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Old 2009-09-11, 00:49   #1
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Default What's the largest known sequential prime?

What's the largest known prime for which all lower primes are also known?

Thanks,
Tony.
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Old 2009-09-11, 01:54   #2
Mini-Geek
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Quote:
Originally Posted by Unregistered View Post
What's the largest known prime for which all lower primes are also known?

Thanks,
Tony.
I don't know, but you could bet that if someone were to say it, somebody will find the next largest prime after that (almost instantly) and thus make the previous statement inaccurate. (and then someone will find the next one above that and so on, ad infinitum)
Seriously though, making such a list would take up a huge amount of hard drive space. It's really just not a practical thing to do. http://primes.utm.edu/lists/small/millions/ has a list of the first 50 million primes (the last one is a little under 1 billion), but even that could be generated on your computer by an efficient sieve program far, far faster than it could be downloaded and read from disk. http://primes.utm.edu/nthprime/ can be used to find the Nth prime with N<10^12 (prime<~3*10^13), but it does so by a clever method involving counting 'bins' of primes and sieving a small chunk of numbers for the actual prime you're looking for, not by storing every prime up to a limit.

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Old 2009-09-11, 02:21   #3
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Default What's the largest known sequential prime?

Quote:
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What's the largest known [sequential] prime for which all lower primes are also known?
The only sequential primes are 2 and 3, therefore the answer is 3.
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Old 2009-09-11, 07:41   #4
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I think a quite good measure of what the OP is looking for can be found at Tomás Oliveira e Silva's site:
http://www.ieeta.pt/~tos/goldbach.html
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Old 2009-09-11, 11:46   #5
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Quote:
Originally Posted by Mini-Geek View Post
I don't know, but you could bet that if someone were to say it, somebody will find the next largest prime after that (almost instantly) and thus make the previous statement inaccurate. (and then someone will find the next one above that and so on, ad infinitum)
Seriously though, making such a list would take up a huge amount of hard drive space. It's really just not a practical thing to do. .
Bingo!

The answer is almost impossible to know anyway. An answer to the
original question would almost certainly not be published. It is not
something that a mathematician would care about. If I do a private
computation, part of which generates all primes to 10^14, does this
mean that 10^14 becomes an answer to the question? Even if the
primes remain in DRAM and are never written to any external source?
What does the word "known" mean in the context of the question.

And I can't think of an application where raising the limit would be
important.
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