diff --git a/phpseclib/Math/BigInteger/Engines/Engine.php b/phpseclib/Math/BigInteger/Engines/Engine.php
index abdf3b47..e46e9609 100644
--- a/phpseclib/Math/BigInteger/Engines/Engine.php
+++ b/phpseclib/Math/BigInteger/Engines/Engine.php
@@ -786,6 +786,11 @@ abstract class Engine implements \JsonSerializable
             $min = $temp;
         }
 
+        $length = $max->getLength();
+        if ($length > 8196) {
+            throw new \RuntimeException("Generation of random prime numbers larger than 8196 has been disabled ($length)");
+        }
+
         $x = static::randomRange($min, $max);
 
         return static::randomRangePrimeInner($x, $min, $max);
@@ -990,6 +995,15 @@ abstract class Engine implements \JsonSerializable
      */
     public function isPrime($t = false)
     {
+        // OpenSSL limits RSA keys to 16384 bits. The length of an RSA key is equal to the length of the modulo, which is
+        // produced by multiplying the primes p and q by one another. The largest number two 8196 bit primes can produce is
+        // a 16384 bit number so, basically, 8196 bit primes are the largest OpenSSL will generate and if that's the largest
+        // that it'll generate it also stands to reason that that's the largest you'll be able to test primality on
+        $length = $this->getLength();
+        if ($length > 8196) {
+            throw new \RuntimeException("Primality testing is not supported for numbers larger than 8196 bits ($length)");
+        }
+
         if (!$t) {
             $t = $this->setupIsPrime();
         }