Hello Secret901:

This is a follow up to a previous equation.  (With a tip this time) -
I forgot to reward the EXCELLENT work as I was traveling.) I could
probably do the quick calculation, but I think you might have some
fun:

The number of digits to the following equation:

2^5130000=x.  This equation is all the possible combinations for a 300
dpi Black and white printer to print on a letter size piece of paper
given a margin of 1 inch all the way around.  so given this is all the
possible combinations.  How tall would the pages stack assuming the
thickness of the paper to be .0025 inches think if each page had a
unique "pattern".

Please convert to miles from inches.   

Bonus what if the printer was 600 dpi???

Here is where I got paper thickness
(http://www.bradenprint.com/articles/paperthickness/PaperThicknessInfoSheet.pdf).

Thanks in advance!
Mr. Sneaky

Hi again Mr. Sneaky!
The number of decimal digits in 2^5130000 is again the floor of its
log base 10 plus 1.
log(2^5130000) = lg (2^5130000)/lg (10)
               = 5130000/3.32192809489
               = 1,544,283.9

Thus there are 1,544,283 + 1 = 1,544,284 decimal digits in 2^5130000.

If each piece of paper was 0.0025 inches thick, then they would stack
up to:
0.0025 inches X (2^5130000) = 1.88667 x 10^1544281 inches
Since there are 63,360 inches in a mile, the stack would be:
1.88667 x 10^1544281/63360 = 2.9777008 x 10^1544276 miles high.

Since the size of the universe is estimated to be about 5.88 x 10^21
miles long (http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/971124x.html)
and the number of atoms in the universe is less than 10^100, you can
be sure that 10^1544276 is an extremely large number.
By the way, I calculated the number of dots in an 8½ x 11 piece of
paper with 300 dpi and 1 inch margins all around is 5,265,000 and not
5,130,000.  Perhaps you used 8 x 11½ instead.  I shall proceed to
answer this question for 5,265,000 as well as for 600 dpi.

2^5265000 has floor(5265000/lg 10) + 1 = 1,584,922 + 1 = 1,584,923
digits.
The stack of that many pages would be 2.1140286546 * 10^1584920 inches
or 3.336535 * 10^1584915 miles high.

For the case of 600 dpi, we shall first calculate the number of dots
per page:
(600 * (8.5 - 2))*(600 * (11 - 2)) = 21,060,000 dots per page.
2^21060000 has floor(21060000/lg 10) + 1 = 6,339,691 + 1 = 6,339,692
digits.
A stack of that many pieces of paper would be 1.2783 x 10^6339689
inches or 2.1075 x 10^6339684 miles high.

I have calculated the values of 2 to each of those powers exactly
using Mathematica.  If you'd like to see them, please let me know, and
I can post them as well.  I hope that this answered your question.  If
you are confused by anything, please request for clarification and
I'll be happy to assist you further.
secret901-ga

Search strategy:
"letter size"
"numer of atoms in the universe"
"size of the universe"

Fast and Excellent yet again!!!

If I understand your question, you want to know how thick a stack of
paper containing each unique pattern as output by a 300dpi printer
would be?

It's not a matter of inches or miles.  Converting from inches or miles
is a factor of about 60,000 or about 5 orders of magnitude, 5 decimal
digits.

2^5130000 has over 1.5 million decimal digits.  Losing 5 to convert
from inches to miles is not a significant change.

If I have understood your question, Secret901 can fire up a copy of
Mathematica to get you an exact answer but the question itself seems a
bit absurd.