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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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closed as too localized by Asaf Karagila, Aryabhata, J. M., Quixotic, Robert Israel Aug 29 '11 at 19:50

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Apparently they keep finding new ones @ PrimeGrid. – J. M. Aug 29 '11 at 16:40
The most recent primes 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. – Arturo Magidin Aug 29 '11 at 16:46
(corrected) According to the Prime Database's list of 100 largest known primes, the largest known prime was discovered in 2008, has 12978189 digits, and equals $2^{43112609}-1$. – Arturo Magidin Aug 29 '11 at 16:47
I just discovered 876797689865765453447867987711 two seconds ago. – Robert Israel Aug 29 '11 at 19:47
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. – Mark Bennet Aug 29 '11 at 20:22

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 is available from here – Américo Tavares Aug 29 '11 at 19:36

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.

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