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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