diff --git a/index.php b/index.php
index 6128a39..c80cd67 100644
--- a/index.php
+++ b/index.php
@@ -2,15 +2,11 @@
 <html lang="en">
 <head>
     <meta charset="UTF-8">
-    <meta name="viewport" content="width=device-width, initial-scale=1">
+    <meta name="viewport" content="width=device-width, initial-scale=1.0">
     <title>Primzahlen</title>
     <style>
-        .wrapper {
-            display: flex;
-            flex-direction: row;
-            gap: 20px;
-
-        }
+        .wrapper { display: flex; gap: 20px; }
+        .mono { font-family: monospace; white-space: pre; }
     </style>
 </head>
 <body>
@@ -19,38 +15,38 @@
     <div>
         <form action="index.php" method="post">
             <label>Input:
-                <input type="number" name="input">
+                <input type="number" name="input" min="2" required>
             </label>
             <button type="submit">Berechnen</button>
         </form>
 
         <?php
-        if(isset($_POST['input'])) {
-            $primeNumbers = [];
+        if ($_SERVER['REQUEST_METHOD'] === 'POST' && isset($_POST['input'])) {
             $max = (int) $_POST['input'];
-
-            for($i = 0; $i <= $max; $i++) {
-                if(isPrime($i)) {
-                    $primeNumbers[] = $i;
+            if ($max < 2) {
+                echo "<p>Bitte eine Zahl >= 2 eingeben.</p>";
+            } else {
+                $primeNumbers = [];
+                for ($i = 2; $i <= $max; $i++) {
+                    if (isPrime($i)) {
+                        $primeNumbers[] = $i;
+                    }
                 }
-            }
 
-            echo "<h3>Primzahlen von " . htmlspecialchars($_POST["input"], ENT_QUOTES, 'UTF-8') . " sind:</h3>";
-
-            foreach($primeNumbers as $number) {
-                echo "<span>" . $number . "</span><br>";
+                $safe = htmlspecialchars((string)$_POST['input'], ENT_QUOTES, 'UTF-8');
+                echo "<h3>Primzahlen von 1 bis {$safe}:</h3>";
+                echo "<p>" . implode(", ", $primeNumbers) . "</p>";
             }
         }
 
-        function isPrime($i) {
-            if ($i <= 1) return false;
-            if ($i <= 3) return true;
-            if ($i % 2 == 0) return false;
+        function isPrime(int $n): bool {
+            if ($n <= 1) return false;
+            if ($n <= 3) return true;
+            if ($n % 2 === 0) return false;
 
-            for ($j = 3; $j * $j <= $i; $j += 2) {
-                if ($i % $j == 0) {
-                    return false;
-                }
+            $limit = (int) floor(sqrt($n));
+            for ($d = 3; $d <= $limit; $d += 2) {
+                if ($n % $d === 0) return false;
             }
 
             return true;
@@ -64,12 +60,17 @@
             <?php
             for ($n = 1; $n <= 100; $n++) {
                 $ln = log($n);
-                $lnFormatted = number_format($ln, 4, '.', '');
+                $rounded = round($ln * 2) / 2;
+                $full = (int) floor($rounded);
+                $half = ($rounded - $full) >= 0.5 ? 1 : 0;
 
-                $starsCount = (int) floor($ln);
-                $stars = $starsCount > 0 ? str_repeat('*', $starsCount) : '-';
+                if ($full === 0 && $half === 0) {
+                    $visual = '-';
+                } else {
+                    $visual = str_repeat('*', $full) . ($half ? '+' : '');
+                }
 
-                echo sprintf("%3d: ln=%6s  %s<br>", $n, $lnFormatted, $stars);
+                echo str_pad($n, 3, ' ', STR_PAD_LEFT) . ": " . $visual . "<br>";
             }
             ?>
         </div>
