From 513f500b222f96676517cc2142ff3a5b526a6637 Mon Sep 17 00:00:00 2001
From: gnieark <gnieark@free.fr>
Date: Sun, 15 Nov 2015 22:53:49 +0100
Subject: [PATCH] verry faster

---
 _functions.php | 42 ++++++++++++++++++++++++++++++++++++++++++
 euler03.php    | 44 +++++++++++++-------------------------------
 2 files changed, 55 insertions(+), 31 deletions(-)
 create mode 100644 _functions.php

diff --git a/_functions.php b/_functions.php
new file mode 100644
index 0000000..768697a
--- /dev/null
+++ b/_functions.php
@@ -0,0 +1,42 @@
+<?php
+
+function isPrimary($number){
+    $i=1;
+    while(getPrimeNumber($i) <= sqrt($number)){
+        if(fmod($i,getPrimeNumber($i))==0){
+            return false;
+        }
+        $i=$i+2;
+    }
+    return true;
+}
+
+function getPrimeNumber($order){
+
+    static $primeNumbersList=array(2,3);
+    //if already finded:
+    if(isset($primeNumbersList[$order-1])){
+        return $primeNumbersList[$order-1];
+    }
+    
+    $i=$primeNumbersList[count($primeNumbersList)-1] + 2;
+
+    while (count($primeNumbersList) < $order){
+        $isPrimaryNumber=true;
+        foreach($primeNumbersList as $pr){
+            
+            if($pr>sqrt($i)){
+                break;
+            }
+            if(fmod($i,$pr)==0){
+                $isPrimaryNumber=false;
+                break;
+            }
+        }
+        if($isPrimaryNumber){
+            $primeNumbersList[]=$i;
+        }
+        $i=$i+2;//sert à rien de tester les nombres pairs
+    }
+    return $i-2;
+}
\ No newline at end of file
diff --git a/euler03.php b/euler03.php
index ff3639b..92fe6a8 100644
--- a/euler03.php
+++ b/euler03.php
@@ -3,37 +3,19 @@
 * Gnieark's anwser to euler problem 3
 * https://projecteuler.net/problem=3
 */
-
+require_once("_functions.php");
+                            
 echo largestPrimeFactorOf(600851475143);
 function largestPrimeFactorOf($number){
-    $primesNumbers=array(2);//non considering value 1
-    $i=3; //begin to 3
-
-    while($i<=sqrt($number)){
-        //echo $i;
-        //is $i a factorOf $number
-        if(fmod($number,$i)==0){
-            //is $i a prime number
-             $index=0;
-             $isPr=true;
-             while(($primesNumbers[$index]<sqrt($i)) && $index < (count($primesNumbers))-1){
-                    if((fmod($i,$primesNumbers[$index])==0)){
-                        $isPr=false;
-                        break;
-                    }
-                    $index++;
-            }
-            if($isPr){
-                $primesNumbers[]=$i;
-                $lastPr=$i;
-            }
-
-        }
-        $i=$i+2;
+    $right=$number;
+    $i=1;
+    $prFact=1;
+    while(getPrimeNumber($i)<=$right){
+        if(fmod($right,getPrimeNumber($i))==0){
+            $prFact=getPrimeNumber($i);
+            $right=$right/$prFact;
+        }        
+        $i++;
     }
-    if (isset($lastPr)){
-        return $lastPr;
-    }else{
-        return 1;
-    }
-}
+    return $prFact;
+}
\ No newline at end of file