Golden Brown

Intelligence

Neheim Havermann origins

Möhnesee area: click to enlarge

When I first started exploring my father's genealogy on the internet, the starting-point location was necessarily Neheim where I was born (the red rectangle in the map; I knew this locality as Bergheim). The larger part of Neheim (the blue rectangle to its right) was of course where many of my ancestors lived and died. There are rectangles around nearby Vosswinkel and Hüsten because they occasionally appear in the records.

Around the time FamilySearch showed me that I had ancestors going back to before 1800, I realized that the focus of the earlier Havermann names was Körbecke (at the top of the map, more to the right). In fact, that had me title an early ancestor chart Havermann: Körbecke ... Neheim ... Toronto. It was Körbecke because of course there was a church there. My very recent exploration of Matricula Online allowed me to look at those church records and the Havermann folk lived mostly in Völlingsen, which stumped me at first until I realized it was a shortening of Völlinghausen (to the right of the Möhnesee, a reservoir built 1908-1912).

Today I looked up the Havermann name in Allagen, another place where FamilySearch had long ago suggested they had church records. These Havermann families lived mostly in Niederbergheim, in between Völlinghausen and Allagen (all on the right of the map). So my revised conjectural travel story for Havermann is: Niederbergheim/Völlinghausen ... Neheim ... Toronto. I have found in Niederbergheim some Havermann-variant names, specifically Haverman and Habermann, which suggests to me that Niederbergheim may have been the local origin point of this Havermann clan, say in the 1600s.

The six-millionth term of A157711

The sum of the first 4388 prime counts of A383675 is 5997438. The sum of the first 4389 prime counts is 6000600. Hence, the six-millionth term of A157711 is a 4389-digit integer:

5997439 10^4388+10^31+10^26+1
5997440 10^4388+10^84+10^57+1
5997441 10^4388+10^86+10^4+1
5997442 10^4388+10^109+10^14+1
5997443 10^4388+10^116+10^4+1
...
5999995 10^4388+10^3965+10^1276+1
5999996 10^4388+10^3965+10^1598+1
5999997 10^4388+10^3965+10^3206+1
5999998 10^4388+10^3966+10^1952+1
5999999 10^4388+10^3967+10^1856+1
6000000 10^4388+10^3968+10^1845+1
6000001 10^4388+10^3968+10^3913+1
6000002 10^4388+10^3970+10^1513+1
6000003 10^4388+10^3970+10^3499+1
6000004 10^4388+10^3971+10^744+1
6000005 10^4388+10^3971+10^1820+1
...
6000596 10^4388+10^4385+10^2720+1
6000597 10^4388+10^4386+10^1368+1
6000598 10^4388+10^4386+10^3412+1
6000599 10^4388+10^4386+10^3792+1
6000600 10^4388+10^4387+10^1484+1

A157711(1*10^6) = 10^1793+10^673+10^615+1 [2025 June 19]
A157711(2*10^6) = 10^2535+10^1160+10^398+1 [2025 July 21]
A157711(3*10^6) = 10^3103+10^2747+10^859+1 [2025 September 10]
A157711(4*10^6) = 10^3583+10^3040+10^2776+1 [2025 December 7]
A157711(5*10^6) = 10^4006+10^2673+10^876+1 [2026 February 14]
A157711(6*10^6) = 10^4388+10^3968+10^1845+1 (above)
A157711(7*10^6) ~ 10^4740

I'll continue to update (here, until the next millionth is reached) my current plot of A383675:

A383675 to n=4447; max=(4425,3647) [updated June 21]  click to enlarge

Ed Pegg's history of the Earth

A little rough around the edges but I love the music/lyrics:

The video is available (in four parts) as online documents starting here.

Entrance to the town of Weston, Ontario

ca. 1942, looking northwest onto Main St. S. at St. John's Rd. click to enlarge

The town of Weston saw its start in 1914. The above photo marks its southern end. How do we know that the crossroad is at St. John's Rd.? Because the Peter Manson auto service station (up a bit, on the left) is just south of Lippincott St. W. (There is today still a car service station at this spot!) I had come across folk who claimed that Weston extended its boundary to Edmund Avenue (one block further south) but when I researched the matter I could only find one attempt by the residents of Edmund Avenue to have this happen and that request was subsequently denied by the Township of York. I forgot when this happened and couldn't locate on my computer the newspaper article that reported it. In a new search today, I found a similar story dating to October 1920.

