Monday, March 24, 2014

A puzzle of primes

This is a fairly old one I first saw in a high school, at one of the Stellenbosch university olympiad camps.  Enjoy.

It's possible to find a string of 1000 consecutive integers with no primes. For example
1001!+2,1001!+3,...,1001!+1001. Does there exist a string of consecutive integers with exactly 5 primes?
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3 comments:

  1. Am With TateMarch 25, 2014 at 12:09 PM

    2-11?

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  2. UnknownMarch 25, 2014 at 12:22 PM

    well 2 through 11 is a string of length 10 (2,3,4,5,6,7,8,9,10,11) and the question is asking about a string of length 1000. So that doesn't work.

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  3. Shaun GriffithMay 16, 2015 at 10:25 AM

    "Does there exist a string of consecutive integers with exactly 5 primes?"

    Yes. But if you insist on 1000, then simply back up 5 primes before 1001!.

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