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.

  • $\begingroup$ 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. $\endgroup$ – Qiaochu Yuan Nov 12 '10 at 22:20
  • $\begingroup$ These are all great answers. Thank you everyone. $\endgroup$ – Martin Nov 12 '10 at 22:38
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    $\begingroup$ @Qiaochu: A shortcut is NextPrime[2^31,-1]. $\endgroup$ – Hans Lundmark Nov 12 '10 at 23:31
  • $\begingroup$ ...and it works on Wolfram Alpha too: wolframalpha.com/input/?i=NextPrime%5B2%5E31%2C-1%5D $\endgroup$ – 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.

  • $\begingroup$ Thank you, that list was exactly what I needed. $\endgroup$ – Martin Nov 12 '10 at 22:39

It is $2^{31}-1$. You might want to check Mersenne prime for similar details.


  • $\begingroup$ Interestingly this is one of the four known Mersenne double prime.en.wikipedia.org/wiki/Double_Mersenne_number $\endgroup$ – user17762 Nov 12 '10 at 22:20
  • $\begingroup$ The fact that this is a prime is taken advantage by pseudo random number generators on $32$ bit machines. $\endgroup$ – user17762 Nov 12 '10 at 22:22
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    $\begingroup$ The first proof of primality was given by Euler, and it remained the largest-known prime for nearly 100 years. $\endgroup$ – Douglas S. Stones Nov 12 '10 at 22:30
  • $\begingroup$ Do you have a link to the proof @douglas? $\endgroup$ – AnonymousCoward Nov 12 '10 at 22:39
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    $\begingroup$ Here's Euler's proof: math.dartmouth.edu/~euler/pages/E461.html Although you might be more interested in the wikipedia page: en.wikipedia.org/wiki/2147483647 $\endgroup$ – Douglas S. Stones Nov 12 '10 at 23:07

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