recursal/Fanatic-Fandom huggingface dataset:
1078絵札素数

概要
--

1078絵札素数は、1078に絵札をつけて作れる素数のことである。

一覧
--

* 107810101111
* 107810101211
* 107810121313
* 107811101311
* 107811111011
* 107811111113
* 107811111311
* 107811121111
* 107811121213
* 107811131011
* 107811131111
* 107811131213
* 107812101013
* 107812101113
* 107812101211
* 107812111313
* 107812131013
* 107813101211
* 107813101313
* 107813111011
* 107813111113
* 107813121011
* 107813121113
* 107813121211
Castor page

Also for testing and trying stuff.

Eventually this will lead to nice pages I hope.

## Current guild projects - new end-game region, Therianor valley

X

As of august 2023 we got a new region in game. There is 3 guild tasks connected to that.

* *Organize ritual of Therianors* to get treaty to build domain there. Requires a lot, hundreds, of guild agreements.
* *Organize the necrofesto* to get a end-game arena for combat training. Requires a lot, hundreds, of Intense runes.
* *Meet the imperial professor* to get end-game recipes. Requires a lot, also hundreds, of wingu bundles and timoral logs.

### How can I help?

* *Organize ritual of Therianors*
	+ Gather uncut gems
	+ Cutting gems, 4C best
	+ *Keep in contact ...*, which takes cut gems and makes favors
	+ And/Or *solicit ...,* in Spying/Influence also makes favors
	+ *Establish contacts in...* for personal agreements
	+ And/Or *solicit ...,* in commerce also makes personal agreements
	+ Draft guild agreements; takes personal agreements and favors and makes guild agreements
* *Organize the necrofesto*
	+ gather runic AF (artifact fragment)
	+ identy runic AF gives dead runes and rune fragments
	+ activate runes
	+ and donate to guild
* *Meet the imperial professor*
	+ get wingu bundles and timoral logs.

#### Draft guild agreement

Each draft guild ... task produces 0.2 of a guild agreement. Hero can do 4 tasks before sleep. So producing one guild agreement takes the hero 14:41:55 including sleep.

The cost for each guild agreement is... <Sorry for the wide table>

Status 2023-08-18: We need this guild agreement

Total 632 guild agreement needed, taking 387 hero workdays to produced

or translated to the personal agreements and favors

## Need to learn wiki...

A good help page : Help:VisualEditor/User\_guide

texts, links, tables, formulas

admin: renaming pages, deleting my buggy pages....

### Text things

* text styles
* fonting
* lists
* cite
* link
* images and media
* mass upload
* insert
	+ infobox, template, table, comment, chemical formula, math formula, code block, gallery, signature, references list

## Filling in the gaps

There is som gaps I would like to see filled...

### Filling in the guild gaps

* A guild place in every region
* A sleeping place in every guild place
* Best practical gathering place for every resource
* Best practical crafting place for every crafting

### Filling in the Castor gaps

* store + sleeping place for best solicit ... in commerce
* secret vault + sleeping place in solicit ... in spying

store and secret vault also works as sleeping place for passive gatheres so a separate one might not be needed.
127

概要
--

127は素数である。語呂はいずな。Qが使える。ジョーカーを使わないで出せる最初の3種3枚素数。

## 127を含む素数

* 7127(無い綱)
* 210127(ニートいずな)
* 510127(後藤いずな)
* (0)814127(霊媒師いずな)
* 8686127(ハムハムいずな)
* 12732101(いずなさん太い)
* 21033127(ニート散々いずな)
* 31264127(サイズ無視いずな)
* 49864127(四駆羽虫いずな)
* 542101127(腰太いいずな)
* 813253127(ハッキングツッコミいずな)
* 3510814127(すごい霊媒師いずな)

## 127を含む合成数出し

* 127 \* 109 = 13843
* 127 \* 593 = 75311(いずなコックさん、和みいい)
* 127 \* 797 = 101219 (いずな泣くな、東急行く)
* 127 \* 811 = 102997
* 127 \* 821 = 104267
* 127 \* 823 = 104521
* 127 \* 827 = 105029
* 127 \* 829 = 105283
* 127 \* 887 = 112649
* 127 \* 1019 = 129413
* 127 \* 1033 = 131191
* 127 \* 1061 = 134747
* 127 \* 1093 = 138811
* 2^2 \* 3^7 \* 127 = 1110996
* 127 \* 48119 = 6111113

## 127の戦略

* 3510814127は、1・3・4・5・7・8・10・12の8種8枚で出せる。

余談
--

* 12月7日はクリスマスツリーの日。1886(明治19)年のこの日、横浜・明治屋に日本初のクリスマスツリーが飾られた。

## 関連項目

* 素数大富豪素数の一覧
* N種N枚素数
* 語呂素数
1021110四つ子素数

概要
--

1021110四つ子素数は1021110を含む四つ子素数である。

例

152591021110, 466511021110, 8453102111011, 9910211101213, 12687102111013, 23708102111011, 28021102111012, 28442102111011, 33889102111012, 39144102111010, 44855102111011, 54073102111012, 66549102111010, 68669102111011, 69698102111011, 85523102111011, 396410211101311, 422810211101311, 651410211101212, 1139210211101110, 1679710211101312, 1822510211101210, 2219810211101113, 2275010211101311, 2765410211101210, 2972810211101011, 3000710211101212, 3252910211101111, 3877910211101113, 4393710211101310, 4448710211101210, 4466910211101010, 4733610211101010, 5138510211101212, 5253910211101312, 5603610211101313, 5939310211101310, 6103310211101311, 6474310211101213, 6661310211101110, 7215110211101110, 7431610211101312, 8368810211101210, 8662010211101110, 8873110211101312, 9046310211101110, 9423710211101212, 9555810211101010, 9961510211101312
4895四つ子素数

