<?php
function eratosthenes_sieve(&$sieve, $n)
{
$i = 2;
while ($i <= $n) {
if ($sieve[$i] == 0) {
echo $i;
$j = $i;
while ($j <= $n) {
$sieve[$j] = 1;
$j += $i;
}
}
$i++;
}
}
$n = 100;
$sieve = array_fill(0, $n, 0);
// 2, 3, 5, 7, ..., 97
eratosthenes_sieve($sieve, $n);
*
* Solution: Use a Eratosthenes sieve to determine primes from
* 2 to 2,000,000, adding as we go. The first attempt without
* a sieve took 900+ seconds to execute. This one takes 1.3 seconds.
*/
include "helper.php";
function eratosthenes_sieve(&$sieve, $n)
{
$i = 2;
$total = 0;
while ($i <= $n) {
if ($sieve[$i] == 0) {
$total += $i;
$j = $i;
while ($j <= $n) {
$sieve[$j] = 1;
$j += $i;
}
}
if ($i % floor($n / 100) == 0) {
echo ".";
}
$i++;
}
echo "\n";
return $total;
}
$n = 2000000;
$sieve = array_fill(0, $n, 0);
result(142913828922, eratosthenes_sieve($sieve, $n));
function eratosthenes_sieve(&$sieve, $n)
{
$i = 2;
$total = 0;
while ($i <= $n) {
if ($sieve[$i] == 0) {
$total += $i;
$j = $i;
while ($j <= $n) {
$sieve[$j] = 1;
$j += $i;
}
}
$i++;
}
return $total;
}
$numFactors = 500;
$sieve = array_fill(0, $numFactors, 0);
eratosthenes_sieve($sieve, $numFactors);
$found = false;
$x = 1;
while ($found === false) {
$tri = triangleNum($x);
$fact = factorCount($tri);
if ($fact >= $numFactors) {
$found = $tri;
}
$x++;
}
result(76576500, $found);
