20170109, 16:15  #1 
"Nuri, the dragon :P"
Jul 2016
Good old Germany
35F_{16} Posts 
Goldbachs Conjecture
I love this conjecture. A lot of time I have wasted...
I´d like to restart research on it. And I could need some help. ;) What is Goldbachs conjecture? Goldbach’s Conjecture says that every even number larger than four is the sum of two odd prime numbers, for example 6 = 3+3, 8 = 3+5, 60 = 43+17, and so on. Christian Goldbach first proposed this in 1742, in a letter to Swiss mathematician Leonhard Euler and it sounds easy enough to understand. Unfortunately, it’s not easy to prove and Goldbach’s Conjecture remains firmly on the ‘to do’ list of mathematical challenges to crack. All important research was done by Tomás Oliveira e Silva, he hitted the value 4x10^18. Why not going a bit deeper? I´ve got some links: http://sweet.ua.pt/tos/goldbach.html https://www.egi.eu/usecases/researc...hsconjecture/ And a dissertation as Attachment. But we need to write an own programm. I´d asked him about porting it into BOINC. "Nope. My program was partially written in assembly and as a limit of (30*2^26)^2, which is slightly larger than 4*10^18. So I already did all that could be done with the program. Note that I do not distribute source code and I do not use primality tests. I use a very efficient segmented Eratosthenes sieve, which is something that can be used, perhaps, up to 10^22 (useless near 10^50, for example)." 
20170109, 16:20  #2 
"Mark"
Apr 2003
Between here and the
3·17·131 Posts 
Such a program could only disprove the conjecture, by finding an even number that cannot be written as the sum of two primes. If a program cannot find an exception, it doesn't prove anything.
IMO running such a program to be a waste of time unless one has some ideas on how to find an exception. Last fiddled with by rogue on 20170109 at 16:24 
20170109, 16:37  #3  
"Nuri, the dragon :P"
Jul 2016
Good old Germany
35F_{16} Posts 
Quote:
I´d like to use the amount of all particels in the universe. (close to 10^80) Source:https://www.quora.com/Howmanyparti...ntheuniverse It might be time wasting, but disaproving it will be a massive shock. 

20170109, 16:54  #4 
Aug 2006
3×1,993 Posts 
Personally, I find a lot of value in knowing the maximal prime gaps, which fell out of TOS's Goldbach work. So at the least I don't think it's a waste of time. (On the other hand doing the search inefficiently would be a waste.)

20170109, 16:55  #5 
"Nuri, the dragon :P"
Jul 2016
Good old Germany
1101011111_{2} Posts 
Fast implementation of the segmented sieve of Eratosthenes
Might be interessting: http://sweet.ua.pt/tos/software/prime_sieve.html

20170109, 17:31  #6 
"Forget I exist"
Jul 2009
Dumbassville
2·5·839 Posts 
using the equidistant from any number version we have
I've been told to post this through PM. 
20170109, 17:43  #7  
"Curtis"
Feb 2005
Riverside, CA
2·2,689 Posts 
Quote:
For a betterknown example, compare prp tests to primality proofs for very large numbers. PRP tests for large numbers are much much better than 1 in 10^85 chance of composite, yet those are not considered proof. 

20170109, 17:54  #8  
"Nuri, the dragon :P"
Jul 2016
Good old Germany
863 Posts 
Quote:
There a lot of unsolve able problems. Even TOS was using resources from the NICS. The amount of CPUtime for douplechecking 4x10^17 up to 5x10^17 will be quite a few years, one a single core. And you´ll need a lot of disk space, too. Overall, it´s not making sense to start in it as a private person. If his project will be reactivted he´ll let me know this. He states this in his reply. Last words for now: Thanks all for replying. 

20170109, 19:14  #9 
Aug 2006
13533_{8} Posts 

20170109, 20:39  #10  
"Nuri, the dragon :P"
Jul 2016
Good old Germany
863 Posts 
Quote:
I´m not sure if this amount (lets say 12GB) is enough of run the full range. But, first off all: I´m running out of time, too. Only 1 week, then I´m going on assembly. RWE is calling me for 4 weeks. A quit dangerous job, the heaters have still about 4050°C. 10 hrs/day. (No weekend work YAY) I don´t think I´ll do anythink after work. (only shower and bed) 

20170109, 21:07  #11 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
909_{10} Posts 
Like Charles, I think there are some good things to come out of the process. Mostly improving software, much as how finding large Mersenne primes is a waste of time in many ways, but yields benefits of faster software and better underlying operations. This benefits other code that I care about.
With Oliveira e Silva's work, we got a cache friendly sieve implementation. primesieve uses a version of it at large sizes. It's not very memory friendly however. We also got some maximal prime gaps and know that all under 4e18 were maximal rather than "largest known". Somewhat similar, people have spent lots of computer time computing massive numbers of zeros of the Riemann Zeta function. At this point I doubt they're holding their breath waiting for a falsifying result. Büthe (2014) gives a nice result given those results, which is useful for practical computations. Forget 10^80, just getting to 2^64 would be a *massive* undertaking. And prove nothing other than be a nifty little result that it holds for all 64bit numbers, which might be important to some implementation of something or other. But you still need an actual proof, as Curtis notes. I like his example of primality  BPSW has been tested (through nontrivial means) for all 64bit numbers, and various projects have attempted to target counterexamples to weakened tests to no avail. No matter how many trillions upon trillions of numbers we test, it's still not a proof for >64bit numbers. I used primesieve on a 20core machine (dual xeon workstation) to do an exhaustive check of prime gaps. It was 2 weeks to go from 4.000e18 to 4.001e18. Memory use would be pretty obnoxious for BOINC users. I saved largish gaps, but didn't do any Goldbach conjecture work, and didn't store counts at intervals. If a project did start, I think it'd be important to note what, for each interval, should be checked and what statistics to store. Disk space shouldn't really be an issue  you're just storing something like the start point and count for a known interval length (e.g. the 2^30 intervals in the paper you give). Note running 20way is going to result in under 20x speedup. I didn't try comparing different parallelization strategies. On a i76700K it looks like 4core gives a 2.5x speedup with parallel primesieve. 
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