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Author Topic: [ANN][GAP] Gapcoin - Prime Gap Search - New Math Algo - CPU / GPU - Zero Premine  (Read 245190 times)
agran
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March 23, 2016, 10:07:42 PM
 #1281

Updated: http://gap.coinia.net/gap/stat.php
http://gap.coinia.net/gap/blockexplorer.php
Do what would be updated every few minutes.
 

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March 23, 2016, 10:22:08 PM
 #1282

Halving rewards will be approximately in 17 September 2016.

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March 28, 2016, 05:57:54 AM
 #1283

Can someone say more or less what the relationship is between the price of the coin and the number of prime gaps found?

For example when it was at 200 there might have averaged a certain number found. At 900 is there more or less 4.5 times as much computing power finding 4.5 times the numbers?

Or is the price of the coin not a good indicator of what the network as a whole is doing?

- - - - -

added
When the price goes up, more people mine the coin? So more computing power is put into using the Gapcoin Algorithm?

[I'm not a miner and have only a vague understanding of mining concepts, including "difficulty", and I'm sure a lot of others are in the same category. No doubt some benefit comes from popularizing coins like this, and the person who recently bought it up did something for the process, I'm just wondering the dynamic of "price vs relative significance of Gapcoin" or "price vs computing power used to find numbers".]

Quote
Is the reward, price, or any other gapcoin feature dependent on setting records?  I thought that was just a side effect.
< >
Agreed. "Records" or "Work done by the algorithm" is the goal. Gap has shown that it's algorithm actually does offer results. No possibility of bullshit as far as I can tell. So at this point those variables [reward, price etc] might be things that could sharpen the work done by the coin. But a person has to understand what the relationship is and I don't.

 - - - - -

The wallet itself seems quite resource intensive

50 % of cpu for quite a while, and several nodes

addnode 73.234.214.49:31469 add

addnode 212.227.143.155:31469 add

addnode 91.155.235.8:31469 add

addnode 62.28.52.105:31469 add

addnode 193.242.148.251:31469 add

addnode 46.138.23.32:31469 add

addnode 82.14.91.254:31469 add

but has not actually gotten past the first few blocks yet. Most coins are zipping along by now even on this old computer. The wallet does seem to need something.

--

Here is an article that is interesting but does not mention Gapcoin
https://www.quantamagazine.org/20141210-prime-gap-grows-after-decades-long-lull/

Also links that seem related to the discussion below

The trailer for a film about Yitang Zhang https://www.youtube.com/watch?v=gCYYDB_ItM0

http://www.zalafilms.com/films/countingabout.html

https://en.wikipedia.org/wiki/Yitang_Zhang

A quote from http://www.newyorker.com/tech/elements/pi-prime-numbers-cybersecurity

"Primes and pi suggest a benign infinity, a pleasing order—pi because of its endlessness and its relation to the circle, and primes because no matter how far you travel on the number line you will always encounter a prime, as Euclid proved in 300 B.C. Recently, Yitang Zhang solved a problem involving prime numbers called bounded gaps that had been open for more than a hundred years. Zhang proved that no matter how far you go on the number line, even to the range where the numbers would fill many books, there will, on an infinite number of occasions, be two prime numbers within seventy million places of each other. (Other mathematicians have reduced this gap to two hundred and forty six.) Before, it had not been known whether any such range applied to prime numbers, which seem to behave, especially as they get larger, as if they appear at random."


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YomKi
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March 29, 2016, 06:09:34 AM
 #1284

Can someone say more or less what the relationship is between the price of the coin and the number of prime gaps found?
Good question if you mean number of gaps over the current difficulty level.  I'm curious.

If you mean number of record gaps found, it is dependent on quite a few factors such as where in the range the searches are happening (shift values), the current records in that range, and who else is setting records.  When gapcoin first submitted records in Dec 2014, the average merit in the range 4000-25000 was 23.6.  It was 24.9 after the most recent gapcoin records were published by Dr. Nicely.  It is now 25.3.  The same effort will result in fewer records set.

Is the reward, price, or any other gapcoin feature dependent on setting records?  I thought that was just a side effect.
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April 03, 2016, 03:46:45 AM
 #1285

I never did it, but I'll try to raise the pool according to the instructions.

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April 03, 2016, 04:47:44 AM
 #1286

has gapcoin achieved any recognition or mentions in the academic world yet?
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April 03, 2016, 07:57:36 AM
 #1287

has gapcoin achieved any recognition or mentions in the academic world yet?
Since this is just generating computational data, it's not something obvious to publish.  I didn't find any papers about record prime gaps in the last couple years.  The closest thing I saw were Kourbatov's 2014 and 2015 papers but this data wouldn't be used for them.  Carella's 2013 paper is probably the closest, but just uses Nicely's aggregated data.

Nicely's site is the main repository.

Jens Kruse Andersen has record lists that get updated once or twice a year.

