There's a fascinating story with respect to this.

Alexandre Grothendieck is a famous mathematician known for his incredibly abstract methodologies. He once compared his technique to mathematics to the norm by relating standard mathematical methods as using a sledgehammer to open a nut. To him, his method was to slowly raise the water level and soak the nut until its shell becomes soft and he can open it with just a little pressure from his hand.

However, his highly abstract nature got him in trouble at least once.

One time in discussion a colleague of Grothendieck asked him to consider the argument for a concrete example of prime number. "You mean an actual number?" replied Grothendieck. "Alright, well then take 57".

And now 57 is known as the Grothendieck Prime.

Asking a mathematician for their favorite constant is like asking a painter what their favorite color is. I like Tao's diplomatic answer.

I'd rather say something like "Fischer–Griess monster" (it is a constant in the set of finite simple groups). Surely a constant, but not a numerical one. The interviewer will probably change the topic immediately for not becoming embarrassed. ;-)

Surely a less diplomatic way than Tao's, admitted.