1. **Stating the problem:** Add the two very large numbers: $$1000000000000000000000000 + 9179274828672936491973829264839274820384728946190275728374728$$. 2. **Write the numbers clearly:** $$\text{Number 1} = 1000000000000000000000000$$ $$\text{Number 2} = 9179274828672936491973829264839274820384728946190275728374728$$ 3. **Aligning and adding:** Since Number 2 is immensely larger, imagine the addition aligning on the right. Adding zeroes to the left of Number 1 does not change it. 4. **Perform the addition:** $$1000000000000000000000000 + 9179274828672936491973829264839274820384728946190275728374728 = 9179274828672936492973829264839274820384728946190275728374728$$ 5. **Conclusion:** The sum is: $$\boxed{9179274828672936492973829264839274820384728946190275728374728}$$