Of course, the residents of Edmund Avenue could have asked again but I deemed it unlikely as I had a 1924 and a 1935 map that still had the St. John's Rd. boundary. In my new search I did find a resolution to all this. On page 34 of the 11 November 1930 Toronto Daily Star was an article on Walter Pollett running for Weston's 1931 mayoralty:

"Mr. Pollett was elected to the [Weston] council a year after he became eligible, since previously his home on Edmund Ave. had been in Mount Dennis. Seven years ago this month a portion of Mount Dennis bounding the southern part of the town of Weston was annexed and Mr. Pollett was one of the most active supporters of this step."

So the boundary expansion happened in November 1923. The 1924 map might have missed the news, being too soon after. A close look at the 1935 map could find no year that was part of the map itself. Perhaps the 1935 was a library misidentification:

south Weston (date unknown, note the misspelling of Elsmere) click to enlarge

Looking further, I found a 1923 map of York Township that I had not previously come across. This map clearly excluded Edmund Avenue from the township, hence placing it in Weston:

York Township (1923) click to enlarge

So, as a small slice of Mount Dennis was added to Weston, would there have been any effort to move the entrance-to-Weston sign south? No. The section that was annexed is entirely on the west side of Weston Rd. One block later we reach the old-border line and Weston is now on both sides. Reference the more recent Welcome-to-Weston sign that is only a few meters south of the same St. John's Rd. — but now renamed — Clouston Ave.:

Welcome to Weston (2019) click to enlarge

The tortured history of St. John's Rd. and Clouston Ave.

When did St. John's Rd. become Clouston Ave.? The answer is slightly more complicated than I expected. Might's (greater Toronto) city directory for 1928 suggests that Clouston Ave. is entirely in Mount Dennis: west from Jane St. to Weston Rd. and west of Centre Rd. to the Humber River. That, one might think, leaves St. John's Rd. as the connecting, in-between part. However, St. John's Rd. is the old border of the town of Weston, where the properties north of the road were part of Weston and properties south, part of Mount Dennis. It seems that in 1928, there's a St. John's Rd. East that is the same roadway as Clouston Ave. (as far as the railroad tracks) but only for the north side of it. There's a St. John's Rd. West running west from Main St. S. to the Humber River that, because of the annexation of that part of Mount Dennis, is on both sides of the roadway until we get to Centre Rd. At that point, St. John's Rd. West uses the same roadway as Clouston Ave., but only for the north side of it.

I don't see a Might's reference to Clouston Ave. prior to 1928, which makes the south Weston map (shown above) problematic because it sports a pre-1924 Weston town border. Have another look at that map. Do you see the dashed/dotted line running parallel to Edmund Ave. but a little south of it? When I look closely, I imagine those dashes continuing up the left side of Centre Rd. That is the new border! I have had another go at sourcing the map (Algate's Toronto & Suburbs) and have found a reference indicating a publication year of 1924. That totally supports the map showing both Weston's old and new southern border since it takes time to properly map such transitions. But the map clearly shows the two-section Clouston Ave. being a thing and I have found a name change from St. John's Rd. to Clouston Ave., in both Toronto newspapers, only for 6 July 1926. The map cannot be older than that.

In 1937, Might's directory noted that the part of Clouston Ave. from Jane St. to Weston Rd. now ran from Weston Rd. to only the railroad tracks. Also in 1937, the name of the part of Clouston Ave. from Centre Rd. to the Humber River became St. John's Drive. This change was still being declared in 1949, but the last actual listing I have found for a St. John's Drive is 1945. To further complicate things, in 1950 the section of Clouston Ave. east of Weston Rd. was renamed Gibson Park.

There's no further mention of Clouston Ave. in Might's, 1951-1955. Then it reappears (1956-1960) with a bracketed Weston and the description: west from St. John's Rd. West. Wait, isn't this St. John's Drive? Well, no. The building names leave little doubt that they are describing Gibson Park (which has its own separate, tandem entries). There is no Gibson Park mention in 1960. Then in 1961, Clouston Ave. reappears with the proper east-of-Weston-Rd. location. Someone figured out the error! They also note that this Clouston Ave. is the south side of the street as the north side is St. John's Rd. East.

