What's significant about this? (or where do you see this) ? 2^n-1

问题

I know this could be a vague question (or not!).

I've seen this somewhere 2^n-1 (or 2^n+1). Where do you see this equation? and why is it significant? And when do you use it?

回答1:

2^n-1 is the highest unsigned integer of n bits.

It's also a number easily tested for primeness, Mersenne prime http://en.wikipedia.org/wiki/Mersenne_prime

It's also the combination on my suitcase.

What's the point question?

回答2:

How about this? http://primes.utm.edu/notes/proofs/Theorem2.html

回答3:

John Smith answered the most common use of it. 2^n-1 is the largest unsigned integer you can store with n bits.

• 8 bits: 255
• 16 bits: 65535
• 32 bits: 4294967295

Oh, and mersenne primes as Beemer pointed out (link from his page).

回答4:

It's also the maximum number of nodes in a balanced binary tree of height n.

来源：https://stackoverflow.com/questions/4130165/whats-significant-about-this-or-where-do-you-see-this-2n-1