How to make a gun in unity?

So I have this code:

 using UnityEngine;
 using System.Collections;
 
 
 public class scrPlayerFire : MonoBehaviour{
     public GameObject bullet;
     public Transform spawn;
 
     void update(){
         if(Input.GetKey (KeyCode.Space)){
             Instantiate(bullet, spawn.position, spawn.rotation);
         }
     }
 }

I made a prefab linked to bullet that has code to move it forward, and I've made an empty object to use for the transform. but when i press space nothing happens. What am I doing wrong?