Seventy-three

According to Sheldon Cooper (AKA Jim Parsons) of The Big Bang Theory, 73 is the best number. The reason is because it's the 21st prime number, and its mirror 37 is the 12th prime number, whose mirror 21 is the product of 7 times 3.

Also in binary 73 is 1001001 which is a palindrome.

As a counterpoint, I note that Rajesh Koothrapalli (AKA Kunal Nayar) of the same show, contends that the best number is 5,218,008. His reason is that if you enter that number into a digital calculator and turn it upside down, it appears to spell BOOBIES.

Any other suggestions?

And yes, all us nerds know that Douglas Adams said 42 was the answer to life, the universe and everything. But he also said he just came up with that number while staring out the window at his garden. " It was a joke. It had to be a number, an ordinary, smallish number, and I chose that one. Binary representations, base thirteen, Tibetan monks [all suggested explanations of why it is 42] are all complete nonsense. I sat at my desk, stared into the garden and thought '42 will do'. I typed it out. End of story."

But if you subtract 42 from 73, you get 31 and according to Christian tradition, there are 3 persons in the 1 God. And  3 is the 2nd prime number and 3 minus 2 is one. And Jesus, as the second person of the Trinity incarnate is said to have 2 natures in 1 person, which adds up to 3. There were twelve tribes of Israel (1+2=3) and twelve apostles (again, 1=2=3) and ... no, I'm pretty sure this way lies madness. Madness, I tell you!

Just be satisfied with 73 ... but if you divide 7 by 3, you have 1 left over -- 3 and 1 again! Aiiiieeee!