# 1366 = 2*683!

1. Nov 27, 2009

### Staff: Mentor

Surprise, surprise. I bought a laptop and its display has horizontal resolution of 1366. I always thought that resolutions are some obvious multiples of 2n, as it makes addressing more efficient. Seems I was wrong.

Edit: no, it wasn't Black Friday deal. No Thanksgiving, no Black Friday here.

Last edited: Nov 27, 2009
2. Nov 27, 2009

### Pinu7

Re: 1366=2*683!

Didn't you just prove 1366 a multiple of 2^n, specifically in the case n=1?

3. Nov 27, 2009

### gel

Re: 1366=2*683!

Is it 4:3 aspect ratio with vertical resolution 1024? 1366 = 212/3, more or less.

Maybe a bit wacky, but could it arrange the pixels along vertical lines in memory?
Or, using RGB, 3 bytes per pixel, gives each horizontal line taking up 1366*3 = 212 +2 bytes. Just over a power of 2, so it would have to mess up the very edge pixels to fit it in nicely.

Just checked my laptop, and the horizontal resolution 1440=25*45, which isn't that round either.

Last edited: Nov 27, 2009
4. Nov 27, 2009

### hamster143

Re: 1366=2*683!

1366 x 768 is a common widescreen LCD TV resolution, 768 horizontal lines of square pixels @ 16:9 picture aspect ratio. It's relatively uncommon among laptops but it could occur in cheap models that reuse television LCD screens, or in models designed with widescreen HD video playback in mind.

Last edited: Nov 27, 2009
5. Nov 28, 2009

### Staff: Mentor

Re: 1366=2*683!

No, 16:9, 1366x768. 768=3*28, so it follows idea of efficient addressing.

At least it is 25

Common resolutions (be it vertical or horizontal) that I remember seeing throughout last 25 years were 192, 256, 320, 480, 640, 768, 800, 1024, 1280 - if you factorize them you see 1366 is from the other planet.

Somehow neither idea seems plausible - while definitely not expensive that's not one of el cheapo models (ASUS UL80Vt), and for connecting to widescreen TV I have HDMI connection, with nVidia chip working in full 1920x1080. But yes, 1366x768 is one of TV resolutions.

6. Nov 28, 2009

### sylas

Re: 1366=2*683!

The equation in the title is incorrect. 2*683! is not actually 1366, but 1266376227051150040750049298975600260378702334455998033658062658948724969769846617561677988973369977136331779827807189406858974521158978576585804736468346618537718043629699239334638697856812580177049291192330226706704493916738338302730276040810580004678928380705329707235495986763310670188555915081036233529889808223794606093734499415673896767013052940286531028949422645002221793324063238530736521782268939572624936117273929434546418818976108863969094532577058659939634278748902816870353784029739897982921626941469244062500516785048971414704152008473094348127772775949598185221459432005855692646058071176945697475061797674217008406837448869144949727544004672401887631512878379090172160238865963673250013561132985069287389297941100754263242045857901804774891400979319923291994043888076432831869746374203459647437796351338230067734227300594809744614053455844144060313636215725614935709102016283760455854559497188718713871836115996848939218107570604556276095638103962254670738212964078301045457178048142067611442874334815596079971611752932520795980380511505366452786040612037922201327276222722709941768267197177043645744775919020049769561328392222964406988829656884032352773672851259868247795118881785221294838037611843104004099244674022527794673522904928479624384470942601608250965167054202850953040417231546545631969092289541436006961226792547767873664802212323740184412256051250094308434464265930769694607340282999540931031220725796106604700384337854304076699180910604451840000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000, which is divisible by 2677.

I'm intrigued to see how this gets displayed.

7. Nov 28, 2009

### Staff: Mentor

Re: 1366=2*683!

When I was starting the thread I couldn't decide whether I should post the exclamation mark, or not. Now you know why... Sigh.

8. Nov 28, 2009

### hamster143

Re: 1366=2*683!

By widescreen I mean playback directly on the laptop. Most "widescreen" 14" laptop displays are 1280x768 or 1280x800 - slightly narrower (15:9 or 16:10). This laptop is exactly 16:9. So, maybe they wanted a screen that allowed widescreen DVD and blu-ray playback with correct aspect ratio and without black bars. They didn't want to go lower than 768 lines, because that would become a usability issue. And the next "true 16:9" standard up from 1366x768 is 1920x1080, and those either don't exist in 14" or they are incredibly expensive.

Of course, you can't really play back blu-ray properly on a 1366x768 screen, because you have to downsample from 1920x1080. Not to mention that the laptop does not even come with a blu-ray player. So that leaves widescreen DVDs.

9. Nov 29, 2009

Staff Emeritus
Re: 1366=2*683!

Ah, youth.

CGA: 640x200
EGA: 640x350
VGA: 640x480
VESA Modes: 800x600, 1152x720, 1440x900, 1600x1200

10. Nov 29, 2009

### Staff: Mentor

Re: 1366=2*683!

Exactly these numbers - plus Spectrum

I remember reading that especially in the case of horizontal resolution, if the line width is a multiply of 2^n it makes addressing of the video memory easier (say, all lines start at addresses that end with binary or hexadecimal zeros - so they are easier to calculate just by shifting or adding, no need for multiplication) and/or video memory can be used efficiently - if you want to use "nice" addresses you don't have to fill the lines up with unused memory.

Could be that was more important in times of slower processors and more expensive memory, but it still makes sense for me.

11. Nov 30, 2009

### rcgldr

Re: 1366=2*683!

The 1366x768 is very slightly stretched 1365.3x768 16x9 image. For the graphics speed, most of the painting is done via macros that describe polygons in that address space, so the addressing issue is handled within the video card. I'm pretty sure that the video card internals put stuff on nice boundaries, and skip bands of memory when refreshing the video.

Resolutions I see with my 'classic' CRT monitor with ATI HD4870 video card. I'm not sure what other options I'd get with a digital monitor. The non 4:3 formats end up being stretched to fill the screen, although I could adjust image size to compensate, but this would cause burn-in issues. I sometimes use 16:9 format even though it's stretched, in order to make videos for youtube. One reason CRT's can handle such a wide variety of resolutions is the CRT circuitry can ignore phosphor boundaries and use resolution based boundaries instead, relying on the partial responses from the phosphors when partially painted, which act as a type of automatic anti-aliasing + upconvert combined. Despite the large list, I mostly use 1280x960, some 1600x1200 for some games, and 1920x1440 when editting hi-def video.

640x480 (4:3)
800x600 (4:3)
1024x768 (4:3)
1280x720 (16:9)
1280x800 (16:10)
1280x960 (16:12)
1280x1024 (5:4)
1360x768 (1365.3x768 would be 16:9)
1360x1024 (1365.3x1024 would be 4:3)
1440x900 (16:9)
1600x1200 (4:3)
1680x1050 (16:10)
1792x1344 (4:3)
1800x1440 (5:4)
1856x1392 (4:3)
1920x1080 (16:9)
1920x1200 (16:10)
1920x1440 (4:3)
2048x1536 (4:3)

For the high end guys, digital cinema projectors have up to 4096x2160 pixels, although 16:9 and 16:10 formats aren't normally used with these.

16:9 => 3840x2160 (not specified as digital cinema standard, but could be used for "red ray").
1.85:1 => 3996x2160
2.00:1 => 4096x2048
2.35:1 => 4096x1743
2.39:1 => 4096x1714

Last edited: Nov 30, 2009