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.
What is the largest prime less than 2^31?
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number-theory
prime-numbers
online-resources
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0...and it works on Wolfram Alpha too: http://www.wolframalpha.com/input/?i=NextPrime%5B2%5E31%2C-1%5D – 2010-11-12
2 Answers
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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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0Thank 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.
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2Here'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/2147483647 – 2010-11-12