Constellation Explorer

[Pttn]

Explore prime constellations found since the second Fork in the Constellation Explorer! https://riecoin.dev/Constellations/

Filter the Constellation Length, sort by the most recent or the largest prime numbers. or show tuplets found by a specific address or person.

If you want to have an address associated to a nickname, please post here and prove that you own the address. Ensure that you are fine with the fact that this also allows people to associate funds sent to this address with you, though you can easily circumvent this for example by sending coins to an exchange and then again to another address.
Pools will also have their address associated.

Original Post:

Now that we have forked, I already started to check the tuples found so far from Block 1482768 to 1484925...

And amazingly we already beat a record :D ! Someone found a 9-tuplet for Block 1482856 while mining on XpoolX!
I also found myself an octuplet for Block 1483153.

I will compile a list of 8-tuples and longer here maybe once a week but feel free to post as well if you spot a 9+-tuple or any new record! Or even if you have yourself found an octuplet or longer!
DeKon is also working to do it automatically as well.
I posted in General rather than Competition as it also covers Mining and we are directly talking about the Riecoin Blockchain/PoW as well.

23 out of 2158 Blocks, or about 1/93.8 = 1.07%, are octuplets. A random even number around 2^D (or at Difficulty D) has 2/log(2^D) chance to be prime (about 1/277 chance, or twice a day, for D = 800), but I think that there are other factors that may increase the probability of n - 6 or n + 26 being prime even if not sieving for 8-tuples and longer. In that case it would be interesting to find out the actual probability. If doing the sieving, then the probability becomes about 1/15 currently, but this also makes mining about 1.5x slower, and ~4x slower if sieving for 9-tuples. The slowdowns would be much lower at higher Difficulties, hopefully many more miners join!

List with Block Numbers of 8-tuplets (base primes n) and longer from Block 1482768 (2021-03-29 19:51:53) to 1484925 (2021-04-02, 13:35:20). Hopefully I did not make a mistake...
Except for the 0, 2, 4, 2, 4, 6, 2, 6 pattern, n was adjusted to normalize to a pattern starting by 0 (-10 for the 9-tuple and -6 for the other 8-tuples).
I have checked formally their primality using the Mpz_Aprcl Code by WraithX.

0, 4, 6, 2, 6, 4, 2, 4, 2
(n, n + 4, n + 10, n + 12, n + 18, n + 22, n + 24, n + 28, n + 30), length 9
New Record!
1482856 188222230225967634309661655085587060551450342803344921889572281354397620540401431148122712635555320426554410028659607324059948749732354734097421741120829413140323023390829642143056404553577798874521933278909478579016646850020034621809

0, 6, 2, 6, 4, 2, 4, 2
(n, n + 6, n + 8, n + 14, n + 18, n + 20, n + 24, n + 26), length 8
1482915 50157467883433740817066806895659641164128727188592514227215940434499223528345852579337582156263962150035596834401321132204229193473301474903318069006989722370680109935358235996305364153716000901337158942063472290392996977854901073
1484081 24455281969554334122719783125647379243427038437019920551816342734249491323274442793860937551107864671293048477628156889008479790850640247794163660048302992455263385470084428619562194443119781842934116293454565583529600648340387087715913
1484402 1048298388241529019867260630586588867320003368138898861090269796384757236635279188330766377504371795295275113281153064515622514654252992227610627600119899407421553234085862320082552980722170871044870713835203936816017844546865695136271113
1484492 169297477020002319462607040064102900248644546156219898550560263013971933862862432135921953852235131748043841471375884482474833509000798531695873215371469789912352243715447421723541472967278876247285914494871968474157369418372597357090273

