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?

The u in update must be capitalized.