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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.

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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: – Hans Lundmark Nov 12 '10 at 23:33
up vote 3 down vote accepted 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.

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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.

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Interestingly this is one of the four known Mersenne double – user17762 Nov 12 '10 at 22:20
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
The first proof of primality was given by Euler, and it remained the largest-known prime for nearly 100 years. – Douglas S. Stones Nov 12 '10 at 22:30
Do you have a link to the proof @douglas? – AnonymousCoward Nov 12 '10 at 22:39
Here's Euler's proof: Although you might be more interested in the wikipedia page: – Douglas S. Stones Nov 12 '10 at 23:07

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