Ever hear of a Mersenne prime? These are prime numbers that are one less than a power of two. Named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century, there is a distributed computing project on the Internet to find Mersenne primes called GIMPS (Great Internet Mersenne Prime Search). The project recently announced they have found the largest known prime.

The number in question is 2^{74,207,281}-1 and with 22,338,618 digits it is almost five million digits longer than the previous record holder. The number is too big to be useful for modern cryptography. Prime95, the software that searches for these unique primes, is often used by overclockers as a CPU stress test (the software has a stress mode to make sure the prime tests are accurate). It was also responsible for uncovering a bug in the Intel Skylake CPU.

We recently discussed prime algorithms in Minecraft. [Mike Szczys] even used a relatively small ARM processor to do the job. You can learn more about the new Mersenne prime in the video below.

Will there be a poster of this one?

With 1mm font => 5000x5000mm. Need a big house/wall for that one.

At 1x1m it would need a 0.2mm font, a bit hard to read?

Yes… But I got a poster of the 41th prime with 7 million digits. It looks gray until you use a magnifying glass =) I think it’s 700mm x 500mm big.

The 41st prime is 179. Did you mean something larger?

41st MERSENNE prime maybe?

Sorry, the 41st Mersenne prime: http://www.mersenne.org/primes/

Not a poster, but still printed on paper: https://youtu.be/tlpYjrbujG0

Hehe. I’ll be watching for this one on “Numberphile.”

That’s numberwang!

Hah!

3?

4?

21?

Pi?

2^74,207,281 – 1?

“The number is too big to be useful for modern cryptography” For the time being I assume.

I can just imagine the interwebs in a few years time…

Your password is insecure, please make sure it conforms to the following:

At least one upper case character.

At least one non alpha-numeric character.

Must contain one Mersenne Prime of at least 22 million digits.

One of the best things about being retired is not having to juggle several passwords, all of which had to be changed every 90 days by policy.

That’s just good security policy, I really worry for the people that never change any of their passwords especially internet banking.

I’m sure it was – however it was a pain in ass nonetheless.

It usually ends up with people having a predictable password system: “passwordMar”, “passwordJun”, “passwordJul”

I wish. This system was real fussy, the new password could share no characters from the last or three previous ones, and it needed to be mixed case and alphanumeric

Good policy until people start writing down passwords because they can’t remember all their random passwords.

It’s also not useful for cryptography because it’s not very secret.

That’s not nessecarily how it works…

iirc a large number of web servers still use the default primes for key exchange.

The decimal representation has been published, but here’s an PNG image representation of the number in binary.

http://i.imgur.com/5GPdSX4.png

(Because it’s all binary 1’s…)

I don’t think they got it.

Are you trying to point out that all the Mersenne Primes are (in binary) continuous strings of 1 because they are defined as 2^n -1 so for the first lot of Mersenne Primes n is in the set [2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257] and the binary representation of each Mersenne Prime is a string of 1s with a length of one less than n.

Yeah…I should have done 74207281-byte text file consisting of all 1’s.

If you look really close, the last black pixel is slightly blue (RGB 0,0,1), because 74207281 doesn’t divide evenly into 24 bits per pixel.

There’s a half decent reward for finding these. I’m not entirely sure how you go about claiming the money though. More research may well be required.

I think it would be amusing to solve it graphically. Render a video game with lots of gpus and solve it backwards. Narrowing where to look by following the line pattern created when you lay out the sequence in two dimensions to reduce the search area.

Sending the result might be an issue.

I don’t get what you mean. Primes look like something to the human eye?

Search for Ulam’s spiral.

https://en.wikipedia.org/wiki/Ulam_spiral

It’s actually quite interesting that you can run something like the Prime95 in burn mode and actually observe a CPU making a miscalculation instead of it just instantly turning belly up.

You’d think that running the thing fast and hot enough to have such a significant probability of computing errors would throw a wrench in the gears and crash your operating system well before it crashes the prime program.

i suspect that most of the cpu time is spent in the prime program. it may rarely return control back to the OS, when it does, the OS has been configured to have nothing to do but run the prime program.

the only reason you’d need to return control to the os is to share resources. it looks like you can configure how much shared resources are used.

from the wikipedia: “The stress-test feature in Prime95 can be configured to better test various components of the computer by changing the fast fourier transform (FFT) size. Three pre-set configurations are available: Small FFTs and In-place FFTs, and Blend. Small and In-place modes primarily test the FPU and the caches of the CPU, whereas the Blend mode tests everything, including the memory.”

Vri kewl ^_^ {I was once a Maths minor.}

Where’s the hack?