sum

Project Euler - Problem 10

Question

The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.

Find the sum of all the primes below two million.

Solution

$sum = 2;
for ($i = 2; $i < 2000000; $i++) {
  if ($i % 2 != 1) {
    continue;
  }
  $d = 3;
  $x = sqrt($i);
  while (($i % $d != 0) && $d < $x) {
    $d += 2;
  }
  if ((($i % $d == 0 && $i != $d) * 1) == 0) {
    $sum += $i;
  }
}
echo $sum;

Time taken to execute: 30.5757 second.

Project Euler - Problem 6

Question

The sum of the squares of the first ten natural numbers is,
1² + 2² + ... + 10² = 385

The square of the sum of the first ten natural numbers is,
(1 + 2 + ... + 10)² = 55² = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 - 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

Project Euler - Problem 1

Question

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

Solution

$sum = 0;
for ($i = 0; $i < 1000; $i++) {
  if (!($i % 3) || !($i % 5)) {
    $sum += $i;
  }
}
echo $sum;

Time taken to execute: 0.0007 second.

Answer

233168