PHP Exercises: Print the number of prime numbers which are less than or equal to a given integer

PHP: Exercise-52 with Solution

Write a PHP program to print the number of prime numbers which are less than or equal to a given integer.

Input:
n (1 ≤ n ≤ 999,999) .

Pictorial Presentation:

Sample Solution:

PHP Code:

<?php
// Initialize an array to mark numbers as prime or not (Sieve of Eratosthenes)
$a = array_fill(0, 1000000, true);
$a[0] = $a[1] = false;

// Iterate through numbers and mark multiples as non-prime
for ($i = 2; $i * $i < 1000000; $i++) {
    if (!$a[$i]) continue;
    for ($j = $i * $i; $j < 1000000; $j += $i) {
        $a[$j] = false;
    }
}

// Initialize an array to store the cumulative count of prime numbers
$sum = array_fill(0, 1000000, 0);

// Calculate the cumulative count of prime numbers up to each index
for ($i = 1; $i < 1000000; $i++) {
    $sum[$i] += $sum[$i - 1];
    if ($a[$i]) $sum[$i]++;
}

// Read input from standard input until the end of file
while (fscanf(STDIN, "%d", $n)) {
    // Print the number of prime numbers which are less than or equal to n
    echo "Number of prime numbers which are less than or equal to n: ";
    echo $sum[$n] . "\n";
}
?>

Explanation:

• Initialization:
• An array $a is created with array_fill(0, 1000000, true) to mark numbers as prime (true) or not (false).
• The first two indices ($a[0] and $a[1]) are set to false since 0 and 1 are not prime numbers.
• Sieve of Eratosthenes Algorithm:
• A loop iterates through numbers starting from 2 to the square root of 1,000,000:
• for ($i = 2; $i * $i < 1000000; $i++).
• Inside this loop, if a number is marked as prime (if (!$a[$i]) continue;), another loop marks its multiples as non-prime:
• for ($j = $i * $i; $j < 1000000; $j += $i) { $a[$j] = false; }.
• Cumulative Prime Count Initialization:
• An array $sum is initialized to hold the cumulative count of prime numbers with array_fill(0, 1000000, 0).
• Calculating Cumulative Counts:
• A loop runs from 1 to 999,999 to compute how many prime numbers exist up to each index:
• The cumulative count is updated by adding the previous count ($sum[$i] += $sum[$i - 1];).
• If the current number is prime, the count is incremented (if ($a[$i]) $sum[$i]++;).
• Input Reading:
• The program continuously reads integer input from standard input (STDIN) until EOF:
• while (fscanf(STDIN, "%d", $n)).
• Output:
• For each input number n, the program prints the number of prime numbers that are less than or equal to n:
• echo "Number of prime numbers which are less than or equal to n: "; echo $sum[$n] . "\n";.

Output:

Sample Input: 50
Number of prime numbers which are less than or equal to n: 15

Flowchart:

PHP Code Editor:

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