PHP Exercises: Compute the sum of first n given prime numbers

Last update on December 20 2024 10:18:11 (UTC/GMT +8 hours)

Write a PHP program to compute the sum of first n given prime numbers.

Input: n ( n ≤ 10000). Input 0 to exit the program.

Pictorial Presentation:

Sample Solution:

PHP Code:

<?php
// Set the maximum value for prime numbers
$max = 105000;

// Create a fixed-size array to store prime flags
$arr = new \SplFixedArray($max + 1);

// Initialize the array with 1 (considering all numbers as prime initially)
for ($i = 2; $i <= $max; $i++) {
    $arr[$i] = 1;
}

// Sieve of Eratosthenes algorithm to mark non-prime numbers
for ($i = 2, $len = sqrt($max); $i <= $len; $i++) {
    if (!$arr[$i]) {
        continue;
    }
    for ($j = $i, $len2 = $max / $i; $j <= $len2; $j++) {
        $arr[$i * $j] = 0;
    }
} 

// Process input until '0' is entered
while (($line = trim(fgets(STDIN))) !== '0') {
    // Convert the input to an integer
    $n = (int)$line;

    // Initialize variables for result and count
    $result = 0;
    $cnt = 0;

    // Find and sum the first N prime numbers
    for ($i = 2; $i <= $max; $i++) {
        if ($cnt === $n) {
            break;
        } elseif ($arr[$i]) {
            $result += $i;
            $cnt++;
        }
    }

    // Output the result
    echo "Sum of first " . $n . " prime numbers:";
    echo $result, PHP_EOL;
}

?>

Explanation:

• Set Maximum Prime Value:
• The variable $max is set to 105000, which will be the upper limit for the prime numbers to be calculated.
• Create Prime Flag Array:
• A fixed-size array $arr is created using \SplFixedArray, with a size of max + 1. This array will hold flags indicating whether each number is prime.
• Initialize Array:
• A for loop initializes the array values from 2 to max to 1, indicating that all numbers are initially considered prime.
• Sieve of Eratosthenes Algorithm:
• The algorithm starts with i set to 2 and loops up to the square root of $max.
• If the current number is marked as prime (i.e., arr[$i] is 1), it enters another loop to mark its multiples as non-prime (0).
• This is done by iterating j and setting arr[$i * $j] to 0 for multiples of i.
• Input Processing Loop:
• The code reads input from standard input until the input '0' is encountered.
• Each input line is trimmed and converted to an integer $n.
• Initialize Variables for Summation:
• Two variables, $result and $cnt, are initialized to 0. $result will store the sum of prime numbers, and $cnt will count how many prime numbers have been found.
• • Find and Sum First N Prime Numbers:
• A for loop iterates through the array of numbers from 2 to max.
• If the count of found primes ($cnt) equals $n, the loop breaks.
• If the current number is prime (i.e., arr[$i] is 1), it is added to $result, and $cnt is incremented.
• Output the Result:
• After summing the required prime numbers, the code outputs the result, indicating the sum of the first n prime numbers.

Sample Input:
25
0

Sample Output:

Sum of first 25 prime numbers:1060

Flowchart:

PHP Code Editor:

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