Finally, in 1965, St. John's Rd. East and St. John's Rd. West were renamed Clouston Ave., likely in preparation for the 1967 amalgamation of Weston and the Township of York. I grieve for St. John's Drive which died without anyone noticing. I expect that it is buried somewhere in St. John's Cemetery on the Humber!

Sergio Reis (choreography)

Kolkata (first time in India)

Russia invades Venice

Meanwhile (current events)

Take Five (cover)

The Bird

Sixty years ago today, I penned this entry in my then-diary:

Since yesterday I've been writing short poems - pretty good ones - if I do say so myself. It's usually about a person. One I especially like is:

Brother Adrian

When the boys go out to play,
Brother Adrian stayed away.
"Have to study," he just said,
"By tonight I will have read
Books of every type and kind,
For I simply have to find
How in French to write the words,
'Reading books is for the birds!'"

A little context: I was at that time in grade ten at De La Salle College "Oaklands" which was run by Christian Brothers, a Catholic teaching order. Brother Adrian was our then-new-to-us (two weeks prior) French teacher. When I read this doggerel a couple of days ago it brought to mind a Brother who had been nicknamed "the bird" by his students, based supposedly, as suggested by my friend Alfy who also went to De La Salle back then, on his behaviour. Now, neither Alfy nor I have a direct recollection (sixty years can do that) of the bird's identity but it makes sense to me that it might have been Brother Adrian, inspiring the poem's raison d'être by way of its terminal double entendre.

That would indeed have been clever but a little subsequent research suggests that "the bird" was actually Brother Michael (O'Reilly), not to be confused with Brother Michael (Dillon) [the former "junior", the latter, "senior"]. It appears that Michael O'Reilly's three-month stay (5 Sep 1966 - 5 Dec 1966, our home room teacher for the start of grade eleven) was scrubbed from his RIP assignment list. Little wonder. We surely were his class from hell!

Janice, the jumping spider

The world

A random 5000-digit emirp pair

Print[DateString[]];
c=0;While[c++;
PrimeQ[IntegerReverse[r=RandomPrime[{10^4999,2*10^4999}]]]==False];
Print[{DateString[], c}]; r

