ASCII Strings within the Largest Known Prime Number

Someone on the Youtube Numberphile Channel was wondering if after converting the Largest Prime Number  to base 26 (see previous post) would there be any interesting ASCII strings within the Number.

I think I have created a Unix Function that will do the conversion.

( echo "obase=16;"; echo "obase=26; 2^74207281-1" | bc | tr -d '\n\\' | sed 's/ /;65+/g' ) | bc | xxd -r -p

This will take a while (maybe several hours, or days), but if I find something interesting, I will report the results.


-- Home Page: https://WA0UWH.blogspot.com

The New Largest Prime Number Found

UPDATED:
Added Details and Links

Recently (Jan 7. 2016) the next and Largest Prime Number has be found (so far), it has about 22 Million Digits long, See, YouTube at: https://goo.gl/C7ngE7.

The number can be expressed as a small-simple math function, that is: "2^74207281-1"

The previous Large Prime Number (17 Million Digits) was found about 3 years ago on Jan 25, 2013, see: http://goo.gl/UbAWK0

Hopefully, and if history hold true, we will see the next Largest Prime sometime within the next 3 to 5 years.

Just for fun, I decided to see how long it would take my 3.4GHz Workstation to perform the calculation and print the full 22 Million Digits to the screen - it took about 154 minutes - it was like watching paint dry.  :-)

Note: To verify that it "is actually prime" would probably take several months (or more actually several years) on my computer.

Here is the linux command that I used to print this New Prime, and a few of the Beginning and Ending Digits of the results:

$ time echo "2^74207281-1" | bc
30037641808460618205298609835916605005687586303030148484394169334554
77232190679942968936553007726883204482148823994267278352907009048364
32218015348199652241372287684310213386284573666361506667532122772859
35986405778025687564779586583214205117110963584426293657265038724071

.
 .  ( 22 Million More Digits )
  .

74801792765597096176486305356033886997788467889060830923906229428002
87770846681535011427622921221836904045477963931367013401448014940470
41169663347456468851607177740147629124621136468794258014451073931002
12927181629335931494239018213879217671164956287190498687010073391086
436351

real 153m50.931s
user 92m34.588s
sys 0m13.496s

Note: To capture the number on the screen, a large display buffer of more than 22 Meg Bytes (of RAM) was necessary.

I need to check with YouTube and/or Numberphile to see if my calculated number is correct  :-)

My computer is current checking four large numbers to see if they are Prime, this consumes about 100% of the Quad Core CPU, but it runs at a very low priority so it does not effect my use of the computer. Each is expected to finish at different times, Below shows the number being tested, and number of days until I should have the results:

• 2^332,338,003-1, results expected in 643 days
• 2^332,338,319-1, results expected in 643 days
• 2^332,338,397-1, results expected in 858days
• 2^332,338,777-1, results expected in 858 days

As you may have expected, . . . I am a fan of Very Large Numbers !

-- Home Page: https://WA0UWH.blogspot.com

More Large Numbers

UPDATED:
Added Details and Links

Update: Jan 7, 2016 - New Largest Prime found: echo "2^74207281-1" | bc, which is 22 Million Digits, the function takes 77.25 minutes to compute on a 3.4GHz Processor. See, youtube at: https://goo.gl/C7ngE7

See previous post.

The largest known prime number is: 17,425,170 digits long, it can be computed with this very short function:

echo "2^57885161 -1" | bc

On my Workstation (2.2GHz) it takes about 82 minutes to compute, but with more than 17M digits, it takes much longer to display or print.

To print, it would require 7.7 Reams of paper; single sided, 80 character per line, 56 lines to a page, and 500 pages pre ream.

Note: The person that finds the "next" larger prime number will be famous.


-- Home Page: https://WA0UWH.blogspot.com