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By last, I mean the most recently discovered prime number. What was the length of time between the discovery of the last two prime numbers?

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    Apparently they keep finding new ones @ [PrimeGrid](http://www.primegrid.com/).2011-08-29
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    This question may be impossible to reasonably answer depending on what you mean by "discovered," but see http://primes.utm.edu/largest.html for a start.2011-08-29
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    @J.M. You seem to be two steps behind the times... (-;2011-08-29
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    The [most recent primes](http://primes.utm.edu/primes/status.php) on the database all date from the last 72 hours, so I would say that these days the "length of time between discovery" is pretty short.2011-08-29
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    (corrected) According to the [Prime Database's](http://primes.utm.edu/primes/) list of [100 largest known primes](http://primes.utm.edu/primes/search.php?Number=100), the largest known prime was discovered in 2008, has 12978189 digits, and equals $2^{43112609}-1$.2011-08-29
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    @Arturo: not to mention primes being generated by implementations of cryptographic algorithms across the globe, some of which may be "new" by sheer luck...2011-08-29
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    As stated, the question is too localized and I have voted to close as such. If you change the question to something like: "Is there a resource which maintains the 'latest' prime?", then consider my close voted withdrawn.2011-08-29
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    I just discovered 876797689865765453447867987711 two seconds ago.2011-08-29
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    Personally I think that the question may not be a good one, but for people at a certain level of mathematical knowledge it is the one they ask, and the comments and answers open up a mathematical world which may be interesting and inspiring for them. The site advertises itself as catering for all mathematical abilities. I agree that a reformulated question might help, but I think there may be many high-school students who aren't aware just how quickly primes are being identified, and that fact is not, so far as I know, in any of the accessible literature. I hope a version of this is reopened.2011-08-29
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    OK, I'll vote to reopen.2011-08-30
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    Perhaps I should mention that you too can discover a new prime number. Go to http://www.wolframalpha.com/ and enter "what is the next prime number after X" where X is a random string of 30 or so digits. The result will be a prime number slightly larger than X which, with very high probability, no human eyes have ever seen before.2011-08-30

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See the page The Largest Known Primes--A Summary by Chris K. Caldwell

(A historic Prime Page resource since 1994!)

Last modified: 16:20:41 Monday August 29 2011 UTC.

In particular this subpage and this one.

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    The Yves Gallot's program Proth.exe based on the [Proth's theorem](http://en.wikipedia.org/wiki/Proth%27s_theorem) is available from [here](http://primes.utm.edu/programs/gallot/)2011-08-29
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Apart from very large "special" primes, it is also possible to make/construct large "certified" primes, using the Pocklington-Lehmer criterion. That is, although one must "search" ("randomly") for primes readily certifiable, once they are found one can "attach" to them a small amount of data that anyone interested could use to verify their primality (via Pocklington-Lehmer, for example). In particular, although the search is obviously probabilistic, the certification is not.