Yesterday I figured I’ll try to factor the first few numbers greater than 10¹⁰⁰⁰⁰⁰⁰⁰⁰ (or at least find their smallest divisors). The idea was to see how hard it is to find the divisors of the first few hundred 100,000,001-digit numbers.

I took a pretty simple approach: for each prime number p, calculate 10¹⁰⁰⁰⁰⁰⁰⁰⁰%p (the remainder after dividing by p). Then I used the result to create a partial sieve. After the first 300,000 primes, I still couldn’t find a divisor for 10¹⁰⁰⁰⁰⁰⁰⁰⁰+37.

Update

10¹⁰⁰⁰⁰⁰⁰⁰⁰+37 is divisible by 6,870,527 (the 468,407th prime). The next one without a known divisor is 10⁹⁹⁹⁹⁹⁹⁹⁹+69 (tried to divide by the first 2,348,559 primes, no factors found so far).

Here’s the smallest prime divisor for the first few 100,000,001-digit integers (I = 10¹⁰⁰⁰⁰⁰⁰⁰⁰):

.------------------.
| number | divisor |
---------+----------
|      I |       2 |
|  1 + I |   10753 |
|  2 + I |       2 |
|  3 + I |       7 |
|  4 + I |       2 |
|  5 + I |       3 |
|  6 + I |       2 |
|  7 + I |     113 |
|  8 + I |       2 |
|  9 + I |     197 |
| 10 + I |       2 |
| 11 + I |       3 |
| 12 + I |       2 |
| 13 + I |      29 |
| 14 + I |       2 |
| 15 + I |       5 |
| 16 + I |       2 |
| 17 + I |       3 |
| 18 + I |       2 |
| 19 + I |    2087 |
| 20 + I |       2 |
| 21 + I |      11 |
| 22 + I |       2 |
| 23 + I |       3 |
| 24 + I |       2 |
| 25 + I |       5 |
| 26 + I |       2 |
| 27 + I |      37 |
| 28 + I |       2 |
| 29 + I |       3 |
| 30 + I |       2 |
| 31 + I |       7 |
| 32 + I |       2 |
| 33 + I |      17 |
| 34 + I |       2 |
| 35 + I |       3 |
| 36 + I |       2 |
| 37 + I | 6870527 |
| 38 + I |       2 |
| 39 + I |     139 |
| 40 + I |       2 |
| 41 + I |       3 |
| 42 + I |       2 |
| 43 + I |      11 |
| 44 + I |       2 |
| 45 + I |       5 |
| 46 + I |       2 |
| 47 + I |       3 |
| 48 + I |       2 |
| 49 + I |      13 |
| 50 + I |       2 |
| 51 + I |      71 |
| 52 + I |       2 |
| 53 + I |       3 |
| 54 + I |       2 |
| 55 + I |       5 |
| 56 + I |       2 |
| 57 + I |      31 |
| 58 + I |       2 |
| 59 + I |       3 |
| 60 + I |       2 |
| 61 + I |      59 |
| 62 + I |       2 |
| 63 + I |  399389 |
| 64 + I |       2 |
| 65 + I |       3 |
| 66 + I |       2 |
| 67 + I |      17 |
| 68 + I |       2 |
'------------------'

A while ago I wrote two widgets for awesome. Later on I’ve added a little more look&feel to my awesome desktop.

Compositing

Very easy, via xcompmgr. I don’t like the huge default shadows (nor pretty much any of the default settings), so I start it from my rc.lua like this:

awful.util.spawn("nautilus -n")
awful.util.spawn("xcompmgr -c -C -f -F -D 2.5 -l -2 -t -2 -r 2 -o 0.25")

Note that I need to start nautilus before running xcompmgr, otherwise tha background won’t word. Passing -n to nautilus will get rid of the desctop icons. Now I get to see the GNOME desktop background instead of my awesome background image, but it’s easy to change using the gconf-editor.

A shiny new GTK engine

While there, I also set up a new GTK engine. For a while I was using the Aurora GTK engine, but I wanted something simpler. Then I stumbled upon the Equinox GTK engine. Simple and nice. The tooltips are very similar to my awesome’s color theme. The buttons are smaller, good for laptop screens. With the light shadows and fading provided by xcompmgr, this engine looks great and works really well with awesome.