More recent data including the in-progress gapcoin data are available: stats and top 20.  Those are updated every few hours.

Mersenneforum has a Prime Gap Searches section.  gapcoin doesn't get much mention, partly because it doesn't seem to be a very efficient method and doesn't offer any insight into better methods.  It's one advantage is that it is a coin.
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April 03, 2016, 07:54:52 PM
 #1288

Is the rev5.1 miner faster than the previous ones for mining or it is specific for larger shifts?
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April 04, 2016, 03:07:13 AM
 #1289

Gapcoin is currently the proof of work for Yitang Zhang conjecture which led to a split in the community those who "understood" it to be correct and those who attacked it. 

Terrence Tao has his own little group and gets much attention and awards but it seems up for debate to make your own choice.

The First Gapcoin with the password hash is not very efficient for mining using small blocks and sieve set like which Terrance Tao and others set as the minimum.  But it is not efficient for computers so it will never be solved.  They only deflect the attention away from Yitang Zhangs work.   

The Rev2 updated inwallet mining is the Yitang Zhang algo with a 33.5 million prime block with a 900,000 sieve set.  Which is half of Yitang Zhangs 70 million, but 33.5 million is the most efficient mining program.  There is no need to use the other programs unless you use a large set up and know how to use the programs themselves.  The inwallet mining for Rev2 is the highest rate it can be. 

Gapcoin=Yitang Zhang

But Gapcoin is the first to implement a variable reward system based on hashrate.  It is intelligent designed. 
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April 04, 2016, 04:37:56 AM
 #1290

Can you explain more why you think any gapcoin result proves Zhang's results (Bounded gaps between primes)?  It doesn't seem to follow at all.  Finding a large or small gap at some fixed point has no bearing whatsoever on a proof that for some even value k where k < 70,000,000, there exist infinitely many primes this distance apart.

What is "the Yitang Zhang algo"?

The algorithm description on github is a partial sieve, Fermat test for each remainder, then scan for large gaps.  This is not a novel technique and has nothing to do with Zhang.  Jonny's CTR work in GapMiner is doing a lot of startup work, but looks like it eventually comes down to sieve the range, Fermat test candidates, then scan for large gaps.  Nothing to do with Zhang.   Edit: When I say "not novel" I mean it's a standard method but there's lots of room for interesting implementation details, not that it isn't any good.
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April 04, 2016, 05:04:43 AM
 #1291

Gapcoin is merely working "towards" the conjecture stated by Yitang Zhang.  The Rev2 setup is done by a member here built into the wallet, I don't think it was Jons work. 

It is simple really this is a large game of "Go".  Except there are no limits for players only the board is shortened and the Primes are allowed to build up to a very large  number along the "number line". 

70 million is the length of digits Yitang Zhang described as the bounded Gap for "Infinity" Twin Primes.  The other group is makes no logical arguments but is supported institutionally to build their own conjecture. 

Gapcoin digit "block" limit is set to 33.5 million in the Rev2 wallet I am unsure what it was in the first wallet I would have to download it and do "Getmininginfo" command. 

Gapcoin is the "Proof of work" for Yitang Zhang.  "Of course only time will tell"
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April 04, 2016, 05:41:25 AM
 #1292

Gapcoin is the "Proof of work" for Yitang Zhang.  "Of course only time will tell"
I believe this is just words strung together with no meaning.
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April 04, 2016, 06:02:47 AM
 #1293

Gapcoin is the "Proof of work" for Yitang Zhang.  "Of course only time will tell"
I believe this is just words strung together with no meaning.

As a nonmathematician trying to keep you two honest, it seems to me that all successful searches for prime gaps will be "proof of work" for any adequate theory that is not proved to the satisfaction of somebody.

More interesting might be the statement from http://www.newyorker.com/tech/elements/pi-prime-numbers-cybersecurity

"Zhang proved that no matter how far you go on the number line, even to the range where the numbers would fill many books, there will, on an infinite number of occasions, be two prime numbers within seventy million places of each other. (Other mathematicians have reduced this gap to two hundred and forty six.)"

If the number really is 246 then is the unique thing about "Gapcoin" that it searches for high merit primes? That it ignores the "246" that might not be as useful to theorists and looks for the "70million" so that others can do something or other on a slightly bigger field?


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April 04, 2016, 09:38:08 AM
 #1294

has gapcoin achieved any recognition or mentions in the academic world yet?
Since this is just generating computational data, it's not something obvious to publish.  I didn't find any papers about record prime gaps in the last couple years.  The closest thing I saw were Kourbatov's 2014 and 2015 papers but this data wouldn't be used for them.  Carella's 2013 paper is probably the closest, but just uses Nicely's aggregated data.

Nicely's site is the main repository.

Jens Kruse Andersen has record lists that get updated once or twice a year.

More recent data including the in-progress gapcoin data are available: stats and top 20.  Those are updated every few hours.

