ''element of'' or ''[[Epsilon]]'' operator), i.e., <code>0 0 1 0 1</code>
* Logically negate (''not'') values in the vector (change zeros to ones and ones to zeros) (<code>∼</code>, logical ''not'' or ''[[Tilde]]'' operator), i.e., <code>1 1 0 1 0</code>
* Select the items in <code>R</code> for which the corresponding element is <code>1</code> (<code>/</code> ''replicate'' operator), i.e., <code>2 3 5</code>
(This assumes the APL origin is 1, i.e., indices start with 1. APL can be set to use 0 as the origin, so that <code>ι6</code> is <code>0 1 2 3 4 5</code>, which is convenient for some calculations.)