GTK Equinox theme

Neutral Plus cursor theme

This is probably the best looking cursor theme in awesome. It’s very similar to the default X cursor theme, so it is unnoticable if an app doesn’t support Xcursor and falls back.

Easy to install, just add this to your ~/.Xresources:

/* Cursor theme: */
Xcursor.theme: Neutral_Plus

Color theme & font settings for urxvt

My ~/.Xdefaults looks something like this:

/* Fonts: */
URxvt*font:             xft:Bitstream Vera Sans Mono:pixelsize=12:autohith=true:antialias=true
URxvt*boldFont:         xft:Bitstream Vera Sans Mono:pixelsize=12:bold:autohint=true:antialias=true
URxvt*italicFont:       xft:Bitstream Vera Sans Mono:pixelsize=12:italic:autohint=true:antialias=true
URxvt*bolditalicFont:   xft:Bitstream Vera Sans Mono:pixelsize=12:bold:italic:autohint=true:antialias=true
/* Colors: */
URxvt*colorBD:          #ffffff
URxvt*foreground:       #b2b2b2
URxvt*background:       #000000
URxvt*color0:           #303030
URxvt*color1:           #b21818
URxvt*color2:           #18b218
URxvt*color3:           #b26818
URxvt*color4:           #1818b2
URxvt*color5:           #b218b2
URxvt*color6:           #18b2b2
URxvt*color7:           #b2b2b2
URxvt*color8:           #686868
URxvt*color9:           #ff5454
URxvt*color10:          #54ff54
URxvt*color11:          #ffff54
URxvt*color12:          #5454ff
URxvt*color13:          #ff54ff
URxvt*color14:          #54ffff
URxvt*color15:          #ffffff
URxvt*underlineColor:   #b26818
/* Borders: */
URxvt*externalBorder:   0
URxvt*internalBorder:   0
/* Scrolling: */
URxvt*saveLines:        12000
URxvt*scrollBar:        false
URxvt*scrollTtyKeypress:true
URxvt*scrollTtyOutput:  false
URxvt*scrollstyle:      plain
URxvt*secondaryScroll:  true
/* Misc: */
URxvt*loginShell:       false
URxvt*urgentOnBell:     true
URxvt*fading:           30
URxvt*shading:          15
URxvt*transparent:      false

This may have been obvious to others, but I have just found out that in Python, when Exceptions get raised, they are converted to strings. That is:

>>> class C(object):
...     __str__ = lambda s: '<C: str>'
...     __repr__ = lambda s: '<C: repr>'

>>> c = C()
>>> exc = Exception(c)

>>> exc
Exception(<C: repr>,)

>>> repr(exc)
'Exception(<C: repr>,)'

>>> str(exc)
'<C: str>'

And now comes the interesting part:

>>> raise exc:
Traceback (most recent call last):
...
Exception: <C: str>

The traceback displays the Exception class’s name (__class__.__name__), and the parameters passed when instantiating the exception, converted to string (str())! The same thing happens in both Python 2 and Python 3.

The thing is, I’d expect repr() instead of str(). But good to know how it works. If I want to see consistent output in both pdb and tracebacks, I just need to use classes where str(obj) == repr(obj), that is, obj.__str__ is obj.__repr__.

David Rock’s amazing talk about how the brain works.

The artsprint was a one-week Python/Pyramid/Node sprint at the ]a[ Academy of Fine Arts, Vienna. 27 Participants were mostly BDA people, with the addition of some other Python enthusiasts.

We’ve been working on a stack of libraries that most of use on a daily basis, focusing mainly on writing documentation, fixing tests, and converting the whole stack from repoze.bfg to Pyramid.

And we even had a button machine.

As a result, we:

• released Plumber 1.0 (an alternative to mixin-based extension of classes)
• updated Node, Yafowil (and its widget libraries) and cone.* to Pyramid
• improved the documentation of the stack
• set up a buildbot to run periodical & on-demand unit-tests and code checks
• worked on agx
• had some productive discussions
• met new friends & did some key signings
• spent some quality time at the Metalab
• had loads of fun in Vienna!

Metalab in Vienna. Picture: Wikipedia.

The Startup Weekend seems great so far. Running surveys, advertizing, planning a business, playing the Kinect, beer, mandarins, lots of interesting people, and planning various cow usage.

So far not much coding though. I’ll just have to make up for it next week at artsprint.