The transcendental integers are a class of huge numbers, defined by Harvey Friedman. If \(n\) is an integer then we call it transcendental iff the following holds: let M be a Turing machine, such that there is proof in ZFC of length at most 21000 showing that M halts. Then M halts in at most \(n\) steps. In other words, \(n\) is greater than halting time of every Turing machine with ZFC proof of halting of length at most 21000.