概要
--

4895四つ子素数は4895を含む四つ子素数である。

例

5454895, 69954895, 140274895, 220134895, 268404895, 275934895, 372984895, 387684895, 488094895, 498354895, 501684895, 549384895, 551454895, 561354895, 616164895, 640554895, 659489512, 772794895, 793644895, 853704895, 903624895, 2307489511, 3716489512, 5512489510, 9991489513, 13543489513, 14414489512, 14863489513, 14865489511, 16208489512, 23832489511, 26374489510, 31017489511, 31384489510, 42889489513, 43165489510, 46595489512, 47731489513, 47804489512, 54430489513, 57276489511, 65140489513, 68183489512, 73214489512, 73813489510, 75043489510, 77029489510, 78243489511, 80922489511, 88243489510, 90853489513, 97837489510, 182448951310, 235448951113, 356748951112, 486048951013, 926848951012, 1446048951313, 1511948951110, 1546048951210, 1668048951010, 1670948951113, 1718448951010, 1799248951312, 1868248951012, 2035148951011, 2043748951210, 2066448951313, 2245648951213, 2255848951210, 2457048951211, 2741148951010, 2925048951310, 3027948951310, 3113048951311, 3195548951311, 3370048951312, 3442548951313, 3869948951011, 4007848951111, 4070648951113, 4093548951010, 4109848951213, 4143448951111, 4376648951113, 4687048951012, 4849748951311, 4862548951111, 4869748951210, 4984648951210, 5023848951112, 5229248951113, 5541848951311, 5677848951013, 5915448951112, 5979348951010, 6045148951012, 6208048951312, 6308148951112, 6414948951010, 6473248951111, 6704248951111, 6899248951012, 7029148951312, 7123648951210, 7190948951212, 7430248951312, 7604948951311, 7762748951212, 7789348951312, 8034348951310, 8233048951111, 8671448951110, 8705748951112, 8734348951312, 8843648951110, 8927148951010, 9020048951212, 9047848951312, 9377348951113, 9499148951311, 9790248951010, 9977348951011
109

概要
--

109は素数である。語呂はトーク。

## 109を含む素数

* 1109(伊藤くん)
* 3109(佐藤くん)
* 7109(納得)
* 9109(工藤くん)
* 91097
* 104104109(どしどしトーク)
* 111111109(JJJトーク)
* 1011109109
* 1112109109
* 1311109109
* 12345678109111213

## 109を含む金太郎飴素数

* 651109(むごいトーク)
* 510510923719(後藤後藤急にみんな逝く)

## 109を含む合成数出し

* 2 \* 3^7 \* 11 = 48114
* 109 \* 877 = 95593 (毒バナナ=休校コックさん)
* 2^10 \* 109 = 111616
* 2 \* 3^6 \* 83 = 121014
* 109 \* 1171 = 127639 (トーク浴びないいずな無策)
* 2^6 \* 3^7 = 139968
* 3^7 \* 97 = 212139
* 109 \* 5147 = 561023 (トーク濃いよな五郎と兄さん)
* 3^6 \* 811 = 591219
* 3^6 \* 911 = 664119
* 109 \* 8821 = 961489 (トークヤバツイ黒石破くん)

## 関連項目

* 素数大富豪素数の一覧/1～4枚出し
* 101
* 103
* 107
645四つ子素数

概要
--

645四つ子素数とは645を含む四つ子素数である。

例

892645, 1561645, 5332645, 6163645, 16618645, 28381645, 28465645, 30889645, 32056645, 38437645, 38692645, 38710645, 43264513, 45178645, 45316645, 46975645, 52414645, 62149645, 76501645, 93145645, 96164512, 392764510, 1308964513, 1332464512, 1336451110, 2069064511, 2190864511, 2299564513, 2431764511, 2724864511, 2772064510, 2802364510, 2956764511, 3481364512, 3966964513, 4273464511, 4850064511, 5365064512, 5421764512, 6509164513, 6757864513, 6948064513, 6949064512, 7169564512, 7228264510, 7556464513, 7736451010, 7754264512, 7836764512, 7966464511, 9145564510, 9162264511, 9353464510, 13366451113, 14436451312, 15036451111, 16846451212, 29946451111, 37696451110, 39806451112, 39896451313, 45036451213, 48696451210, 60036451210, 61586451211, 65086451113, 73036451113, 73736451211, 74086451311, 78706451113, 83506451311, 89646451312, 106906451212, 116096451112, 121916451310, 122006451010, 128246451313, 132276451312, 134156451112, 141956451010, 165976451110, 168146451310, 174656451112, 191376451012, 191546451010, 192866451013, 194376451312, 207646451311, 229196451310, 229736451313, 240316451110, 251016451213, 260496451111, 261876451210, 264806451010, 282856451113, 287736451012, 319896451012, 355916451313, 364236451111, 367176451213, 373936451311, 377376451012, 396206451313, 419216451211, 419416451011, 421656451210, 432186451210, 438176451310, 439186451110, 440826451213, 442706451013, 443146451011, 445246451212, 454166451112, 457096451311, 479636451313, 480726451210, 509996451310, 527956451011, 539066451313, 556736451211, 582046451311, 584576451112, 587136451312, 588246451210, 600576451210, 602606451310, 615756451213, 618766451311, 659356451311, 684036451012, 720276451210, 724436451310, 730496451112, 741426451111, 770726451013, 776596451212, 784906451311, 801156451012, 824906451010, 870246451210, 887886451012, 889886451310, 896096451010, 908736451213, 913606451311, 915996451312, 968716451113, 971266451011
2610876四つ子素数

