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

20118Re: 2^m+3^n and 2^n+3^m

Expand Messages
  • David Broadhurst
    Apr 17, 2009
    • 0 Attachment
      Submitted to OEIS:

      Numbers n such that 2^x + 3^y is never prime when max(x,y) = n

      1679, 1743, 4980, 4982, 5314, 5513, 5695, 6100, 6578,
      7251, 7406, 7642, 8218, 8331, 9475, 9578, 9749

      Mark Underwood found that for each non-negative integer n < 1421
      there is at least one prime of the form 2^m + 3^n or 2^n + 3^m
      with m not exceeding n.

      This sequence consists of numbers for which there is no such prime.

      David Broadhurst estimated that a fraction in excess of 1/800
      of the natural numbers belongs to this sequence and found
      17 instances with n < 10^4.

      For each of the remaining 9983 non-negative integers n < 10^4,
      a prime or probable prime of the form 2^x + 3^y was found with
      max(x,y) = n.

      Each probable prime was subjected to a combination of
      strong Fermat and strong Lucas tests.

      http://physics.open.ac.uk/~dbroadhu/cert/marktest.txt

      David Broadhurst, Apr 17 2009
    • Show all 22 messages in this topic