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Ten prime numbers describing an arithmetic sequence

  1. Feb 17, 2009 #1
    Ten distinct prime numbers, each less than 3000, when arranged in increasing order of magnitude describe an arithmetic sequence.

    What are these ten prime numbers?
     
  2. jcsd
  3. Feb 17, 2009 #2

    disregardthat

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    wrong
     
    Last edited: Feb 18, 2009
  4. Feb 17, 2009 #3
    Why p+p+d = p+3d ???
     
  5. Feb 17, 2009 #4
    199 + n * 210 (where n = 0, 1, 2, ..., 9) are all primes.
    I found this by brute force. Here's an easy question. This is a run of length 10. There are two runs of length 9. What are they?
     
    Last edited: Feb 17, 2009
  6. Feb 17, 2009 #5
    Are you implying that there are more runs of 9 besides the 2 included within your run of 10?

    But while we're doing brute force:
    There's only 1 run of length 10 within all the primes up to a max of 3000. But how high do you have to push the max before you find another run of 10? How many runs of 10 are there with all the primes below 1 million?

    DaveE
     
  7. Feb 17, 2009 #6
    p + p + d =/= p + d+d+d simple mistake
     
  8. Feb 18, 2009 #7
    This isn't jeopardy. Pose your answer in the form of an answer.
     
  9. Feb 18, 2009 #8
    Ok, just checking.

    And another brute forcer: what's the longest run of arithmetically sequenced primes below 1 million?

    DaveE
     
  10. Feb 24, 2009 #9
    So, just so I don't leave these questions without answers:

    There's only 1 run of length 10 within all the primes up to a max of 3000. But how high do you have to push the max before you find another run of 10?

    53813

    How many runs of 10 are there with all the primes below 1 million?

    144

    What's the longest run of arithmetically sequenced primes below 1 million?

    The longest run is 15 primes

    DaveE
     
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