20170727, 19:52  #1 
"Carlos Pinho"
Oct 2011
Milton Keynes, UK
2^{2}·11·113 Posts 
Prime Gap Searches Crowdfunding
Hi team,
Was wondering if we could create a Crowdfunding to buy some big machines or individual 4/8 core machines, don't know each option is the best, so members could run them as I think this is a long and interesting project. There's no way this can be "Boincfied" so why not try to fund members with computers being the electricity bill supported by the members? What else can we do to grab people's attention to this project? Any thoughts? Carlos. Last fiddled with by pinhodecarlos on 20170727 at 19:56 
20170727, 20:32  #2 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
3^{2}·101 Posts 
We're moving along with, wild guess, 1 month per 1e18 range? That means there are only ~12 more ranges to go before we need a substantial change in the software. On the other hand, we'll have covered all 64bit n values, which is a big plus.
Perhaps offtopic, but a common question at Q/A sites seems to be "what is the biggest prime such that we know all the primes less than it." The question meanders off onto questions about "knowing", storage, primality test speed, etc. But realistically I believe TOeS's Goldbach project did calculate all the primes up to 4e18, and the prime gaps were a secondary result. He also stored prime counts at various intervals, which is relevant to that question. In contrast, this project does not do this  it purposefully skips swaths of unknown numbers which probably include some primes (but we've determined that we wouldn't get a large enough gap regardless so we leave them unknown). 
20170727, 21:48  #3  
Jun 2015
Vallejo, CA/.
3·337 Posts 
Quote:
This in turn was used to improve estimates of te Brun's constant B ≈1.902160583104 So, in answer to the common question "what is the biggest prime such that we know all the primes less than it." I would assume that is is very close to 4e 18 . (perhaps as low as 4 e 18 +1e9) 

20170727, 22:53  #4  
"Dana Jacobsen"
Feb 2011
Bangkok, TH
38D_{16} Posts 
Quote:
But any number one comes up with can be trivially extended by a billion in less time than it takes to update the post, making it very fluid. Anyway, it was a thought about one result from the earlier gap computations. The gapcoin project makes a number of claims, such as "[...] lead to new breakthroughs in the bounded gap, it may also help proving the Twin Prime Conjecture and maybe even the millennium problem, the Riemann hypothesis." which is stretching things pretty severely. Finding new jumping champions helps bound the absolute gap size for some practical computations. It's possible the results will lead to some insight or data about gap size conjectures. It drives development of open source number theory software, which can be used for other tasks. 

20170727, 23:17  #5  
Jun 2015
Vallejo, CA/.
3×337 Posts 
Quote:
I would agree that extending the range a la TOeS would have some practical effects, not those exaggerated claims by the gapcoin project to wit "Researches about prime gaps could not only lead to new breakthroughs in the bounded gap, it may also help proving the Twin Prime Conjecture and maybe even the millennium problem, the Riemann hypothesis" But it would at the very least give useful insight on the distribution of Twin Primes, Cousin Primes Sexy Primes, Primes with Gaps of 30, 210, 2310 and other primorials, etc. 

20170728, 07:29  #6 
(loop (#_fork))
Feb 2006
Cambridge, England
1100100101001_{2} Posts 
It would give numbers. I am far from convinced that it would give insight; having enumerations up to 2^64 instead of 2^62 burns an awful lot of natural gas in return for a tiny extension to a graph that analytic number theorists are absolutely confident of the shape of.
I would not approve 'push the limit up a bit' even were I a grantgiving body spending somebody else's money. Last fiddled with by fivemack on 20170728 at 07:30 
20170728, 07:52  #7  
"Dana Jacobsen"
Feb 2011
Bangkok, TH
909_{10} Posts 
Quote:
One thing that would be useful is to calculate remaining coremonths or something. The point I was kind of trying to make earlier is that the whole thing may be over in a year. The amount of processing remaining is fairly low in some sense. The argument for continuing past 64bit is more tenuous to me. It also has some significant programming challenges (e.g. we don't have a nice list of base2 pseudoprimes already tabulated for us, just to name one). Those might be readily solved, perhaps not. Quote:
The Gapcoin project forum has regular discussion of how they want to get "math departments" interested in running Gapcoin mining software. It's a rather bizarre place, with a third of the people interested solely in ways to pump the price, a third who cannot form coherent thoughts but apparently the government is spying on them, and a third really wanting it to Help Science in some way while also mining coins. 

20170728, 08:38  #8 
Jun 2003
Oxford, UK
19·103 Posts 
My two pence worth.
Back to the original question  I would not be a contributor of a crowdfund  firstly I'm a pensioner with limited funds and secondly, one of the reasons I wanted to take up prime hunting was that it was basically a "free" hobby. That's not to say that "buying in" computer time is a bad thing, its just not for me. I thought about the ToS project when thinking about this coordinated project, and there was a real temptation to consider an extension of the same. Decided against it in the end because I was primarily interested in first occurrence large gaps. In terms of the return per effort  this project is basically rather thin gruel compared to others. So beyond 2^64 will be a tough decision. I feel for Steve Cole who has completed 850e15 with just one record, and that being one which may get taken out by a smaller candidate pair of primes. We have been pretty lucky in the 5e18 range, I am sure we will find 6e18 harder. I'm hopeful that there is a large gap in there somewhere which will emulate the 1132 find. And that is what drives me on. 
20170728, 10:16  #9  
"Antonio Key"
Sep 2011
UK
3^{2}·59 Posts 
Quote:
I started gap searching as a way of learning to program in Perl, and I have enjoyed the search for large prime gaps aspect. As a nonprogrammer and nonmathematician it has all been very instructive. As I only have the one computer (I don't count my laptop  they are not intended for heavy continuous use) I am already debating if I should go back to my original large gap search. 

20170728, 10:20  #10  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
5,923 Posts 
Quote:


20170728, 16:47  #11  
"Robert Gerbicz"
Oct 2005
Hungary
2727_{8} Posts 
Quote:
I'd say here the biggest goals: find maximal gaps, already achieved, but not proved, if it would not be a maximal gap, then we find another (smaller) maximal gap. Not a small success, in the previous 8 years there was no such find. Even larger goal: find a new record for g_n/log(p_n)^2, where g_n=p(n+1)p(n). Quote:
The 64 bits limitation is a real bottleneck, though still not there. You can't tell a lot of number theory problem that has been solved up to 2^64 and the difficulty is ~N. Last fiddled with by R. Gerbicz on 20170728 at 17:00 Reason: small math correction 

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