0, 2, 4, 2, 4, 6, 2, 6
(n, n + 2, n + 6, n + 8, n + 12, n + 18, n + 20, n + 26), length 8
1482982 1108554004601827223060107705352018702158727347524638562099605726377912023873763304251383170686858754802223561830108846760982082010027649749667912003421808794958534792684675629438196306461633748963849168885663467556676863479389531
1483053 2730721343633390742904459781004866786977890261688966746056081487099836735016702819478857688262111727980234584116098833399876465475294611570037157060859165217115977474965724337607484483956587967294346255612849399876923451537021
1483153 812008654794734104555511878180839079717908272872285729042119960048549495587121806153961293983438019260802451204035036639364445123222042529923059310540048785707939731261691724746175518740678681882997528925907182093559711672625531
1483369 1146122641739201662480427768936944760519576205337830312602032659448128071454747925296155061602787040584002912445539304547180573418230690164996154181884590054019413543730185926477357177873274694942997195905866882920370542596925155751801
1483430 7810059435041037808289241789841365996480289024327931707460457963402426023028587196464370825843003027298723022100696615722514059579910900919901908884897260218849818485619058837442435353339209246073609294871155408979594388306575006490371
1483504 32168692041529552886706918831513682489177971622022385705293103547676116396958861532128887784120082506309545202589204395861790555415632241166999137146318093891358215020061674366493905883721417589938820331626471119670951895347447106071
1483642 141909754527188177072671953875449776319119237334617006584431093952101417672961853477261784094061057176340534458140784141532282734810089702019748978541743198471901658273235350802849792627665934343124228000223403638891988458435616720031
1483687 397774254387739356422823005743572346127184089139347064367136382811584929178503952004936549131964422248077607650719976156665685761046692731158379817428092070156182999930963929099365418388589096921308392765200658923606881736976684215981
1483897 17169367612253636737968813129733126488943408928254880637005884700255020244871424387361480108628706999018004040956640433359882843210828647468172832218381557277700673014667158913236081068797180181690314086500270131729079909608780852944127861
1484065 31404967477831574284974707302766891485348307259770534589467332364425995818696541508965981612510225862487334480334161919588466733823702990623264774921857417570325133990989524653752619380923313852581772549451683205945216128442669683234851
1484103 19160462044176877236860039954112890378186000260331071904863766240594604013922341577326170753486865050674130744707186862002757346841996999494695894622961836052957471374369344055627585551331228069193412765548680159113350275462708118635631
1484161 313834504732149622184295257696874461617617285203573274814991806751021370442807463500690950809735002043716872375932047577763336292555706592797297855198905451636094020020387389391888211256869449907961165151149342293786693333080544090873741
1484334 32008242423091523384621395430123868351029657371954311341906407019042054859457379913625548126939208854507253354006867211515008425110393053470929710166793858312633307387060741260101222280987257204858127961645543967863257228993933153581375125971
1484476 982248703955649912041381871962691298590712466655917189954707522759645148420483485624179002405919907301106088802485311666971028191461412473894753481528837202033688310084652051987880681486972986478031984127345234888396631557190786376515691
1484625 1197076034734246275087766998691696829690890859740767304620954851919494941648923808984486177462963958475627597642259517774044156982276036223432471130153459179110696438131617333183484244924043374541631945836545617613314408196682223971186024191
1484775 1494564165382944098113811519696173540337627736268131332309107410549618603380164721109839713653348442651603115990270235592451342070016543063288928563890112388857093822734160168121513031159455094557744039543358949857923516126855738239738600502771
1484873 43235146051642993430892410553333595804672092157668695474037833230955051668178513316462245283768980959966652991046636160859224916524851139813690658079996391439369660531419325029881053370247143028021146194843873329685459916335919091096184497277491
1484916 4138105676015891448989316046725787138634432300226086541112080311524277822840565300242811804291256957337882801403627988576402023964164912645836157815001275237771702701344929781465065179028538613617091496596663517214927127534829464689932943249361901

[Pttn]

Rather than doing a list manually once a while, I finally ended up writing a Constellation Explorer, https://riecoin.dev/tools/Constellations/
We can now see at a glance if a new 9-tuplet was found! And hell yes, two were found this Saturday, and both broke the record :D ! I am going to submit them to Tony Forbes...

The explorer is for now basic but useful to find easily recent and largest 8+-tuplets, as well as ones found by a given address. All of them are automatically checked with Mpz_Aprcl.
About 1/71 or 1.4% of the blocks found so far were 8-tuples, so that would mean that we will currently find in average 8 of them every day, and about 3 9-tuple every month. But only a 10-tuple every 2 years and a 11-tuple every 125 years...

i edited the first post and this topic is now the Constellation Explorer's one.

[Pttn]

Indeed, that is a known problem since long, and it is rather unfortunate that Bitcoin Developers still did not bother fixing this despite solutions already existing...
When I will have some time again, I plan to write some authentication software using Riecoin Addresses that can replace passwords, act as a 2nd factor authenticator, or in the present case allow automatic registrations to the Constellation Explorer.