Mersenneforum has a Prime Gap Searches section.  gapcoin doesn't get much mention, partly because it doesn't seem to be a very efficient method and doesn't offer any insight into better methods.  It's one advantage is that it is a coin.

Thanks! At least the PoW does something meaningful
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April 04, 2016, 02:36:31 PM
 #1295

Thanks! At least the PoW does something meaningful
To the best of my knowledge, gapcoin's PoW's are doing effective work, and finding large prime gaps.  These are computationally difficult to find, but relatively easy to verify (very much so in the range gapcoin is looking at), and Gapcoin is producing results that some people care about.  Looking at the distribution might tell someone something, and particularly large merits might also provide more information (useful for bounds on c in the Cramér-Granville conjecture for instance).

In terms of efficiency, gapcoin is rapidly throwing darts with a blindfold on.  The CRT work at least points one in the right direction.  Other search methods are aiming the darts at high-probability areas which is why they generate more records.  There is arguably a benefit to searching in areas that wouldn't be covered by the traditional methods.  If gapcoin had more computational resources, it would generate more results of course, as would other methods.

Zhang's work, and the follow-on work from Tao et al. are theorems, so don't need any computational "proof of work", nor would any record prime gap result help prove, disprove, or provide supporting data for their work.  Record large prime gaps provide supporting data to hypotheses about prime gap upper bounds and averages.
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April 04, 2016, 10:17:38 PM
 #1296

a lot of factual information, thanks guys

http://bitcoin.1free.eu/ - site for fun, will evolve in future.
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April 04, 2016, 11:00:20 PM
 #1297

... finding large prime gaps.  These are computationally difficult to find, but relatively easy to verify ...

Does verifying them involve only

1) Make sure the two numbers are prime
2) Make sure there are no primes between them

And it seems like with large primes both those would be relatively hard


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tromp
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April 04, 2016, 11:20:58 PM
 #1298

Does verifying them involve only
1) Make sure the two numbers are prime
2) Make sure there are no primes between them

yes, except it uses a fast probabilistic primality test, which has a minuscule probability of being wrong.

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And it seems like with large primes both those would be relatively hard

These tests are very fast, and we only need a few thousand of them...
YomKi
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April 05, 2016, 03:07:37 AM
 #1299

... finding large prime gaps.  These are computationally difficult to find, but relatively easy to verify ...

Does verifying them involve only

1) Make sure the two numbers are prime
2) Make sure there are no primes between them

Yes, that should be all that is necessary.  To give you an idea, gapcoin has found 257 record gaps in the last 4 months across the whole network.  Verification of them all took 36.5 seconds on a single core.  There is still a very small chance the end points are pseudoprimes (this verification was with BPSW rather than a simple Fermat test).  After results get submitted to Dr. Nicely, proofs are eventually run on the endpoints if they're small enough, and that threshold is much higher than the sizes Gapcoin is producing.

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And it seems like with large primes both those would be relatively hard
It depends on "large" and "hard".  Gapcoin is finding primes in the 80-400 digit range, which isn't very large.  A verification for the high end is about half a second.  It gets more interesting at 4000 digits, taking maybe 10 minutes.  At 40,000 digits it's certainly possible but quite time consuming.  Martin Raab's monster 4.7 million digit prime can have the endpoints verified with good probable prime tests in 1-2 days but the interior looks like it would take months.
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April 05, 2016, 02:32:33 PM
 #1300

Finding first occurrence or record (first known occurrence) prime gaps tells us something about the structure of the primes.  How much is debatable.  The recreational/computational task of finding them may lead to new ideas.  It demonstrably leads to more efficient software, parts of which can be re-used for other tasks.

Finding new first occurrence gaps would be, in my opinion, more useful in terms of final results, as the results are concrete: "no prime under this point starts a longer gap" vs. "we did lots of work and this is the best we found".  The process involves doing an exhaustive search, and one problem would be verification that people actually *did* the work.  The final results are flawed if anyone cheats or if a block gets skipped.  How to do a quick verification isn't immediately obvious.  Lastly, the network could compute for years and find no actual result, but just move the "no results below x" forward.  Useful, but not exciting.

Finding "the next gap" is a much easier problem, and takes as long to verify as it does to find (very slightly less, but within a few percent).  Given the task of finding record prime gaps, improving the performance of finding the next gap (or primes in a range) is important.

Large prime gaps, like twin primes, are pointing out "hey, something interesting is happening here."  That is why it is more interesting than just listing billions of primes, or finding the next prime.  From a project point of view it has the nice features of "hard to find, easy to verify", relatively linear effort/reward (unlike factoring), and a bonus reward (we broke ## first known occurrence records) to keep up interest.

There are lots of computational problems like this, many with distributed projects.  I think record prime gaps is interesting and well structured for what gapcoin wants.  I think it's easier to see the possible mathematical benefits than, say, record Mersenne primes, large arithmetic progressions, or Riesel prime searches.
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