概要
--

2610876四つ子素数は2610876を含む四つ子素数である。

例

58572610876, 132102610876, 133152610876, 134622610876, 203502610876, 314562610876, 395172610876, 564072610876, 919752610876, 2177261087611, 7981261087612, 9236261087611, 21517261087612, 22781261087611, 56436261087613, 56990261087611, 64798261087612, 71694261087613, 73575261087613, 97310261087611, 319826108761213, 325726108761310, 358826108761312, 1280826108761113, 1466026108761112, 1468326108761011, 2310526108761013, 2375526108761212, 2452426108761310, 2560626108761311, 2875826108761012, 3353526108761113, 3534026108761312, 3586626108761011, 3631426108761211, 4127226108761311, 5521026108761311, 5526926108761111, 6126926108761312, 6372126108761311, 6961626108761110, 7091826108761110, 7372926108761113, 8021226108761311, 8059126108761010, 8532826108761013, 9554026108761310, 9586826108761312, 9768526108761211
1129四つ子素数

概要
--

1129四つ子素数は1129を含む四つ子素数である。

例

16891129, 103651129, 111181129, 114961129, 268051129, 386521129, 399931129, 406861129, 425112913, 500341129, 545851129, 553441129, 579511129, 661771129, 717451129, 846811129, 8235112912, 9380112913, 11608112911, 11650112911, 12314112910, 13130112910, 14840112913, 19505112910, 21006112912, 27116112913, 31675112911, 32396112913, 33329112913, 37018112911, 38942112910, 40285112911, 43201112911, 44811291010, 49576112911, 50290112911, 57239112913, 58408112911, 58552112911, 59228112910, 60296112910, 62039112910, 66229112911, 68105112913, 69244112911, 73420112911, 81547112911, 82472112910, 91608112912, 94536112912, 96398112910, 222511291210, 238911291013, 486711291211, 603711291013, 698211291310, 875111291311, 1008711291211, 1077411291013, 1160511291112, 1319711291113, 1368711291211, 1413811291210, 1475111291011, 1547511291112, 1579511291011, 1713611291110, 1721511291013, 1835411291113, 1916111291113, 1940211291310, 2047611291013, 2175611291110, 2236611291013, 2688611291110, 3109111291312, 3197411291212, 3265411291213, 3606011291212, 3608511291313, 3780711291313, 3946011291211, 3952211291110, 3971011291213, 4062111291211, 4254211291312, 4405411291111, 4409211291313, 4690511291212, 4795411291312, 4862211291313, 4939211291110, 5311811291113, 5795511291211, 5819711291311, 6143211291313, 6155711291311, 6239011291213, 6303011291011, 6347411291110, 6406811291212, 6721911291112, 6872711291311, 7112911291111, 7249111291012, 7353111291310, 7397411291212, 7568611291312, 7680011291011, 7815111291013, 7958411291113, 8032011291013, 8139311291212, 8437311291013, 8481611291212, 8545911291013, 8720511291112, 8937911291212, 9106711291210, 9157211291212, 9169911291010, 9468411291013, 9674511291112, 9811511291212
Abandoned Cities

An **Abandoned City** is a city that has no population. If a city gets abandoned, you will get this pop-up:

#### City Abandoned

*Your settlers have abandoned [city], leaving only eerie streets and empty homes behind. All facilities have automatically ceased operations and, for now, the city is a ghost town.*

If you try to use a facility in an abandoned city, it will say *No effect (city abandoned)*. To regain population, build a new habitation.

## Causes

There are many ways to make your city become abandoned, such as accidently disabling the only habitation of that city.

#### Events that cause this

**Fire**

The Fire event destroys a facility, so a habitation facility can be destroyed, making your city become abandoned.

**Rumble and Roll**

Although usually nothing happens, sometimes bigger earthquakes strike, destroying a facility.

**The Sky is Falling**

A meteor can impact a city and destroy its habitation unit.

**Facility Crushed**

This can destroy a habitation facility , therefore making it abandoned.

**Plague Outbreak**

The plague can kill off everybody in a city, making it abandoned.

## How to prevent it

To prevent a city being abandoned, add an emergency habitation, only a Hab Unit.

## Trivia

* If a facility is being built in a city, and that city gets abandoned, the facility will continue to build.
417310四つ子素数

概要
--

417310四つ子素数は417310を含む四つ子素数である。

例

58593417310, 85092417310, 92799417310, 583441731010, 1387141731013, 3136241731012, 3215341731010, 4099241731012, 4163741731012, 5868541731013, 6359941731013, 6376441731010, 6901941731011, 6954841731010, 7056541731013, 8225541731011, 9284173101211, 16394173101013, 43324173101011, 57094173101110, 58244173101010, 65954173101211, 151924173101212, 196724173101013, 257894173101010, 258294173101210, 266594173101313, 279304173101311, 290114173101310, 303314173101112, 305644173101011, 309194173101112, 368264173101310, 384914173101211, 403744173101011, 436344173101210, 462974173101310, 500634173101210, 506534173101010, 511904173101310, 527984173101211, 548444173101112, 551124173101213, 556394173101112, 557614173101011, 629114173101013, 629884173101011, 781844173101010, 786394173101113, 808964173101211, 826344173101210, 860264173101112, 860974173101113, 874244173101013, 879924173101111, 898024173101011, 898814173101013, 901574173101313, 901854173101213, 933564173101213
Guen McNichol

**Guen McNichol (グエン・マクニコル, *Guen Makunikoru*)** is a minor character in the Madlax anime series who appears in episode 3. He was the Military Commander of the Gazth-Sonika Royal Army.

## Background

After his wife was killed in a terrorist attack by Galza, he started fighting for the Gazth-Sonika Royal Army, soon becaming a war hero and eventually being appointed to the position of Military Commander, keeping that role until his assassination by Madlax.

## Events of the series

Strangely enough, it was he himself who requested his assassination. Madlax finds this fascinating, and on the night before she kills him, she goes to his hotel and has a long talk with him.

