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Old 2017-12-16, 23:28   #1
preda
 
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"Mihai Preda"
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Default What's the use for Mersenne primes?

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".

Last fiddled with by preda on 2017-12-16 at 23:41
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Old 2017-12-17, 00:13   #2
ewmayer
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I use much the same argument, but jazz it up with "it's to protect ourselves against invasion by hostile alien races". Broadcasting one's known M-prime exponents is probably the most bit-compact way to convey one's overal state of technological development. So assume there are alien races out there listening for faraway signals, and further assume that not all of them are doing so for benevolent reasons. Your best chance to dissuade a hostile imperial species from turning your world into a trophy is to convince them your technology is likely as good or better than theirs.

Of course one must factor the time-delay into this - if you get a signal from a world N light-years distant indicating a given level of advancement, you must extrapolate N years ahead to gauge where the sending civilization may be at present, and were you planning a visit (whether firendly or hostile) you'd additionally factor in the time your ships need to get there. Let's face it, interstellar travel, by any reasonable energy-required computation appears to be much, much more daunting than popular SciFi makes it out to be. But better safe than sorry, so it's best to keep crunching! :)

Last fiddled with by ewmayer on 2017-12-17 at 00:14
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Old 2017-12-17, 00:19   #3
science_man_88
 
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Quote:
Originally Posted by preda View Post
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".
depends on if the mersenne exponents have some property that other primes have or not. if so then it could be just one of these other prime types it fits into.

Last fiddled with by science_man_88 on 2017-12-17 at 00:23
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Old 2017-12-17, 01:57   #4
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Yes, the Mersenne index is a simple but meaningful proxy measure for the level of advancement of any civilization.

We did our best, but Oumuamua has already reported back that we rate a mere 49 and are ripe for conquest.
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Old 2017-12-17, 08:30   #5
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https://www.youtube.com/watch?v=PLL0mo5rHhk#t=4m54s

"For the glory! For the glory. Because mathematicians will thank you for it. Like the perfect numbers, we don't know if there's infinitely many perfect numbers.
We don't know if there are infinitely many Mersenne primes or not.
So that's another open question, something that maybe, hey, you could work out."


I think mersenne prime numbers are a bad measure for level of advancement of civilization. Otherwise we could just use the TOP500 supercomputers to become civilized.

Last fiddled with by heliosh on 2017-12-17 at 08:43
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Old 2017-12-17, 08:34   #6
pinhodecarlos
 
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Why are we worrying about the possible existing of other civilisations when we can’t feed ourselves in a sustainable way.

Thermodynamic laws are a bitch.
All this CPU, whatever the project is, is a waste of energy resources.
This is a hobby, nothing else.

Carlos
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Old 2017-12-17, 10:35   #7
ET_
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Quote:
Originally Posted by pinhodecarlos View Post
Why are we worrying about the possible existing of other civilisations when we can’t feed ourselves in a sustainable way.

Thermodynamic laws are a bitch.
All this CPU, whatever the project is, is a waste of energy resources.
This is a hobby, nothing else.

Carlos
Agreed.

What are diamonds for?
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Old 2017-12-17, 10:44   #8
pinhodecarlos
 
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Quote:
Originally Posted by ET_ View Post
Agreed.

What are diamonds for?
I’m a lucky guy whose wife it’s not keen on diamonds...lol
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Old 2017-12-17, 18:05   #9
xilman
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Quote:
Originally Posted by ET_ View Post
What are diamonds for?
Diamonds are "for" a hell of a lot of things. High temperature optics, for one. I happen to know where there is a ~1cm optical window made out of diamond which is lying out in the open ready to be picked up by anyone willing to go there.

High temperature semiconductors are another application. They should be usable up to 2000K or so.

The sooner that optical quality diamond can be made in metre-scale pieces the better in my view. Ditto for (almost) perfect crystals suitably doped with boron and nitrogen.
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Old 2017-12-17, 18:12   #10
GP2
 
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Quote:
Originally Posted by heliosh View Post
I think mersenne prime numbers are a bad measure for level of advancement of civilization. Otherwise we could just use the TOP500 supercomputers to become civilized.
Using all the computers in the world would boost the Mersenne index score, but not by that much.

Here is a post from the Amazon blog that announced the p3 instance type for AWS cloud.

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).

Similarly, the p3.16xlarge is 781 thousand times faster than the Cray-1 "supercomputer" of 1976.

In the end, there is no substitute for technological progress and faster computing. A single person with a modest budget can do more computations today than the entire world's computing resources combined from forty years ago.

Compare the space race of the 1960s. There, we actually did something similar to what you suggest: at its peak, the NASA budget was using up 4% of America's GDP. As a result, we landed on the Moon a few decades earlier than we would have otherwise, nothing more.

Last fiddled with by GP2 on 2017-12-17 at 18:13
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Old 2017-12-18, 03:33   #11
Uncwilly
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Quote:
Originally Posted by xilman View Post
Diamonds are "for" a hell of a lot of things. High temperature optics, for one. I happen to know where there is a ~1cm optical window made out of diamond which is lying out in the open ready to be picked up by anyone willing to go there.
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?
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