Tue 24 Mar 2026 13:20:15

{Thu 2 Apr 2026 14:16:15, 1459}

13734728109222387308771911883098209504266491220378415449228996256958556204646209255426997204731352359449756449041282911838827753960110717667741546300796170994606405370205525990467395376009947818863867098443204707446280728853460347596959087028624624873124154773387129505731773658548559945072217868331005644146148486987796403656801876947383547342120251584407014371145256380254312563183866535417598667871824487793918102277168404192702988592723616031279706185729027937193115459363751801100834619648559534755862280622532330328020545564913373716599937718339772157065308727535050239049475309383701181923039664677398022448040478292058445782572749973954471541202254146634154863136377224819621843776574351493423099417717302803582947518052391674365890421676801423682263895436033477349103616708548394962338144244739840618759795636515556851999913235196980652229399132598337576053168937606823091007475684552339301961892031641961714248878071017023578324887088755960213127771073546703472455657291745675975849520494469065429206686852364253408177225968538981379921456249713012719550869982628800215250141536070000956939408031634199798833269213339776024607090221636520868945020007583404435400304984816689218801098149473216367358358482560919964155113665854879162787733470212782577499299460614936316249501982462197582182962661480246316492791906606967203513849810898912521723364783300800397527161480006666132471635152505857552637781618190671943929866125374286353526295866879589156528069268446360659588156073182367126878655885846017841827594449729142868018298455042670803762560261034102071781850653996720652827866216113764531977499870831481877699820219265369589791816326483849854098097404115191627985774704862207480350650524253157202313714981369031023817964668976804563887152280560591825099628968174198256928594455474900614206201208779564019513967006148424961575107554035816503265109246522149031864758498683614882701625685700872773227021642782062868941145310351815390646299885415571562126969030978677691992248131837773010974896587969945625215247802998599555149844869576921906654915655378310960741531349433956427372335169637595119451916257126526280015229284620103272436514641785833667906959477216083771551052106172820461661921196270515411038383894689853536962945436545227700069617650926512319248691302624136735627062344420181527288419813974095715282212691583319754787733622431421874596766566781210035118902671019438169295573224505091585397715351315220211971040233736523974341495533949868364720277377782599728157350029382463638680674321687547356330765388203811846145371779763392852911636547647481956184757017178391537543535061700390946825273445872542682841891167992835988152856822682714317459393194812472058333096943727715717938929497658790667620293930654794830364719577049887208648521075972113202459509425634726291406990514668964980723429065928682562597336923568312002853777432281023039930293635129199440948687280466516218157232869951411288874973458368152724148075445625803015700585387849533731143257417116714188837383227808909962194283481216500073402466043334005782482811768333556062299980861037631738960230903988141466474914973109939569029008994447469841264687420328226975199672037910132356689256318605922099489971249725724478498782743882782690449251101947062584707755445477591011686309629814598618824681005820262188651690555030066130820115706496744154662972097838464620864109248150554977389731984069894739940147765980248175151267385448245010741453588017824020636560200828952438588646996716310593319136256633679956860537422448902141226501877981016117706838811826647919831942614642062404688464031914722034158404047771516715512437734236041562161536854739816352115170865325632600798156951738783115882250368309347812703075264217063439654304694709966393200029975921707823139029998209103051390416799743854828992885437521880547367118888862322413374719343146756530741790302078652676659228463250342071145099375265620764389943047611045428183649445593679065081627297218931027072918317542023094964352985593971204351149921620655199890626051131805882424498700115214465774587948209887902292657524952455402231405821109075638114959572631886949305122157028523531876233977699646931396075719474191681597682924071799804008775563101404661918081796360660189113306106394092364326877126214067888878532744860157995659689449232748995366653945094234108364647434237692992245404080070494425022553082178108569582011506349785726297495243949030211388665827342268742694968604680029493370744659894200765912072030956961758839895603163676944756552653917173731760257052296666264677111508448519434784124629839512816675234329603341834304686287860364334731171629288773512175476941081385777926407651284584960519842623921169707152430953904143362518957259889371822834194124362865942682637039390381181943090487239006104649608076772200752347770219391585047496141065719922022050533141603543274273449631439746074641670898190472653657991251980586966500792504004728827518312237017772593842641588253316664038908417318413936902013666661226800919070758421595913214002598621253

IntegerReverse[r]

35212689520041231959512485707091900862216666631020963931481371480983046661335288514624839527771073221381572882740040529700566968508915219975635627409189807614647064793413694437247234530614133505022022991756014169474058519391207774325700227767080694640160093278409034918118309393073628624956826342149143822817398895275981526334140935903425170796112932624891506948548215670462977758318014967457121537788292617113743346306878268640343814330692343257661821593892642148743491584480511177646266669225075206713737171935625565744967636130659893885716965903027021956700249895644707339492008640686949624786224372856688311203094934259479262758794360511028596580187128035522052449407008040454229929673243474646380143249054935666359984723294498695659975106844723587888876041262177862346329049360160331198106606369718081916640410136557780040899717042928679518619147491757069313964699677933267813532582075122150394968813627595941183657090112850413220455425942575629220978890284978547756441251100789442428850813115062609899155602612994115340217939558925346949032024571381927072013981279272618056097639554494638182454011674034998346702656257399054117024305236482295667625687020309714703565764134391747331422326888881176374508812573458829982845834799761409315030190289992093132870712957992000239366990749640345693436071246257030721874390386305228851138783715965189700623652356807151125361893745863516126514063243773421551761517774040485143022741913046488640426024641624913891974662811883860771161018977810562214120984422473506865997633665263191339501361769964688583425982800206563602042871088535414701054284458376215157184208956774104993749896048913798377945505184290146802646483879027926645144769460751102803166003055509615688126202850018642881689541892690368611019577454455770748526074910115294409628728834728789487442752794217998499022950681365298665323101973027699157962282302478646214896474449980092096593990137941947466414188930903206983713673016808999226065533386711828428750043334066420437000561218438249126990980872238373888141761171475234113733594878358500751030852654457084142725186385437947888211415996823275181261566408278684904499192153639203993032018223477735820021386532963379526528682956092432708946986641509960419262743652490595420231127957012584680278894077591746303849745603939202676609785679492983971751772734969033385027421849139395471341728622865825188953829976119814828624527854437252864909300716053534573519387171075748165918474674563611925829336797717354164811830288356703365374578612347608683636428392005375182799528777377202746386894933559414347932563733204017911202251315351779358519050542237559296183491017620981153001218766566769547812413422633778745791338519621228251759047931891488272518102444326072653763142620319684291321562905671696000772254563454926963535898649838383011451507269112916616402827160125015517738061277495960976633858714641563427230102648292251008262562175261915491159573696153327372465933494313514706901387355651945660912967596844894155599589920874251252654996978569847901037773813184229919677687903096962126517551458899264609351815301354114986826028724612072237727800758652610728841638689485746813094122564290156230561853045570157516942484160076931591046597780210260241600947455449582965289147186982699052819506508225178836540867986646971832013096318941731320275135242505605308470226840747758972619151140479089045894838462361819798596356291202899677818413807899477913546731161266872825602769935605818717020143016206526730807624055489281086824192794449572814871064858855687862176328137065188595606364486296082565198597866859262535368247352166892934917609181618773625575850525153617423166660008416172579300800338746332712521989801894831530276960660919729461364208416626928128579126428910594261363941606499299477528721207433778726197845856631155146991906528485385376361237494189010881298661848940300453440438570002054986802563612209070642067793331296233889799143613080493965900007063514105251200882628996805591721031794265412997318983586952277180435246325868660292456096449402594857957654719275655427430764537017772131206955788078842387532071017087884241716914613029816910393325548657470019032860673986135067573389523199392225608969153231999915865551563659795781604893744244183326949384580761630194377433063459836228632410867612409856347619325081574928530820371771499032439415347567734812691842277363136845143664145220214517445937994727528754485029287404084422089377646693032918110738390357494093205053572780356075127793381773999561737331946554502082303323522608226855743595584691643800110815736395451139173972092758160797213061632729588920729140486177220181939778442817876689571453566838136521345208365254117341070448515202124374538374967810865630469778968484164144650013386871227054995584585637713750592178337745142137842642682078095969574306435882708264470740234489076836881874990067359376409952550207350460649907169700364514776671701106935772883811928214094465794495325313740279962455290264640265585965269982294451487302219466240590289038811917780378322290182743731

