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10^k

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  • Jon Perry
    Is there a k such that there exists a primitive region of 10^k such that all regions after this one have less primes than such given k. e.g. let k=1 between 90
    Message 1 of 1 , Jan 28, 2003
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      Is there a k such that there exists a primitive region of 10^k such that all
      regions after this one have less primes than such given k.

      e.g.

      let k=1

      between 90 and 99, there is 1 prime, 97

      However, between 100 and 109, there are 4 primes.

      But consider k=2,

      Does every region of 100 have less primes than [0,100]? Or does some region
      [j*10^2,(j+1)*10^s-1] have more primes than a lesser region
      [i*10^2,(i+1)*10^2-1]?

      If not, is this true for k=3, i.e. [0,1000] is a maximal prime set?

      I guess what I am trying to say is that, does some minimal k exist such that
      the primitive ([0,10^k-1]) set of primes is of maximal magnitude for this k?

      Jon Perry
      perry@...
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