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

Simple Complexity - By Proxy

UPDATED:
Added Details and Links

For sometime I have struggled with how to allow public access to my home web servers and Esp8266 modules without opening up my network to abuse. In the past I have managed public access via my Router, by changing its configuration of Port Forwarding and NAT.  This works, but it is a pain to manage and generally requiring a re-boot of the network for each change.

Recently, I have discovered (actually re-discovered) that an Apache2 Web Proxy Server is much easier to manage, but it has a bit of a steep learning curve, with a lot of manual pages to read. One key concept is that Apache2 ReWriteRules are a super-set of the functionality of ProxyPass, each have their own documentation web pages.

After building the Required Config files

Now, on my Router I allow only Ports: http 80, 8040, 8160, and a private ssh port for access from the Internet. Ports 8040, and 8160 are still open for historical reasons, that is, they are used for my published Web Pages at: http://www.WA0UWH.com:8040, and my Esp8266 Server Farm devices.

The Apache2 Web Server supports: Virtual Host Names with Proxy Redirects, ReWriteRules, and ProxPass. By setting up "*.wa0uwh.com" as a CNAME (an aliases) to "www.wa0uwh.com" at my DNS Provider, I can use any "device name" I would like in the config files to initiate a proxy process. For example: I can now use and publish "http://node129.wa0uwh.com" for one of my Esp8266 Web Server modules. The actual connection details and security are all hidden behind the proxy curtains.

The normal web page port 80 is setup with a default virtual host page of; "Error 404", only configured virtual hosts and named devices are let through the proxy.

Note: The service and/or host that is selected is a combination of both Port Number and Host Name (or alias). For an incoming connection, the file is scanned from top to bottom, only the first match is used to select the service.

The following are excerpts from my Apache2 Default Virtual Host configuration file.

ServerName default.wa0uwh.com
LogLevel alert rewrite:trace1

<VirtualHost *:80>

    ServerAdmin webmaster@localhost
    DocumentRoot /var/www/DEFAULT/Public

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined

</VirtualHost>

# End

The following are excerpts from my Apache2 Named Virtual Host configuration file.

## Main Web Pages

## Loft Raspberry PI
<VirtualHost *:8040 *:80 >

    ServerName  rp21.wa0uwh.com
        RewriteEngine on
        ServerSignature Off
        RewriteRule /(.*)$      http://192.168.___.___/$1 [P,L]

</VirtualHost

## Loft Raspberry PI
<VirtualHost *:8040 *:80 >

    ServerName  rp22.wa0uwh.com
        RewriteEngine on
        ServerSignature Off
        RewriteRule /(.*)$      http://192.168.___.___/$1 [P,L]

</VirtualHost>

# Esp8266 Node on Published Port 8160
<VirtualHost *:8160 >

    ServerName  node.wa0uwh.com
    ServerAlias node*.wa0uwh.*
    ServerAlias localhost
        RewriteEngine on
        RewriteRule /(.*)$    http://192.168.___.___/$1 [P,L]

</VirtualHost>

## Loft Esp8266 Nodes
<VirtualHost *:8040 *:80 >

    ServerName  node.wa0uwh.com
    ServerAlias node*.wa0uwh.com
        RewriteEngine on
        ServerSignature Off
        RewriteCond %{HTTP_HOST} ^node(129|162|164|168|169|170|172)\.wa0uwh\.com [NC]
        RewriteRule /(.*)$      http://192.168.___.%1/$1 [P,L]
        RewriteRule /(.*)$ -  [R=404,L]

</VirtualHost>


## Loft WA0UWH Web Server
<VirtualHost *:8040 *:80>

    ServerName www.wa0uwh.com
    ServerAlias *.wa0uwh.com
    ServerAlias localhost 192.168.__.__ 
        DocumentRoot    /var/www/WA0UWH/Public
        Alias /gallery  /var/www/WA0UWH/Public/Gallery

</VirtualHost>

# End

Note, the above is just an excerpt from my Apache2 Virtual Host config file. For security reasons, the details; actual IPA's (___), BlackListing, Hacker Traps, Web Abuse Traps, and HoneyPots, are NOT included . Google is your friend for suggested configurations.

Now, with simple edits of the Apache2 Virtual Host config file, I can turn ON or OFF, devices and/or services as desired, while leaving only the http and ssh ports open for public access at the router.

Also note: each of my Raspberry PI Web Servers also have similar Apache2 Virtual Host config files, that is: Proxies are serving Proxies, and most often the actual destination is at different physical locations, and on different Networks! All unseen for my Internet users.


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