Why do you peel it? All the "good stuff" is in the skin.
If you're worried about bad chemicals that can't be washed off then the core would likely be poisoned as well because it's going through the skin.
For dirt, you can just wash it. Dirt is not harmful and doesn't penetrate the fruit.
About chemicals, a large part stays in the skin of fruits / vegetables, so it's always better to remove it when you're eating non organic food.