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

RE Observations on binary representation

Expand Messages
  • Jose Ramón Brox
    I don t have the theory tools either to assure it, but I think that since the growth of your numbers is exponential, the number of primes you will find in
    Message 1 of 1 , Jan 31, 2004
    • 0 Attachment
      I don't have the theory tools either to assure it, but I think that since
      the growth of your numbers is exponential, the number of primes you will
      find in every interval (0,2^k) should remain quite constant.

      Jose Brox


      ----- Original Message -----
      From: "John Olsen" <infix@...>
      To: <primenumbers@yahoogroups.com>
      Sent: Friday, January 30, 2004 11:02 PM
      Subject: [PrimeNumbers] Observations on binary representation


      > I'm new to the list, so just smack me if this is old stuff. Is there a
      name
      > for primes that are somewhat similar to Mersenne, but having a single bit
      > set to zero and not necessarily having the power be prime? For example,
      > take 2^24-1. Out of the 23 numbers you can get by zeroing a single bit
      > (ignore zeroing the top bit since it can be dropped making it a 23 bit
      > number), 7 are prime (30%) which would seem to make these sorts of numbers
      a
      > good target for big prime hunts. The main problem is they seem at first
      > glance to be much harder to factor than Mersennes, since the equation is
      not
      > so clean:
      >
      >
      >
      > ((2^n) - 1) - (2^m) for m ranging 0 to n-1.
      >
      >
      >
      > For the curious, these are the 24-bit primes I was playing with, from a
      list
      > I built with a simple sieve.
      >
      >
      >
      > 1101 1111 1111 1111 1111 1111 14680063
      >
      > 1111 1111 0111 1111 1111 1111 16744447
      >
      > 1111 1111 1101 1111 1111 1111 16769023
      >
      > 1111 1111 1111 1011 1111 1111 16776191
      >
      > 1111 1111 1111 1111 1101 1111 16777183
      >
      > 1111 1111 1111 1111 1110 1111 16777199
      >
      > 1111 1111 1111 1111 1111 1101 16777213
      >
      >
      >
      > From what I've seen, these sequences are relatively thick with primes, no
      > matter the size of n. It would be really nice to figure out what the
      > percentage of primes is as n grows. All I would bet on initially is that
      it
      > beats the usual 1/log x probability by quite a bit. I've no idea if the
      > probability curve is the same Order or not. (Rusty math and/or lack of
      > background)
      >
      >
      >
      > John M. Olsen
      >
      > infix@...
      >
      >
      >
      >
      >
      > [Non-text portions of this message have been removed]
      >
      >
      > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
      > The Prime Pages : http://www.primepages.org/
      >
      >
      >
      > Yahoo! Groups Links
      >
      > To visit your group on the web, go to:
      > http://groups.yahoo.com/group/primenumbers/
      >
      > To unsubscribe from this group, send an email to:
      > primenumbers-unsubscribe@yahoogroups.com
      >
      > Your use of Yahoo! Groups is subject to:
      > http://docs.yahoo.com/info/terms/
      >
      >
    Your message has been successfully submitted and would be delivered to recipients shortly.