Click on either number to check its primality.

A random 2000-digit emirp pair

Print[DateString[]];
c=0; While[c++; PrimeQ[IntegerReverse[r=RandomPrime[{10^1999,2*10^1999}]]]==False];
Print[{DateString[], c}]; r

Mon 23 Mar 2026 16:19:04

{Mon 23 Mar 2026 18:37:09, 305}

14855218387530938731264800899806518554251409448753318067281617721104517975019660570816502191121802141387619791604557638640603077054520997318307203718761757739257990957393586487037638214729490346907077085366489735302991920794042479840185960548800113792237378778189700214336498150535494706550605947647886952709343445154850786791334376804237058351294799668452160206131345032141325576891497636422462012076224432607954324056613347607288129441043897934814166919553140730183934337952784895386915184278773673374499327984879217657567333750360009291505056111578053084511773793397248168145190194638081779158080985373127557284411266286462358754778798450217253924795704562031795767586150594858361787012654211320033792723983297048174107728830987370130777266997038517867493302588134280307951436792574170079530221417396081625730302595728237532318481405855540975409890906976902320267307459218191770761431037983144020890302946754575512111129239578508080696921714584513835630889334839362187530001616420174589110874531666851407830633657753457085270606608334710585505853591828745779378101187982074326317494916222176946818501389870085531903573860851057307085813978075441446820544507426572075052156092931837527279166150509917972776167153657340031646179631733906184205918255895475754364175238057482645899534235102077183676796749323690141704894319808779172119291942162868677765137547565809194418652476017816016763486268007290212946536413065587272480288193061788482406655351702586154143963745149534333768316994754590468906962685037527510130840705726077739498669858651281009519862797180044407205030051742292526137434721833180012034655794438599828098375237119761007728650703770787960212849241788574933755087711157262236337487014829313684940715849983628697605605634086992019999606613109048737110152003061306410080888361354585657807374315692388968946536330992803388106574848702486355828678460394253967147711575515270818557921500146950778382811866201918398021331397625888200120115790700195112386497426010970976957364112704151652043

IntegerReverse[r]