McNichol admits that he feels he was manipulated into the position of military commander, and that even his wife's untimely death at the hands of the Galza might have been a planned event to make him hate the resistance group, and end up a Gazth-Sonika war hero. He felt he had no control over his life, and that the government was using him. As a result of this manipulation, he says he wants to decide his own life's ending. Madlax holds her hand out to Gwen, approaches him, and lets him embrace her.

At the end of the episode, after she's killed him, Madlax throws a photograph of Gwen into the river, saying that last night was a lot of fun.

## Trivia

* Although nothing is shown, it could be assumed that McNichol and Madlax spent the night together.

### Name Origin

* Guen comes from *gwenn*, meaning white or blessed (figurative meaning) in Breton.
* McNichol is a Scottish and Irish patronymic surname from the Viking settlers of ancient Scotland and derived from Nichol, or Nicholas, which means *"victory of the people"*, being a compound of the Greek words νίκη nikē *"victory"* and λαός laos *"people"*.

## Gallery

Madlax aiming at Guen McNichol with her M24 Sniper Rifle.The body of the commander lyng on the ground, seen through the scope of Madlax's sniper rifle.The photo of the commander, thrown into a river by Madlax after his assassination.
Gazth-Sonika Royal Army

The **Royal Army of Gazth-Sonika** is the main army of the Kingdom of Gazth-Sonika. It serve the King of Gazth-Sonika, Cawthran IV. The Gazth-Sonika civil war is predominantly a conflict between the armed terrorist group Galza and the royalists, AKA the King's Army. At least, that's what the general public is told. In reality, the civil war is pointless, and is continually kept ongoing by Enfant. The King's Army receives weapons from Bookwald Industries and new fighters from Enfant.

It's likely that high-ranking officers know this truth. We see one example in episode 18, when Limelda Jorg confronts the high-ranking army captain who was also shown to be working with Enfant when he attacked Madlax and Vanessa in episode 17. The unnamed captain says he knew about the truth of the civil war the whole time. In her fury, Limelda Jorg shoots and kills the captain.

In episode 17, when Vanessa and Madlax attempt to publish the data files of Enfant's involvement in the civil war, the Royal Army issues fake news through the media, accusing the two of murdering the King's cousin, Jaham Korslan, putting them on a special wanted list and become targets of the King's Army.
Sarkus Sark

***Sarks Sark*** (Japanese: サークス・サーク Sākusu・Sāku) are the only words identified from Secondary. They are also called "the words of the Essence."

## Effects

Written in Elies Characters, they have supernatural properties, but exactly how and when they work (or don't work) is never clearly explained. In general, for them to take effect, the words must be directed at the person which the speaker wants to affect. If a person wants to use the words on himself, he must say them aloud and direct it at himself. Upon hearing the words directly spoken to them, people may experience visual and/or auditory hallucinations, as well as flashbacks from their memories.

The main effect of *Sarks Sark* is making people act in accordance with their true intrinsic natures. They may, for example, act very differently than the normal self they show the world, or the self they wish to be. It can also cause people to realize the truth about themselves: their true nature, real identities, suppressed memories, or their deep desires.

## List of Known Users

* Friday Monday can use this incantation along with the other two.
* Margaret Burton used this incantation under Friday's power.

### Victims

† indicates deceased in the series.

* Maurice Lopez (Episode 6) merely read the words in Secondari.
* Vanessa Rene † (Episode 22)
* Elenore Baker † (Episode 24)

## Related Pages

* Elies
* *Elda Taluta*
* *Ark Arks*
4897四つ子素数

概要
--

4897四つ子素数は4897を含む四つ子素数である。

例

26554897, 80944897, 128434897, 136204897, 138964897, 164314897, 179284897, 218944897, 315544897, 327334897, 383794897, 424144897, 426004897, 431704897, 474544897, 500104897, 540904897, 566254897, 583534897, 627634897, 670624897, 698974897, 796654897, 923494897, 996364897, 4797489712, 5047489711, 8743489711, 9728489713, 17713489711, 17900489710, 19242489712, 20165489713, 20885489710, 21608489710, 22510489711, 23509489711, 24391489711, 24839489713, 26667489712, 32666489710, 36885489712, 42681489712, 45202489711, 46062489712, 46532489713, 52845489712, 55319489713, 55933489711, 56415489712, 62557489711, 68428489711, 70181489710, 73708489711, 79556489713, 85877489713, 95526489712, 346648971112, 457148971312, 526448971312, 1235348971111, 1574448971110, 1730948971312, 2054048971210, 2134548971110, 2179648971211, 2401348971313, 2681648971111, 3091548971110, 3216248971111, 3333748971313, 3405648971212, 3671848971010, 3696148971112, 3824948971012, 3950648971312, 4027448971012, 4304348971312, 4308348971113, 4674048971212, 4720348971010, 4986648971011, 5303948971312, 5369848971310, 5568248971111, 5861648971312, 5899548971212, 6267948971212, 6548548971112, 7143548971312, 7281748971211, 7474948971313, 7544548971310, 7575148971010, 8026348971313, 8059948971112, 9049948971211, 9491148971011, 9588948971311, 9698948971111, 9756348971113, 9799648971010, 9809448971113, 9891648971011, 9986148971011
1013

概要
--

1013は素数である。

## 1013を含む素数

* 101359
* 101383(時計屋さん)
* 861013(ハムTK)
* 6681013(むむっヤドキング)
* 10131019(時計トーイック)
* 810261013(パイオツ無敵)
* 961161013(黒い色時計)
* 101371101383(時計ない時計屋さん)

## 1013を含む合成数出し

* 11143 = 11 \* 1013
* 125612 = 2^2 \* 31 \* 1013
* 321171 = 317 \* 1013
* 641229 = 3 \* 211 \* 1013

