Use the Sieve of Eratosthenes to find all the primes from 2 up to a given number.
The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e. not prime) the multiples of each prime, starting with the multiples of 2.
Create your range, starting at two and continuing up to and including the given limit. (i.e. [2, limit])
The algorithm consists of repeating the following over and over:
Repeat until you have processed each number in your range.
When the algorithm terminates, all the numbers in the list that have not been marked are prime.
The wikipedia article has a useful graphic that explains the algorithm: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
Notice that this is a very specific algorithm, and the tests don't check that you've implemented the algorithm, only that you've come up with the correct list of primes.
Go to the root of your PHP exercise directory, which is <EXERCISM_WORKSPACE>/php
.
To find the Exercism workspace run
% exercism debug | grep Workspace
Get PHPUnit if you don't have it already.
% wget --no-check-certificate https://phar.phpunit.de/phpunit.phar
% chmod +x phpunit.phar
Execute the tests:
% ./phpunit.phar sieve/sieve_test.php
Sieve of Eratosthenes at Wikipedia http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
It's possible to submit an incomplete solution so you can see how others have completed the exercise.
<?php
class SieveTest extends PHPUnit\Framework\TestCase
{
public static function setUpBeforeClass() : void
{
require_once 'sieve.php';
}
public function testNoPrimesUnderTwo() : void
{
$this->assertEquals([], sieve(1));
}
public function testFindFirstPrime() : void
{
$this->assertEquals([2], sieve(2));
}
public function testFindPrimesUpTo10() : void
{
$this->assertEquals([2, 3, 5, 7], sieve(10));
}
public function testLimitIsPrime() : void
{
$this->assertEquals([2, 3, 5, 7, 11, 13], sieve(13));
}
public function testFindPrimesUpTo1000() : void
{
$this->assertEquals(
[
2,
3,
5,
7,
11,
13,
17,
19,
23,
29,
31,
37,
41,
43,
47,
53,
59,
61,
67,
71,
73,
79,
83,
89,
97,
101,
103,
107,
109,
113,
127,
131,
137,
139,
149,
151,
157,
163,
167,
173,
179,
181,
191,
193,
197,
199,
211,
223,
227,
229,
233,
239,
241,
251,
257,
263,
269,
271,
277,
281,
283,
293,
307,
311,
313,
317,
331,
337,
347,
349,
353,
359,
367,
373,
379,
383,
389,
397,
401,
409,
419,
421,
431,
433,
439,
443,
449,
457,
461,
463,
467,
479,
487,
491,
499,
503,
509,
521,
523,
541,
547,
557,
563,
569,
571,
577,
587,
593,
599,
601,
607,
613,
617,
619,
631,
641,
643,
647,
653,
659,
661,
673,
677,
683,
691,
701,
709,
719,
727,
733,
739,
743,
751,
757,
761,
769,
773,
787,
797,
809,
811,
821,
823,
827,
829,
839,
853,
857,
859,
863,
877,
881,
883,
887,
907,
911,
919,
929,
937,
941,
947,
953,
967,
971,
977,
983,
991,
997
],
sieve(1000)
);
}
}
<?php
function sieve(int $limit): array
{
if (1 >= $limit) {
return [];
}
if (2 === $limit) {
return [2];
}
// Create an array of numbers to process
// key: (int) number
// value: (boolean) whether it's prime or not
// By default assume every number is a prime number
$numbers = array_fill(2, $limit - 1, true);
// Get next number which is a prime
$nextPrime = function () use (&$numbers, $limit): Generator {
foreach ($numbers as $number => $isPrime) {
if ($number >= sqrt($limit)) {
break;
}
// Avoid looping over numbers which were determined as not prime
if (true === $numbers[$number]) {
yield $number;
}
}
};
// Loop over multiplies of the number and
// Mark them as not prime
$markMultiplies = function (int $number) use (&$numbers, $limit) {
$multiply = 2;
while (($index = $number * $multiply) <= $limit) {
$numbers[$index] = false;
$multiply++;
}
};
// Loop over every prime number and
// Mark their multiplies as not prime
foreach ($nextPrime() as $number) {
$markMultiplies($number);
}
// Filter numbers which are not primes
return array_keys(array_filter($numbers));
}
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