What's the use for Mersenne primes?

[chalsall]

Originally Posted by preda

Almost every time when I explain to a new person what my desktops are computing, they ask "so what are these prime numbers good for?"

My standard answer:

They aren't good for anything, in and of themselves. They are too large for anything, except to admire.

But...

The amount of effort devoted to writing the optimized code to find them, building the communities who donate their efforts, building the distributed systems which coordinate all this work.

Yes Virginia. There is value in trying to find large prime numbers. It's a "driving problem".

[MooMoo2]

Originally Posted by preda

Almost every time when I explain to a new person what my desktops are computing, they ask "so what are these prime numbers good for?"

The primes themselves may not be of much value, but the search for them can uncover hardware problems. Here's the most recent example:
https://arstechnica.com/gadgets/2016...lex-workloads/

[George M]

Originally Posted by preda

Almost every time when I explain to a new person what my desktops are computing, they ask "so what are these prime numbers good for?"

Recently I got a new idea about the usefulness of large Mersenne primes.

You may remember that Voyager included a message for extraterrestrial civilizations: https://en.wikipedia.org/wiki/Voyager_Golden_Record

In any future such message for extraterrestrials, we should include a binary representation of the exponent of the largest known Mersenne prime.

This is an extremely compact scientific-technological benchmark:

in under 30bits we transmit a self-explicit (i.e. that can be understood by itself, without reference to a codebook or other external info), high-precision information about the level of our scientific and technological development.

After contact, we could maybe introduce the "prime civilization score", simply resumed to "my prime is log-bigger than yours".

Every now and then, my friends would ask me, “How is algebra ever going to help you in life? What use is it going to be to figure out how many times a wheel makes a full 360 degrees rotation when you roll it down a 50m hill and the wheel is 3m in diameter?” That was actually a genuine question and I remember it because I loved how detailed it is.

[Dr Sardonicus]

Originally Posted by George M

Every now and then, my friends would ask me, “How is algebra ever going to help you in life? What use is it going to be to figure out how many times a wheel makes a full 360 degrees rotation when you roll it down a 50m hill and the wheel is 3m in diameter?” That was actually a genuine question and I remember it because I loved how detailed it is.

To me, the importance lies not in finding the answer to a specific question (BTW, a wheel 3m in diameter is a big wheel indeed), but rather in thinking about what you actually need to know to find the answer, and how to use what you know.

It is perfectly legitimate to lambaste "word problems" or "story problems" as unrealistic. One aspect of them I find most unrealistic is, how they are presented. I have told people who have asked me about how to solve them, "Read the sentences in reverse order." The reason I say this is, in real life, the problem usually presents itself first, and then you are left to figure out what you have available to deal with it. Word problems usually have this bassackwards. They give a litany of seemingly random information, followed -- finally -- by the actual question to be answered.

In using logic and algebra to answer questions, you are using some aspects of critical thinking. Alas, this art seems to have fallen out of favor.

[ATH]

You can use them to find Primitive Trinomials (if p=1 (mod 8) or p=7 (mod 8)):

https://maths-people.anu.edu.au/~brent/trinom-old.html
https://maths-people.anu.edu.au/~brent/trinom.html
https://arxiv.org/abs/1005.1967

Trinomials can be used for random number generators and error correcting code:
https://www.maplesoft.com/applicatio...3464&view=html

[Stargate38]

They can also be used to find perfect numbers:

2*3
2²*7
2⁴*31
2⁶*127
2¹²*8191
2¹⁶*131071
2¹⁸*524287
2³⁰*2147483647
2^43112608*M43112609
2^57885160*M57885161
2^74207280*M74207281
2^77232916*M77232917

[bhelmes]

1. As the order of a prime is p-1 in N and p²-1 in the complex field
you can use them perhaps as sorting or merging indecies
if you know the factorisation of p-1 and p+1

You can calculate the f. root of 1 with f | p-1 and the g. root of 1 with g | p+1

2. if you know the factorisation of the discriminant b²-4ac of a quadratic polynomial you could easy determine an algorithm to generate primes concerning that discriminant

3. if you have the factorisation of f | p-1 and g | p+1 it might be possible to calculate pi a little bit more exact.

4. As money losts its value sooner or later, it might be senseful to have some nice primes for paying.

5. if the earth explodes, the universe goes down, the stars switch off
what will be the mathematical basics in order to describe the physical background for a new universe, if not the distribution of primes.

6. Personally i like patterns and logical structures which can be explained and programed, maybe the religions answers do not satisfy me,
and the search for better algorithms for finding primes and factorisation algorithm is both beautiful and joyful together.

Greetings from the primes
Bernhard

[bgbeuning]

Why climb Mt. Everest?
Because it is there!

[lukerichards]

There are very large chunks of maths that were completely useless when they were discovered but since found to be very important. I think fractals were one such example.

Investigating for the sake of investigation is not an otherwise fruitless task.

[xilman]

Originally Posted by Uncwilly

Is it attached to anything (anymore)? If I could book you a trip to get you more than 99.9% of the way, would you be willing to pay the fare to get back?

Nope. It's on the surface of Venus

[tServo]

After the announcement has come the predictable slew of articles trying to explain the answer to this question. After explaining the usual security/encription answer, I also mention something similar to what chalsall posted that the tools and processes used to discover it are significant.

Originally Posted by GP2

It points out that the p3.16xlarge instance is 2.37 billion times faster than the 8087 math coprocessor for the original IBM PC from 40 years ago. So if you started a calculation back then that would take 80 years to complete, it would only be halfway finished as of today, but the p3.16xlarge could complete the whole calculation in one second (at a total cost to the user of approximately one quarter of one US cent = $0.0025 in the cloud).

OT: When I read this I had a flashback to a rather interesting SF short story I read as a young lad, probably by one of the greats like Clarke or Asimov, about Earth launching a "generational" starship toward the nearest solar system that might have inhabitable planets we could colonize, It was going to take 100 or so years to get there. When they arrive, they find that every planet occupied by us Earthers who got there decades before in a starship that had a much faster drive !!!