The hyper-leviathan number is defined like so: 1. * Let \(|1|_1(x) = x\). 2. * Let \(|1|_n(x) = \prod^{x}_{i = 1} |1|_{n - 1}(i) = x!n\) 3. * Let \(|2|_1(x) = |1|_x(x) = T(x)\) using the Torian. 4. * Let \(|2|_n(x) = \prod^{x}_{i = 1} |2|_{n - 1}(i)\) 5. * Let \(|3|_1(x) = |2|_x(x)\). 6. * Let \(|3|_n(x) = \prod^{x}_{i = 1} |3|_{n - 1}(i)\) 7. * Continue in this fashion. Now define \(||1||_1(x) = |x|_x(x)\). 8. * Let \(||1||_n(x) = \prod^{x}_{i = 1} ||1||_{n - 1}(i)\) 9. * Let \(||2||_1(x) = ||1||_x(x)\). 10. * Let \(||2||_n(x) = \prod^{x}_{i = 1} ||2||_{n - 1}(i)\) 11. * Let \(||3||_1(x) = ||2||_x(x)\). 12. * Let \(||3||_n(x) = \prod^{x}_{i = 1} ||3||_{n - 1}(i)\) 13. * Continue in this fashion. Now define \(|||1|||_1(x) = ||x