## RE Observations on binary representation

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• 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
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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@...>
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]
>
>
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