## 1013を含む金太郎飴素数

* 4126848121013
* 68121013
* 3121063278121013
* 15121063278121013
* 1065121063278121013
* 2127278121013
* 512121212378121013
* 912121212378121013
* 65121212378121013
* 421212378121013
* 181212378121013
* 111381212378121013
* 615378121013
* 135378121013
* 2391312578121013
* 8691312578121013
* 991312578121013
* 3578121013
* 4126578121013
* 109126578121013
* 46578121013
* 7578121013
* 621013
* 11721013
* 9210122721013
* 93913510122721013
* 1123122721013
* 563762721013
* 1283762721013
* 10683762721013
* 7683762721013
* 272721013
* 5721013
* 1171212119721013
* 9571212119721013
* 12391212119721013
* 34391212119721013
* 1233119721013
* 11733119721013
* 8733119721013
* 7963119721013
* 2124119721013
* 3124119721013
* 129721013
* 1231921013
* 631921013
* 10122101191921013
* 111103122101191921013
* 33122101191921013
* 73122101191921013
* 139122101191921013
* 42101191921013
* 3101191921013
* 121191921013
* 371191921013
* 113671191921013
* 63671191921013
* 3291921013
* 12461113921013
* 63513921013
* 6105121093513921013
* 15121093513921013
* 12393513921013
* 1213393513921013
* 493513921013
* 613921013
* 57921013
* 41287921013
* 3491287921013
* 12987921013
* 96119331013
* 10111329331013
* 11313111329331013
* 431193429331013
* 241193429331013
* 111011105429331013
* 9105429331013
* 138429331013
* 1011131199331013
* 1211131199331013
* 612121311131199331013
* 83121311131199331013
* 111351061199331013
* 213951061199331013
* 513951061199331013
* 913951061199331013
* 1245399331013
* 13845399331013
* 13381065399331013
* 981065399331013
* 7365399331013
* 9465399331013
* 613665399331013
* 3138399331013
* 101298399331013
* 9399331013
* 1191011631013
* 411131211631013
* 18102131211631013
* 131238102131211631013
* 9731238102131211631013
* 21338102131211631013
* 51338102131211631013
* 1161338102131211631013
* 942136621212661338102131211631013
* 96621212661338102131211631013
* 861338102131211631013
* 108131211631013
* 78131211631013
* 61215631013
* 6315631013
* 515631013
* 1312933815631013
* 712933815631013
* 1173815631013
* 9121273815631013
* 291273815631013
* 691273815631013
* 95631013
* 41191026931013
* 1291026931013
* 310591026931013
* 910591026931013
* 8124591026931013
* 94591026931013
* 121510926931013
* 3213510926931013
* 23109213510926931013
* 969213510926931013
* 79213510926931013
* 2121813510926931013
* 109813510926931013
* 331399813510926931013
* 5631399813510926931013
* 699813510926931013
* 1012926931013
* 412926931013
* 912926931013
* 2366931013
* 81013

## 関連項目

* 素数大富豪素数の一覧
* 肉ない肉屋さん素数
1345絵札素数

概要
--

1345絵札素数は、1345に絵札をつけて作れる素数である。

一覧
--

* 134510101111
* 134510111311
* 134510121113
* 134510121211
* 134510121313
* 134510131013
* 134510131313
* 134511101311
* 134511111013
* 134511111113
* 134511121013
* 134511121313
* 134511131011
* 134511131113
* 134512101013
* 134512121011
* 134512121311
* 134512131113
* 134513111011
* 134513121011
* 134513121311
* 134513131211
* 134513131213
4336四つ子素数

概要
--

4336四つ子素数とは4336を含む四つ子素数である。

語呂
--

* 410143361113(酔ったしざさらJK)
* 5694336101212(語録しざさらTQQ)
* 7564336121212(なごむしざさらQQQ)
* 81974336111113(バイクなしざさらJJK)

例

6334336, 61954336, 80434336, 1463433613, 3535433611, 4425433612, 141843361213, 170643361213, 207043361311, 344743361110, 410143361113, 486743361112, 490943361310, 638543361013, 659443361011, 722243361010, 3364336131010, 5294336131213, 5694336101212, 7564336121212, 13204336131313, 14154336111112, 28374336121213, 30704336111011, 30984336111013, 31484336111212, 32704336131211, 33034336131112, 37434336121012, 40304336111110, 40924336131211, 42564336121210, 55104336111112, 76284336111112, 76304336111011, 76884336121213, 77814336131113,

81974336111113, 82564336131310, 84484336111213, 87204336131011, 88824336101212, 90174336121012, 93104336101012, 94284336111211, 95384336111011
Algae Colony

## Introduction

The **algae colony** has the ability to raise the biomass of the body it is on. Water levels will drop because these algae live in the water.
Levels beyond **V** are only reached through events.

"*During the early phases of terraforming, large-scale plantlife will have a much harder time surviving on an alien planet. The biosphere will need to be built up from smaller lifeforms, beginning with patches of genetically targeted algae placed in exposed gardens on the surface. From there humble beginnings, you can build paradise.*
*" - Ingame Description*

## Level Charts

Beginner Mode differs in time needed compared to Normal Mode. The Culture modifiers accounts for the total *Biomass*, *Population*, *Credits*, *Research Time* and/or *Construction Time* gained/lost for the buildings/research.
6868四つ子素数

