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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.2010-11-12
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    These are all great answers. Thank you everyone.2010-11-12
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    @Qiaochu: A shortcut is `NextPrime[2^31,-1]`.2010-11-12
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    ...and it works on Wolfram Alpha too: http://www.wolframalpha.com/input/?i=NextPrime%5B2%5E31%2C-1%5D2010-11-12

2 Answers 2

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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.

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    Thank you, that list was exactly what I needed.2010-11-12
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It is $2^{31}-1$. You might want to check Mersenne prime for similar details.

http://en.wikipedia.org/wiki/Mersenne_prime

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    Interestingly this is one of the four known Mersenne double prime.http://en.wikipedia.org/wiki/Double_Mersenne_number2010-11-12
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    The fact that this is a prime is taken advantage by pseudo random number generators on $32$ bit machines.2010-11-12
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    The first proof of primality was given by Euler, and it remained the largest-known prime for nearly 100 years.2010-11-12
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    Do you have a link to the proof @douglas?2010-11-12
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    Here's Euler's proof: http://www.math.dartmouth.edu/~euler/pages/E461.html Although you might be more interested in the wikipedia page: http://en.wikipedia.org/wiki/21474836472010-11-12