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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

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Apparently they keep finding new ones @ PrimeGrid. –  J. M. Aug 29 '11 at 16:40
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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
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(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
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I just discovered 876797689865765453447867987711 two seconds ago. –  Robert Israel Aug 29 '11 at 19:47
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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. –  Mark Bennet Aug 29 '11 at 20:22

2 Answers 2

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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