概要
--

6868四つ子素数は6868を含む四つ子素数である。

例

43686868, 178056868, 184956868, 247986868, 367866868, 395796868, 484206868, 546996868, 687066868, 729066868, 740686810, 766686868, 803886868, 852156868, 859506868, 964086868, 966576868, 980226868, 1116686812, 2132686813, 4004686813, 6860686813, 8216686810, 9966686812, 12570686812, 15596686813, 19102686811, 22571686810, 23873686810, 24523686811, 28368681010, 28913686810, 32335686811, 33234686812, 34739686810, 41449686811, 41509686811, 41519686813, 47252686813, 49111686811, 54782686813, 55445686810, 67130686810, 70030686811, 76036686811, 87709686811, 96394686811, 97226686810, 97684686811, 98545686811, 184268681311, 207068681011, 253568681311, 326068681312, 365968681111, 646768681312, 1004868681013, 1083568681210, 1256868681211, 1302068681212, 1476568681213, 1501768681012, 1519468681312, 1543768681012, 1727968681213, 1811268681013, 1850368681213, 1922268681313, 2243368681111, 2415068681212, 2494368681211, 2543168681110, 2664468681010, 2705968681312, 2777268681013, 3065468681110, 3110468681311, 3116968681312, 3140368681213, 3243468681211, 3388468681312, 3694968681013, 3838168681210, 3866568681211, 4609268681113, 4677968681212, 4784868681010, 4847768681311, 5066868681010, 5176868681311, 5291768681011, 5302068681010, 5456868681211, 5664468681313, 5942868681013, 5953068681313, 6078268681012, 6176268681010, 6322268681011, 6533468681311, 6649568681113, 6661068681013, 6687868681012, 6794968681012, 6835468681210, 6979968681010, 7074768681310, 7159568681212, 7297968681013, 7307368681210, 7431468681010, 7444168681111, 7674468681013, 7720468681210, 7787568681310, 8034868681213, 8363868681211, 8678968681213, 8869368681211, 8952268681312, 9188968681210, 9294468681310, 9381468681112, 9483268681213, 9701168681212, 9739568681011, 9846968681110, 9922668681112
Thirstary

**Thirstari** (Japanese: サースタリ Saasutari) is the third of the three holy books in the anime series, first appearing in Episode 16. It is a green book - and within it, written in Elies characters, are the words *Ark Arks*, the words of Truth.

## History

It is unknown who created the three books, so the history of Thirstari is merely derived from the anime series.

### 1999

Friday Monday used the three books to begin Gazth-Sonika's civil war. At some point, after getting shot by Colonel Burton, Friday lost the books.

### 2011

Thirstari remained in Quanzitta Marison's possession in Doaiho Village as the civil war waged for twelve years. In Episode 19, Quanzitta said she will give Margaret Thirstari if she can find Firstari to put with Secondari already in her possession. In Episode 20, Madlax read Thirstari, while Margaret tried to read Secondari, and the two were able to see a glimpse of what happened twelve years ago. Then Carrossea Doon joined Margaret with Firstari, which allowed them to use all three books in Episode 21 to summon the Door of Truth, resulting in Carrossea's death, Margaret getting captured by Friday along with the books. All three books were used again in Episodes 25 and 26. By the end of the last episode, Thirstari and the other books were destroyed by fire.

## Powers

*See also The Gift.*

Each of the books hold great supernatural powers. Individually, even though not shown, Thirstari can be used to chant the words of Truth but simply looking at the pages can cause people to be affected as well, much like Firstari and Secondari. Put them all together, they can be used to summon the Door of Truth, which would then lead to the Door of the Era.

## Trivia

* Prior to the creation of books, particularly the codex, stone tablets and scrolls were used by ancient civilizations for writing. So, it could be speculated that the three books were created no earlier than the first century (CE). Furthermore, it is uncertain if the pages are made of papyrus or paper, but it could be speculated that the books were made in Asia since the first papermaking process was documented in China during the Eastern Han period (25–220 CE).
* Thirstari can be mistaken for Firstari due to *th*-fronting in English.

### Name Origin

* The names of the books are most likely derived from spatial, or chronological, ordinal numerals (*first*, *second*, and *third*). This is consistent with the order in which the words of the books are chanted.

## Related Pages

* Firstari
* Secondari

## External Links

* Book (Wikipedia)
* Ordinal Numerals (Wikipedia)
1213

**1213**は、素数大富豪にて2枚出しで出すことのできる最大の素数である。クイーンとキングを一枚ずつ使う、4桁の素数である。この素数は、その性質から「2枚出し最強素数」と呼ばれる。「2枚出し最強の数」と呼ばれることがあるが、下のように合成数出しによるカウンターが可能なため誤りである。

## 1213に対するカウンター

2人対戦で相手が1213を出してきた場合、1310,1311,1312または1313を合成数出しで出さなければ相手の手番になってしまい不利になる。そのため、合成数出しで1213より大きい数を出すことは重要な戦略である。場が1213の時にそれより大きい数を出すことを**1213に対するカウンター**という。

カウンターの方法は上の表のように11通り存在するが、実戦で出されたものはこの試合の2試合目で出されたKQ=2^5\*41のみであるとみられる。

## 1213を含む金太郎飴素数

* 1111213
* 121311610211213
* 19611610211213
* 5753910211213
* 9511112671143211213
* 91112671143211213
* 33810212671143211213
* 9810212671143211213
* 12212671143211213
* 101113212671143211213
* 1113213212671143211213
* 671146212671143211213
* 6213846212671143211213
* 139513846212671143211213
* 1243211213
* 73211213
* 3511213
* 611213
* 131213
* 641213
* 10841213

## 関連項目

* 【実況】第２回素数大富豪大会 01
* 素数大富豪素数の一覧
* 素数大富豪素数の一覧/1～4枚出し
* 99998888777766665555444433332222131313131313121212121111111011010101111
58613四つ子素数

