I for one applaud the Fermat-like comment and lack of additional information.

For one it is larger than 7373170279850.

in jest or in seriousness? if in seriousness, would you mind elaborating?

Jest. I couldn't resist.

Presumably testing this is hard? If so, I like it.

It has just 5 different prime divisors. That's kind of cool for such a large number.

Not at all -- a "typical" number N has ln(ln(N)) distinct prime factors, and ln(ln(4,556,543,113,106,166,912,761,976,150) is about 4.15. Having 5 prime divisors is perfectly normal for a number of this size.

Now I'm wondering if someone will provide a 4 cube division of this.