More progress

solutions/ProjectEuler/046/solve.php

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+<?php
+/*
+It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
+
+9  = 7  + 2 * 1^2
+15 = 7  + 2 * 2^2
+21 = 3  + 2 * 3^2
+25 = 7  + 2 * 3^2
+27 = 19 + 2 * 2^2
+33 = 31 + 2 * 1^2
+ 
+It turns out that the conjecture was false.
+
+What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
+*/
+
+$primes = [2];
+$composites = [];
+$twicesquares = [];
+
+function is_prime(int $n) :bool{for($i=$n**.5|1;$i&&$n%$i--;);return!$i&&$n>1;}
+
+for ($i= 3; $i<6000; $i += 2) {
+    if (is_prime($i))
+    {
+        $primes[] = $i;
+    }
+    else
+    {
+        $composites[] = $i;
+    }
+}
+
+for($i=1; $i<100; $i++)
+{
+    $twicesquares[] = 2*($i*$i);
+}
+
+foreach($composites as $composite)
+{
+    $count = 0;
+    foreach($primes as $prime)
+    {
+        if($prime > $composite)
+        {
+            break;
+        }
+        if(in_array($composite-$prime, $twicesquares))
+        {
+            $count++;
+            break;
+        }
+    }
+
+    if($count == 0)
+    {
+        echo "Found $composite\n";
+        die;
+    }
+}
+