## Re: [PrimeNumbers] A amusing idle speculation

Expand Messages
• ... The number of such blocks is limited, albeit to a very large (by human standards) number. If we only had 3 blocks in base 2^24, there would be (2^24)^3
Message 1 of 2 , Jul 25, 2003
xed wrote:
>
> Folks;
> And now for something completely different...
> (As the Pythons were wont to say)
> When searching for visual patterns in base-k
> representations of the primes (patterns formed
> by an n by m display of the base-k form of the
> prime number in question) it occurs to me you're
> thinking too small.
> So far, various folks have discussed small
> patterns (32 x 32, etc.) formed by base-2
> representations of primes. That's all well and
> good as far as it goes...but what if we think
> bigger?
> Suppose instead of base 2 we represent
> the prime number in the form base 2^24 and
> suppose instead of small blocks we visualize
> the base 2^24 representation as a 720 x
> 480 block. (Yes, you can see where this is
> This happens to be the format used by DVDs to
> represent single frames from movies (in NTSC
> -- for those of you in Europe, the sequences
> would be represented in base 2^24 as 720 x
> 576 blocks).
> Q: Do there exist infinitely many such Truecolor
> 720 x 480 pictures encoded in the infinity of primes?
> Or is the number of such blocks limited?

The number of such blocks is limited, albeit to a very large (by human
standards) number. If we only had 3 "blocks" in base 2^24, there would
be (2^24)^3 different possibilities, or 2^72 ~= 4.7x10^21. Now, with
the American encoding of these pictures there are (2^24)^(720x480) =
(2^24)^(345600) = 2^8294400 ~= 10^2496863.196 which is indeed a big
number, but still finite. In the European encoding scheme we have that
there are (2^24)^(720x576) = (2^24)^(414720) = 2^9953280 ~=
10^2996235.835 So, the total number of possible pictures encoded this
way, in either system, is less than a 3 million digit base-10 number.

Now, while not all of these numbers (pictures) are primes, I would
venture a guess that there are alot that are. And, personally, I think
it would be amusing to see which frames of some movies already out there
are prime. I also think it'd be neat to find out if any of those frames
have a simple formula to describe them.

-David C.
Your message has been successfully submitted and would be delivered to recipients shortly.