概要
--

58613四つ子素数とは58613を含む四つ子素数である。

例

173358613, 358158613, 692058613, 733158613, 2115861310, 2959158613, 4465758613, 4585458613, 5001258613, 6124758613, 6644058613, 7741758613, 7753458613, 7835358613, 8980758613, 30475861312, 35115861313, 63665861311, 67015861312, 224145861313, 232945861312, 249545861311, 346525861312, 491595861310, 529205861311, 531795861313, 535555861312, 589095861310, 759625861312, 769465861312, 790285861312, 846805861312, 885995861311, 890675861311, 3062586131011, 3258586131013, 4706586131110, 6091586131312, 7156586131012, 9483586131010, 10268586131212, 14990586131113, 15773586131110, 16875586131013, 20742586131013, 21814586131210, 23826586131211, 23832586131310, 24378586131112, 32671586131210, 32940586131010, 36047586131110, 38997586131211, 42132586131310, 42909586131112, 43734586131010, 44499586131010, 44654586131011, 46525586131312, 46733586131011, 56062586131312, 59928586131013, 61108586131111, 62508586131211, 64524586131010, 67321586131012, 69246586131313, 70622586131011, 72124586131312, 74052586131310, 74998586131213, 79234586131111, 82953586131013, 84740586131311, 84881586131212, 87166586131213, 91700586131110, 99079586131312, 99919586131312
226411333

概要
--

226411333は素数ではない(23 \* 673 \* 14627)。九つ子素数の幹。JかKが使える。筒ロシア朝散々。

## 226411333ファミリー

* 2264113331
* 2264113333
* 2264113337
* 2264113339
* 22641133313
* 4226411333
* 6226411333
* 10226411333
* 12226411333

## 同族素数

* 223
* 22643
* 226433
* 2333
* 331
* 3313
* 31231 (サインコサイン素数)
* 63232x(x=1,3,7,9 四つ子素数)
* 64x(x = 1,3,7)
* 6421
* 64123
* 641213
* 6412333
* 2264113(筒虫ジミー)

* 226411331
* 226411337

## 同族金太郎飴素数

* 6231223
* 1261223
* 163381223(エロみ三倍包み)
13101211

概要
--

13101211は素数である。4枚出しで3番目に強い素数。

通称KTQJ(ケーティーキュージェー)

## 13101211を含む素数

113101211

713101211

1513101211(いちごKTQJ)

1613101211

3713101211

3913101211

4513101211

4813101211

5113101211

5513101211

5713101211

6313101211

6613101211

6913101211

8413101211

9413101211

21013101211(ニートKTQJ)

21413101211(バレンタインKTQJ)

24413101211

31013101211(水戸KTQJ)

44813101211

46213101211(城にKTQJ)

46813101211(ヨーロッパKTQJ)

61313101211

66613101211

68213101211(ロバにKTQJ)

75913101211(南国KTQJ)

88313101211(やばみKTQJ)

96313101211

96913101211(クロックKTQJ)

112913101211(いい肉KTQJ)

681013101211(ロバートKTQJ)

4121113101211

5101013101211

6111013101211

6111113101211

7101013101211(納豆とKTQJ)

7111013101211(セブンイレブンとKTQJ)

9121213101211

10111213101211

11111113101211

## 13101211の戦略

4枚出しで3番目に大きい素数のため、4枚出しの切り札としてかなり有効な素数。

また、10、J、Q、K、をそれぞれ1枚ずつ使用するため、バランスがよい。

13101211で相手に勝てる見込みが薄いと感じた場合、13101211を含む素数に切り替えて5枚以上出しに戦略をシフトすることも考えられる。
2754四つ子素数

概要
--

2754四つ子素数は2754を含む四つ子素数である。

例

672754, 882754, 4272754, 29502754, 49182754, 71682754, 128352754, 166632754, 177762754, 181902754, 199392754, 211152754, 232722754, 273312754, 274932754, 302922754, 333522754, 373872754, 379782754, 421302754, 506592754, 558642754, 712182754, 794112754, 804162754, 804552754, 873852754, 1926275410, 3583275412, 3878275411, 4674275413, 12193275412, 15198275410, 24206275411, 24753275410, 25173275410, 30421275412, 34864275412, 35229275413, 35892275413, 37762275412, 38004275410, 38936275411, 40806275410, 41880275410, 46771275412, 47673275413, 50751275410, 51360275410, 51828275413, 53027275411, 64598275411, 67256275411, 70017275410, 78195275413, 79353275410, 80001275413, 81233275411, 84234275413, 92100275410, 93903275413, 98391275410, 216027541210, 226627541113, 449127541213, 472527541111, 692627541313, 707127541312, 753327541111, 802327541212, 868727541211, 884427541210, 1028727541012, 1313927541211, 1363027541011, 1446627541012, 1710027541111, 1724427541210, 1943727541012, 1951527541111, 2057327541013, 2162627541313, 2162727541210, 2341127541313, 2380527541012, 2419827541213, 2465927541313, 2603727541012, 2764327541113, 2804827541113, 2826527541010, 2863327541212, 2993227541011, 3126027541012, 3203627541010, 3571927541311, 3674427541111, 4000927541110, 4088427541213, 4096927541113, 4204027541311, 4214627541013, 4284327541210, 4352927541313, 4460727541012, 4511627541013, 4671927541111, 4786827541210, 4879727541013, 4948327541113, 5095827541012, 5536227541213, 6275927541010, 6450127541110, 6486127541113, 6619127541010, 6742527541312, 7232027541310, 7398827541313, 7521427541113, 7551427541311, 7598527541011, 8452727541112, 8524627541113, 8631327541210, 9139327541011, 9177327541012, 9205427541112, 9237127541311, 9797627541112
131311

概要
--

131311は素数である。3枚出し最強素数。

通称KKJ（ケーケージェー）

## 131311を含む素数

* 3131311
* 6131311
* 48131311
* 52131311
* 63131311
* 64131311(虫KKJ)
* 69131311(ロックKKJ)
* 82131311
* 85131311
* 97131311
* 393131311(酢酸KKJ)
* 396131311(ザクロKKJ)
* 399131311
* 459131311(四国KKJ)
* 654131311
* 663131311
* 664131311

* 753131311
* 823131311(羽生さんKKJ)
* 838131311(矢沢KKJ)
* 852131311
* 862131311
* 883131311(やばみKKJ)
* 969131311(クロックKKJ)
* 987131311
* 4410131311(しし唐KKJ)
* 9103131311(工藤さんKKJ)
* 38310131311(サバサンドKKJ)
* 863102131311836593(ハムサンドにKKJ挟むコックさん)
* 4213381024371131311(静けさや岩にしみないKKJ)

