Loading ...
Sorry, an error occurred while loading the content.

where to find a prime gap and what is its minimum length

Expand Messages
  • Bill Krys
    i think you can find a gap anywhere the following way: for a number = Pi X Pj X Pk X ... X Pz, where P is a prime number and i, j, k, ... ,z are in sequence
    Message 1 of 1 , Nov 20, 2010
    • 0 Attachment
      i think you can find a gap anywhere the following way:

      for a number = Pi X Pj X Pk X ... X Pz, where P is a prime number
      and i, j, k, ... ,z are in sequence from lowest to hightest for that prime number, but they may be the same prime. e.g #1:

      4290 = 2 X 3 X 5 X 11 X 13, the prime gap exists at 4290 - 2 (4288) and runs at least another 7 - 2 = 5 numbers to 4284, so the gap is 4288, 4287, 4286, 4285 & 4284. the minimum length is determined thusly:

      arranging the prime factors in ascending order: take the prime number that is missing in the sequence of all prime numbers arranged in ascending order, (in this case 7) and subtract 2 to get a minimum gap length of 5.

      e.g. 2

      12012 = 2 X 2 X 3 X 7 X 11 X 13, so the gap starts at 12012 - 2 = 12010 and is a minimum length of 5 - 2 = 3. 5 is the missing prime in the ascending order of the prime factors of 12012, even though there are 2 2s.

      to determine the exact length of the prime gap would require an ability to determine the prime factors of successively smaller and successively larger even numbers, and apply the same formula: e.g. if we new the prime factors of the successivelyreferencing the next successively larger even number 12014 and the successively smaller even number of 12010, then we could establish the minimum lengths of the gaps starting at 12014 and 12010 starting at 12014 - 2 = 12012 and 12010 - 2 = 12008, respectively, and thus should by iteration be able to determine the exact length of the prime gap starting at any point we like.

      Bill Krys

      This communication is intended for the use of the recipient to which it is addressed, and may contain confidential, personal, and or privileged information. Please contact the sender immediately if you are not the intended recipient of this communication, and do not copy, distribute, or take action relying on it. Any communication received in error, or subsequent reply, should be deleted or destroyed.
    Your message has been successfully submitted and would be delivered to recipients shortly.