34025615140721146375967907901062479468321159100709751102100288852679313312089381910266811828387705964100512975581807251557511774176935249306487682855368420784847560188330829903363564986988329651347370875658545316388808001460316030025101173784090131660699991029968043650650679682638994851704948631392841078473363226275111778055733947588714294821206978707730705682770016791173257389082899583449755643021008133812743473162529224715003050270444008179726891590018215685896689493777062750704803101572573058626960986409545749961386733343594154736934145168520715355660428488716039188208427278556031463564921209270086268436761061871067425681449190856574573156777686826124919291127197780891349840714109632394769767638177020153243599854628475083257146345757459855281950248160933713697164613004375635176167727971990505166197272573813929065125057027562470544502864414457087931858070375015806837530913558007898310581864967122261949471362347028978110187397754782819535850558501743380660607258075435775633603870415866613547801198547102461610003578126393843398803653831548541712969608080587593292111121557545764920309802044138973013416707719181295470376202320967960909890457904555850418481323573282759520303752618069371412203597007147529763415970308243188520339476871583079966277703107378903882770147184079238932729733002311245621078716385849505168576759713026540759742935271205489787745785326468266211448275572137358908085197718083649109154186184279339737711548035087511165050519290006305733376575671297848972399447337637787248151968359848725973343938103704135591966141843979834014492188270674331665042345970623442267021026422463679419867552314123054313160206125486699749215385073240867343319768705845154434390725968874674950605560749453505189463341200798187787373229731100884506958104897424049702919920353798466358077070964309492741283673078468539375909975293775716781730270381379902545077030604683675540619791678314120812119120561807506691057971540112771618276081335784490415245581560899800846213783903578381255841

Click on either number to check its primality.

A random large emirp pair

One might think from my previous post that large base-ten emirps congregate near — or at least involve —  powers of ten. Well, record ones certainly do but that is surely an artifact of the convenience of searching for such integers in those locations, expressing them without having to show all of their digits, and even proving their primality.

I recently found that Mathematica has a RandomPrime function which can be configured to generate primes with a specific number of digits. By repeated application of it and checking each against the primality (most often lack-of-primality) of the integer created by reversing its decimal digits, I can now create random emirps.

While[PrimeQ[IntegerReverse[r = RandomPrime[{10^999, 10^1000}]]] == False]; r

3279288520829477235642879267287999159015788532533738855066046440495522398413879852102369701530100869580838076083149157548206285059151203914266414912431580164820025933969565023665242290427065104497454406152915882315883324964117545072539206755054402862798019415649139491569247916954175149446689650326543522910485350967102290630555006513883295579511863580034048864302120190250042483217978026251237207016901362308898161048199473494827584506196053490289923397647958362118557321048941198888848619470770742015547396263817662528411868482723797066437421483218035169802940903987225108903574471943089572864902145297776096342849868617007993544349744145780223402039236076990018520939944400626427281300176781542771736168164872520396475344293444882067084862153824121702601618059184428161120858343524815906494130051717507462817874659446095816309231120150861019479629358822063445459770400310760092233488204681637298530785169163900358943079863912831713129072815997830914582590098549219524593979172161769855800664064007

The reverse of this is:

7004604660085589671612719793954259129458900952854190387995182709213171382193689703498530093619615870358927361864028843322900670130040779545443602288539269749101680510211329036185906449564787182647057171500314946095184253438580211618244819508161062071214283512684807602884443924435746930252784618616371772451876710031827246260044499390258100996706329302043220875414479434453997007168689482436906777925412094682759803491744753098015227893090492089615308123841247346607973272848681148252667183626937455102470770749168488888911498401237558112638597467933299820943506916054857284943749918401618988032631096107027321526208797123842400520910212034688404300853681159755923883156005550360922017690535840192253456230569866449415714596197429651949319465149108972682044505576029352705457114694233885132885192516044547944015607240922425663205659693395200284610851342194146624193021519505826028457519413806708380859680010351079632012589783148932255940446406605588373352358875109519997827629782465327749280258829723

I did not think that I would be able to prove their primality, but factordb (click on either number to see its evaluation there) apparently has some "elves" who download the smallest probable primes in the database and run deterministic tests on them. I guess I got lucky.

Some recent large emirps

Let it be understood that all emirps come in pairs, say (p, q) where the number of (decimal) integer digits of p and of q are identical, but p < q. Since, in the following, we are dealing with record large integers, I will explicitly state the value of q, the larger of the pair, followed by a linked p in square brackets.

