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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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    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 ra$n$dom stri$n$g 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.