I associated your address to your name. Welcome to the competition and good luck finding interesting tuples :D !

=====

Association removed since he said nasty things on the Riecoin Discord and was banned.

[Pttn]

The Constellation Explorer was improved and moved to https://riecoin.dev/Constellations/

There are more available search criteria, and registered people now have a profile. Blocks also have their own page.
Rankings with points were also implemented so we have a true competition taking place!

For now, new users still have to be added manually so you still have to post here, but there will soon be a way to create directly new accounts there. It will be possible when the next version of Riecoin Core is out, later this month or on September.

A few more additions will come over time.

[Pttn]

As said in another post, the Constellation Explorer code was improved, and it is now possible to register an address directly in the Explorer using Riecoin Core 22.03. If you register the same address in the Explorer and in the Riecoin Forum, your miner score will be shown in your posts and profile. A manual intervention is still necessary if wanting to register more than one address, just ask me.

An API was also added in order to fetch basic information about the Constellations or the miners. More importantly, it allows mining pools to register who found their blocks. For this, a private token is needed, please send me a message to get one.

[ghost14]

I just joined the competition :)
But I'll always stay last haha

My computer's too slow for solo mining but I'm glad Stelo.xyz can register my blocks!

[Pttn]

Cool! And you found your first block for Stelo.xyz in Round 89! You can register it by going in the round's page while logged in.

[ghost14]

I even found two blocks!! Didn't expect to find even a single block so quickly!

[Pttn]

I played a bit with some new score systems. Points are now decaying with time in order to favor current miners and those that keep mining.

- 7-tuples yield 1 point, decreasing linearly to 1/64 over 12960 blocks (~22.5 days);
- 8-tuples yield 4 points, decreasing linearly to 1/16 over 207360 blocks (~360 days) - 4x more points and 16x longer;
- 9-tuples yield 128 points, decreasing linearly to 2 over 414720 blocks (~720 days) - 32x more points and 2x longer;
- 10-tuples yield 256 points, decreasing linearly to 4 over 414720 blocks (~720 days) - 2x more points.

This also makes a monthly ranking meaningless so it was removed.
The idea behind some choices: the tuple ratio is near 64, 4x16 and 32x2 are 64. Of course these are still arbitrary choices and the ranking may be improved at any time. Like before 10-tuples yield only 2x more to not make such finder basically unbeatable during a long time.

[pzktupel]

I saw on CONSTELLATION EXPLORER this: 11-tuplets : 0 (estimated once every 85.02 years)
...but this is not possible ! Near 100%, the offset for finding 7-10 tuplets have for the 11th condition small factors <p#

BTW, I'm the holder of the prime k-tuplet main page

regards

[Pttn]

Yes, this is intended: the default offsets have some properties that makes mining a bit faster (more 7, 8, 9, 10-tuples), but in exchange it is impossible to find 11-tuples and longer. Since it would probably take many decades to find a 11-tuples, it is a good compromise.

It is up to the user to change the offsets to make finding 11-tuples possible.
I removed the 11-tuple estimated time to clear the confusion.

[pzktupel]

Okay. But I ask me , why the prime sieve not sieving 10 conditions first (instead of 7)....so 8,9,10 tuplets comes earlier and the ratio is much better then to look for 8,9,10 tuplets after a 7-tuplet was found ?! I believe, the sieving-time-effort is the same. [Or is the coin-reward to expensive :-) ?]

[Pttn]

For most miners, the goal is to find as many 7-tuplets as possible to earn more coins, and sieving for longer constellations significantly reduces the number of 7-tuplets currently. I think I explained somewhere else that if a lot of new miners joined and raised the difficulty a lot, the reduction would become negligible and we could consider sieving for 8, 9, 10... primes by default like you suggest instead. But now, it would actually hurt to sieve all the conditions by default (significantly less 7-tuples -> difficulty significantly reduced -> smaller and less interesting 9-10-tuples) and it should only be done on a volunteering basis.

[pzktupel]

Prime 8-tuplets by Riecoin...

Duplicate is done :
https://pzktupel.de/ktuplets.php#largest8

Congratulation for the 6000th prime octuplet ! [2022-12-24]
Congratulation for the 100th prime nonuplet ! [2022-12-26]