In 2007, Jens Kruse Andersen noted the 10007-digit 10^10006+941992101*10^4999+1 [p] as the then-largest-known emirp. Eighteen years later, Stephan Schöler managed to up this by four decimal digits with his 3867632931*10^10001+1 [p]. One month ago today, this was highlighted in an episode of Numberphile, precipitating (of course) a couple of new records:

Two days after the video, gamer Gelly Gelbertson found 10^10056+10^6692+10^5872+1 [p] (a 10057-digit term in OEIS A393530). Another two days and Vishwath Ganesan discovered 10^20000+518406362*10^9996+1 [p] (a 20001-digit emirp). As Vish's record was not initially noted beyond his PrimeGrid Discord chat, it created, unfortunately, a large number of claims of record that were (coming after February 20 and being fewer than 20001 digits) not actually records. That included a 10069-digit (still not proven) random emirp made possible by AI.

Updates

March 19: Serge Batalov captured a near-repunit 10^22822-10^63-1 [p] emirp.

March 26: Justin Auger posted 10^39988+5417497422*10^19990+1 [p].

March 27: Serge Batalov posted 10^47253-22*10^21607-1 [p].

April 6: Ryan Propper & Serge Batalov claim 10^77763-4*10^25683-1 [p].

April 19: Ryan Propper & Serge Batalov claim 10^111956-7*10^53855-1 [p].

Email me if you spot any errors or have something to add.

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Kids dancing

Emirps in A157711

After watching Matt Parker's February 16th Numberphile video on Stephan Schöler's largest currently known emirp, I wondered of course if any of the primes that are the sum of four distinct powers of ten (A157711, on which I have been working now for nine months) were emirps. It turns out there were a healthy number and I decided to create two new OEIS sequences for them: A393530 and A393531.

While more than half (533) of the first 1000 digit-lengths had no solutions, the others had anywhere from 1 to 7 (digit-length 41) solutions. Moreover, the accumulation of emirp-pair counts showed a steady rise, giving me hope that this would continue for larger digit-lengths:

emirp-pair count accumulations for the first 1036 digit-lengths (click to enlarge)

I will see if I can increase my counts to 2000+ digit-lengths. I was going to attempt a search for a record large pair but gamer "Gelly Gelbertson" beat me to it with his Numberphile video comment (10^10056+10^4184+10^3364+1, 10^10056+10^6692+10^5872+1), apparently made on February 18th (although I discovered it only on March 14th):

click to enlarge

The five-millionth term of A157711

The sum of the first 4006 prime counts of A383675 is 4998755. The sum of the first 4007 prime counts is 5001521. Hence, the five-millionth term of A157711 is a 4007-digit integer:

4998756 10^4006+10^39+10^18+1

4998757 10^4006+10^104+10^53+1

4998758 10^4006+10^108+10^16+1

4998759 10^4006+10^177+10^120+1

4998760 10^4006+10^192+10^59+1

...

4999995 10^4006+10^2671+10^2184+1

4999996 10^4006+10^2672+10^696+1

4999997 10^4006+10^2672+10^1708+1

4999998 10^4006+10^2673+10^392+1

4999999 10^4006+10^2673+10^530+1

5000000 10^4006+10^2673+10^876+1

5000001 10^4006+10^2673+10^1124+1

5000002 10^4006+10^2675+10^1928+1

5000003 10^4006+10^2676+10^1232+1

5000004 10^4006+10^2677+10^1160+1

5000005 10^4006+10^2677+10^2092+1

...

5001517 10^4006+10^4003+10^3570+1

5001518 10^4006+10^4003+10^3818+1

5001519 10^4006+10^4003+10^3854+1

5001520 10^4006+10^4004+10^609+1

5001521 10^4006+10^4005+10^1892+1

A157711(1*10^6) = 10^1793+10^673+10^615+1 [2025 June 19]

A157711(2*10^6) = 10^2535+10^1160+10^398+1 [2025 July 21]

A157711(3*10^6) = 10^3103+10^2747+10^859+1 [2025 September 10]

A157711(4*10^6) = 10^3583+10^3040+10^2776+1 [2025 December 7]

A157711(5*10^6) = 10^4006+10^2673+10^876+1 (above)

A157711(6*10^6) ~ 10^4388

Rubik's cube record

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Vieux Farka Touré (2019)

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