20171216, 23:28  #1 
"Mihai Preda"
Apr 2015
5^{3}·11 Posts 
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 scientifictechnological benchmark: in under 30bits we transmit a selfexplicit (i.e. that can be understood by itself, without reference to a codebook or other external info), highprecision 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 logbigger than yours". Last fiddled with by preda on 20171216 at 23:41 
20171217, 00:13  #2 
∂^{2}ω=0
Sep 2002
República de California
2D9A_{16} Posts 
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 Mprime exponents is probably the most bitcompact 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 timedelay into this  if you get a signal from a world N lightyears 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 energyrequired 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 20171217 at 00:14 
20171217, 00:19  #3  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}·131 Posts 
Quote:
Last fiddled with by science_man_88 on 20171217 at 00:23 

20171217, 01:57  #4 
Sep 2003
5·11·47 Posts 
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. 
20171217, 08:30  #5 
Oct 2017
++41
5^{3} Posts 
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 20171217 at 08:43 
20171217, 08:34  #6 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
3·1,663 Posts 
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 
20171217, 10:35  #7  
Banned
"Luigi"
Aug 2002
Team Italia
1001011100010_{2} Posts 
Quote:
What are diamonds for? 

20171217, 10:44  #8 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
3·1,663 Posts 

20171217, 18:05  #9 
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2^{4}×13×53 Posts 
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 metrescale pieces the better in my view. Ditto for (almost) perfect crystals suitably doped with boron and nitrogen. 
20171217, 18:12  #10  
Sep 2003
5×11×47 Posts 
Quote:
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 Cray1 "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 20171217 at 18:13 

20171218, 03:33  #11 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
277E_{16} Posts 
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?

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Mersenne Primes p which are in a set of twin primes is finite?  carpetpool  Miscellaneous Math  3  20170810 13:47 
Distribution of Mersenne primes before and after couples of primes found  emily  Math  34  20170716 18:44 
GaussianMersenne & EisensteinMersenne primes  siegert81  Math  2  20110919 17:36 
A conjecture about Mersenne primes and nonprimes  Unregistered  Information & Answers  0  20110131 15:41 
Mersenne Wiki: Improving the mersenne primes web site by FOSS methods  optim  PrimeNet  13  20040709 13:51 