1. **State the problem:** Calculate the value of the expression $1 + 1 + 13 + 2763 - 16 \times 15$. 2. **Recall the order of operations:** Multiplication must be done before addition and subtraction. 3. **Calculate the multiplication first:** $$16 \times 15 = 240$$ 4. **Rewrite the expression with the multiplication result:** $$1 + 1 + 13 + 2763 - 240$$ 5. **Perform the addition and subtraction from left to right:** $$1 + 1 = 2$$ $$2 + 13 = 15$$ $$15 + 2763 = 2778$$ $$2778 - 240 = 2538$$ 6. **Final answer:** $$\boxed{2538}$$