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Php Program to Count Primes in Ranges

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  • Last Updated : 13 Jan, 2022
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Given a range [L, R], we need to find the count of total numbers of prime numbers in the range [L, R] where 0 <= L <= R < 10000. Consider that there are a large number of queries for different ranges.
Examples: 
 

Input : Query 1 : L = 1, R = 10
        Query 2 : L = 5, R = 10
Output : 4
         2
Explanation
Primes in the range L = 1 to R = 10 are 
{2, 3, 5, 7}. Therefore for query, answer 
is 4 {2, 3, 5, 7}.
For the second query, answer is 2 {5, 7}.

 

A simple solution is to do the following for every query [L, R]. Traverse from L to R, check if current number is prime. If yes, increment the count. Finally, return the count.
An efficient solution is to use Sieve of Eratosthenes to find all primes up to the given limit. Then we compute a prefix array to store counts till every value before limit. Once we have a prefix array, we can answer queries in O(1) time. We just need to return prefix[R] – prefix[L-1]. 
 

PHP




<?php
// PHP program to answer queries for 
// count of primes in given range.
$MAX = 10000;
  
// prefix[i] is going to
// store count of primes
// till i (including i).
$prefix = array_fill(0, ($MAX + 1), 0);
  
function buildPrefix()
{
    global $MAX, $prefix;
      
    // Create a boolean array value in
    // prime[i] will "prime[0..n]". A 
    // finally be false if i is Not a
    // prime, else true.
    $prime = array_fill(0, ($MAX + 1), true);
  
    for ($p = 2; 
         $p * $p <= $MAX; $p++) 
    {
  
        // If prime[p] is not changed, 
        // then it is a prime
        if ($prime[$p] == true)
        {
  
            // Update all multiples of p
            for ($i = $p * 2; 
                 $i <= $MAX; $i += $p)
                $prime[$i] = false;
        }
    }
  
    // Build prefix array
    // $prefix[0] = $prefix[1] = 0;
    for ($p = 2; $p <= $MAX; $p++) 
    {
        $prefix[$p] = $prefix[$p - 1];
        if ($prime[$p])
            $prefix[$p]++;
    }
}
  
// Returns count of primes 
// in range from L to
// R (both inclusive).
function query($L, $R)
{
    global $prefix;
    return $prefix[$R] -
           $prefix[$L - 1];
}
  
// Driver code
buildPrefix();
  
$L = 5;
$R = 10;
echo query($L, $R) . "
";
  
$L = 1;
$R = 10;
echo query($L, $R) . "
";
  
// This code is contributed by mits.
?>


Output:  

2
4

Please refer complete article on Count Primes in Ranges for more details!


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