On not proving the twin prime conjecture with AutoCAD

As an HVAC engineer by trade, [Carlos Paris] spends a lot of time in AutoCAD designing all those hidden pipes, tubes, and ducts hidden in a building’s rafters. One day, [Carlos] read of an open contest – the prize was over a million dollars – to generate a prime number with a billion digits. [Carlos] misheard this as, ‘a prime number greater than one billion’ and of course said this was a trivially easy task and opened up his favorite tool – AutoCAD – in an effort to discover the largest prime ever. [Carlos] never generated a remarkably large prime, but he did come up with a very, very cool visualization of prime numbers on a number line, as well as a great justification of the twin prime conjecture, a problem in mathematics that has remained unsolved for several generations.

[Carlos] started his investigations into the properties of prime numbers by drawing a series of circles on a number line in AutoCAD. These circles were of diameters of all the integers, and going down the number line, these circles started to have an interesting, chaotic pattern (see above picture). [Carlos] found that whenever two circles intersected, that position was a prime number. It’s really nothing more than a Sieve of Eratosthenes, but it’s a very cool-looking visualization nonetheless.

Looking deeper into his graph, [Carlos] discovered there were certain primes that had another prime number just two places down the number line. For example, the numbers 3 and 5, 29 and 31, and 41,and 43 are twin primes, as the difference between the primes is only 2. The idea there are infinitely many twin primes is a famous unsolved problem in mathematics – it’s obvious it must be true, but no mathematician has yet come up with a proof of this conjecture.

[Carlos] looked at his number line and simplified it to a generic prime number. By taking a generic number line and overlaying the multiples of other prime numbers on this graph, [Carlos] had a very, very clever way of understanding exactly how twin primes come into existence.

In the end, [Carlos] is no closer to proving the twin prime conjecture than anyone else. We’ve got to hand it to him, though, for nerding out with an engineer’s favorite tool – AutoCAD – and managing to derive some fairly obscure mathematics on his own.

After the break you can see [Carlos]‘s videos describing the though process that went into his creation. Very, very cool work.

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The smallest NES controller ever

A few months ago, [Ben] saw a video of the world’s largest NES controller. “I bet I could make the smallest,” he thought in a strange game of one-upmanship. Now [Ben] has the smallest fully functional NES compatible controller, a feat of engineering that can only end in very, very sore thumbs.

The old NES controller is a very simple device: eight buttons are connected directly to a 4021 shift register. Every time the NES is looking for a change in input, it reads out the data in the shift register and gets the status of all the buttons.

After finding the  smallest footprint 4021 shift register he thought he could solder, [Ben] found some very small SMD push buttons and a very tiny resistor network for the pull ups. The result is tiny, and thanks to the sacrifices of a few NES controller extension cables he found on Amazon, 100% compatible with his old NES.

You can grab all the schematics over on [Ben]‘s git. Tip ‘o the hat to [Troy] for sending this one in.

Prosthetic foot and ankle have amazingly natural movement

The natural movement and functional power of the ankle and foot during a step , while appearing fairly simple, are amazingly difficult to replicate with a prosthetic. Usually it requires a fast and fairly powerful motor to provide the forward push and then whip that foot up as we pull our leg forward. However, recent projects have managed to do some amazing jobs at achieving this difficult task. Belgium’s Vrije Universiteit Brussel has released the video (below the break) of the “AMP-Foot 2.0″ that pulls this off very well.

The main idea behind the AMP-Foot 2.0 is to have the actuator work longer with a lower power rating while the produced energy is stored in elastic elements and released when needed for propulsion. The device is designed to provide 100% of push-off for a 75 kg subject walking at normal cadence on ground level.

[via Engadget]

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Chromium on the Nexus7

[Hexxeh] is at it again, porting the chromium OS to whatever seems to appear in front of him. This time he’s ported it to the Nexus 7. Last time we saw him, he was raspberry chomping at the pi. The details are very scarce, so we would like to issue this request.

[Hexxeh] we realize you don’t think your every-day-joe would be up to the task of putting chromium on their nexus 7. This is Hackaday however, and we know that at least a few of our readers would LOVE to join you in your efforts and could possibly contribute to your fun. Share some details with us… please.

You can see a video of it in action after the break.


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hijinks at 50,000 amps

So you happen to have a really beefy transformer sitting around in your living room. What are you going to do with it? Short stuff across it to watch it glow of course!

This video is exactly that. While we flip flopped between “what is this guy doing?” and “ooooh, look at it glow!”, we thought you would surely enjoy this video. If you’re in a hurry, jump to around 5:30 to see a crowbar lit up completely.

[Alan] from HackedGadgets pointed out an interesting thought. Often the government pinpoints marijuana grow houses by their electricity usage. Though he’s not using this on a regular enough schedule to realistically get raided, the thought of that misunderstanding is quite humorous.

[via HackedGadgets]