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

Relative twins frequency

Expand Messages
  • chrisdarroch
    Hi all, Consider the set of natural numbers and filtering them by 3,5 and 7 (but not 2!) Within an interval of 105 I will find 15 pairs of numbers that differ
    Message 1 of 1 , Oct 22, 2009
    • 0 Attachment
      Hi all,

      Consider the set of natural numbers and filtering them by 3,5 and 7 (but not 2!)

      Within an interval of 105 I will find 15 pairs of numbers that differ by 2.

      If I add 11 to the filtering set and look at the interval which of course is the product of the filtering set i.e. 3.5.7.11 = 1155. I will find 3.5.9 = 135 pairs which differ by two.

      I want help in considering the idea of the number of pairs I might expect in fractions of the product of the filtering primes.

      I understand that the distribution of the pairs is 'irregular' and the largest gap between two pairs is perhaps unknown for any n, number of filtering primes.

      I can see that given the paragraph above one cannot simply say that since there are 15 pairs in 105 therefore there will be 15/3 pairs in 105/3 or that since there are 135 pairs within the interval 1155 then there will be 135/5 pairs within an interval of 1155/5 etc.

      But surely there is some kind of generalisation that one can use for fractions of these intervals.

      Can anyone lead me to an understanding of whether there is such a generalised process that can be applied and what it is?

      Just in case I have been a bit vague at the end there; I might expand my request by saying that with the interval 1155; if I wanted to consider how many pairs I might expect within the fraction 1155/15; I might say something like there are 77 + or - a; pairs in that fraction; where a is a whole number. Where 'a' could denote the degree of inaccuracy of course.

      Have I asked a silly question here? If so, then could someone enlighten me as to why?

      Thankyou in advance for any consideration.

      Chris
    Your message has been successfully submitted and would be delivered to recipients shortly.