What is the largest prime less than 2^31?

I'm sorry for this kind of specific question, I'd love if you could link to resources (prime lists, etc) that can answer similar questions more generically.

-
Mathematica should be able to answer this question quickly; it has a function that will tell you how many primes there are less than 2^{31} and another that tells you what the nth prime is. Use one, then the other. –  Qiaochu Yuan Nov 12 '10 at 22:20
These are all great answers. Thank you everyone. –  Martin Nov 12 '10 at 22:38
@Qiaochu: A shortcut is NextPrime[2^31,-1]. –  Hans Lundmark Nov 12 '10 at 23:31
...and it works on Wolfram Alpha too: wolframalpha.com/input/?i=NextPrime%5B2%5E31%2C-1%5D –  Hans Lundmark Nov 12 '10 at 23:33

http://www.prime-numbers.org/prime-number-2147480000-2147485000.htm tells you that it's 2147483647 (about 2/3rds of the way down, third column). This website seems like a good resource if you're looking for lots of primes.

-
Thank you, that list was exactly what I needed. –  Martin Nov 12 '10 at 22:39
It is $2^{31}-1$. You might want to check Mersenne prime for similar details.
The fact that this is a prime is taken advantage by pseudo random number generators on $32$ bit machines. –  user17762 Nov 12 '10 at 22:22