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

WIP - have you seen this?

Expand Messages
  • Bill Krys
    Hello, please comment on below: take (Px)*(P1*P2*P3*...*Pn)+(Pn+1), (Px)*(P1*P2*P3*...*Pn)+(Pn+2), etc. where Px is a varying prime or 1 to get all primes.
    Message 1 of 2 , Feb 18, 2006
    • 0 Attachment
      Hello,

      please comment on below:

      take (Px)*(P1*P2*P3*...*Pn)+(Pn+1), (Px)*(P1*P2*P3*...*Pn)+(Pn+2), etc. where Px is a
      varying prime or 1 to get all primes. e.g.

      P1*P2*P3 = 2*3*5

      now add Pn+1 = P4 = 30 + 7 = 37

      P5 = 11, so => 41

      continue:

      13 => 43, 17 => 47, 19 => 49 (okay not prime so add again to 2*3*5 = 79 (in other words,
      Px = 2, here))

      continue:

      23 => 53, 29 => 59, 31 => 61, 37 => 67, 41 => 71, 43 => 73, 47 => 77 (okay not prime so
      add again to 2*3*5 = 107 (in other words, Px = 2, here))

      continue:

      53 => 83, 59 => 89, 61 => 91 (okay not prime so add again to 2*3*5 = 121 (okay still not
      prime so add again to 2*3*5 = 151 (in other words, Px = 3, here)))

      coninue:

      67 => 97, 71 => 101, 73 => 103, 79 => 109 (but we already created this prime, so add
      again FOUR MORE TIMES to 2*3*5 = 229 (in other words, Px = 5, here))

      continue:

      83 => 113, 89 => 119 (okay not prime so add again to 2*3*5 => 149 (Px = 2, here)

      continue:


      97 => 127, 101 => 131, 103 => 133, (okay not prime so add again to 2*3*5 => 163 (Px = 2,
      here)

      continue:

      and so on ...

      Bill

      Bill Krys
      Email: billkrys@...
      Phone: 780.474.9493
      Cell: (780) 995-6214
      ICQ: 122663993
      12112-50 Street
      Edmonton, Canada T5W 3C5

      __________________________________________________
      Do You Yahoo!?
      Tired of spam? Yahoo! Mail has the best spam protection around
      http://mail.yahoo.com
    • Werner D. Sand
      Hello Bill, your observation is well-known. It is simply because of the fact that by N=p1*p2*p3*... +px the p1, p2, p3… are excluded as prime divisors and
      Message 2 of 2 , Mar 1, 2006
      • 0 Attachment
        Hello Bill,

        your observation is well-known. It is simply because of the fact that
        by N=p1*p2*p3*... +px the p1, p2, p3… are excluded as prime divisors
        and therefore N with relatively large probability is prime. If N is
        nevertheless not prime and you add 30 until it is prime, that is
        because of the fact that after Dirichlet each arithmetic sequence of
        the form a*n+b (thus also 30*n+N) contains infintitely many prime
        numbers. Btw you may as well choose - instead of +: N=p1*p2*p3*... -px
        and powers of p: N=p1^k1*p2^k2*p3^k3... + or - px^kx, where px^kx may
        also be 1. By + or - you get a sort of symmetry in the distribution of
        (small) prime numbers.

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