## 131311の戦略

3枚出し最大素数なので、手札にKKJがそろっている場合はそれを切り札と考えて戦略を組む。

初期手札11枚の場合、手札分けにはいくつかのパターンが考えられる。

* （3枚の小さい素数）→（3枚の中くらいの素数）→（KKJ）→（2枚出し素数）
* （3枚の小さい素数）→（KKJ）→（5枚出し素数）
* （3枚の小さい素数）→（KKJ）→（グロタンカット）→（3枚出し素数）
* （3枚の小さい合成数出し）→（KKJ）→（1～2枚出し素数）
* （KKJ）→（8枚消費の3枚出し合成数）
* （KKJ）→（グロタンカット）→（グロタンカット）→（4枚出し素数）

先手でKKJがある場合は、以上のような戦略で勝ち筋が見える。

## 関連項目

素数大富豪素数の一覧/1～4枚出し

13111211
210四つ子素数

概要
--

210四つ子素数とは210を含む四つ子素数である。

例

538210, 6421012, 8026210, 8290210, 8707210, 10579210, 12982210, 15490210, 24754210, 25318210, 33100210, 37228210, 39034210, 42109210, 43693210, 45154210, 46675210, 47863210, 50089210, 60853210, 62680210, 67297210, 92014210, 94597210, 99406210, 176521012, 179121013, 204821011, 318721012, 419021011, 538721011, 539121010, 640521010, 999721012, 1069021012, 1293021010, 1479121012, 1508921011, 1967121010, 2248121011, 2441821012, 2498421010, 2828821012, 2987321011, 3255121012, 3614821012, 4318221010, 4924221013, 5378821012, 5519421010, 5545721011, 5613921013, 5796121012, 5935721011, 5945621011, 5987821012, 6082121011, 6230321011, 6299521012, 6912101113, 7055021011, 7212121012, 7396821013, 7435221013, 7637121010, 7772721010, 8146621012, 8193821011, 9121021012, 9165021010, 9573021013, 9653821012, 9825021013, 9962921011, 10632101110, 17902101313, 24542101111, 27242101111, 43682101111, 46772101111, 65792101210, 66752101312, 72582101110, 76772101213, 86742101311, 88402101112, 91952101312, 92192101111, 97622101312, 110662101310, 130102101211, 138002101210, 141852101011, 142522101013, 149732101111, 163172101312, 166472101213, 169702101010, 177682101313, 179832101212, 181372101013, 182602101013, 193072101013, 199762101211, 223232101312, 252732101212, 259022101210, 276132101110, 277392101113, 282752101213, 286632101311, 305412101011, 319292101210, 323122101013, 323812101313, 332132101012, 341092101211, 351832101010, 356052101212, 366082101211, 377682101011, 378592101310, 381582101113, 386862101113, 394862101012, 396722101210, 398402101312, 414772101112, 423312101311, 433922101210, 449012101210, 457162101313, 479412101311, 482042101213, 519822101011, 524522101213, 527092101112, 541112101213, 551912101312, 552932101312, 585702101113, 585762101212, 602002101310, 612212101012, 617262101011, 626422101310, 632012101012, 637012101010, 637482101212, 641592101011, 648872101312, 658202101210, 658492101310, 660912101011, 669152101210, 682962101113, 707802101011, 714462101113, 714972101212, 716282101111, 719752101010, 724472101111, 737302101112, 766182101011, 777882101011, 780042101011, 784352101312, 794532101011, 794802101110, 806032101010, 857882101312, 859732101313, 876682101310, 923192101210, 924852101311, 935092101112, 963022101112, 974102101213, 976052101312, 990862101013, 996392101111
7109四つ子素数

概要
--

7109四つ子素数は7109を含む四つ子素数である。

例

67887109, 131727109, 158157109, 252687109, 332667109, 372627109, 460377109, 548757109, 558057109, 561807109, 619317109, 749757109, 780027109, 2544710911, 3658710910, 4476710911, 4516710913, 4557710911, 6973710913, 10134710911, 10597710910, 12368710912, 12494710912, 12958710910, 15487710913, 15795710911, 20034710911, 24676710910, 25894710913, 28456710913, 41664710911, 42399710911, 46254710911, 48235710913, 51450710911, 58236710911, 71800710910, 74592710911, 74855710912, 77617710913, 79861710913, 80852710912, 82015710913, 89103710911, 135271091212, 202571091112, 307571091112, 492771091111, 579371091010, 611471091010, 644571091312, 676471091311, 752171091313, 755771091211, 848871091111, 1064371091311, 1110571091110, 1225771091011, 1284771091213, 1638271091110, 1652571091111, 1700571091213, 1792471091311, 2113771091113, 2309071091113, 2340371091112, 2490771091210, 2610971091013, 2747071091110, 2987971091110, 3040171091212, 3061271091313, 3062671091110, 3086171091013, 3090671091112, 3320771091013, 3404171091112, 3578771091211, 3604871091211, 3716371091212, 3816071091313, 3872071091311, 3995071091110, 4038671091010, 4284071091310, 4287071091313, 4349571091111, 4428571091113, 4488171091111, 4581271091311, 4686971091010, 4693471091212, 4708571091010, 4733571091012, 4792571091211, 4908171091213, 5443471091110, 5567171091310, 5678071091110, 5884171091011, 6116871091012, 6188971091110, 6255071091211, 6617971091110, 6689971091212, 6700171091113, 6716371091113, 6772971091213, 7045871091313, 7201571091013, 7287771091210, 7298971091011, 7386971091211, 7454771091211, 7611771091111, 7630971091210, 8526371091211, 8961671091313, 9116271091210, 9373771091011, 9461671091113, 9468371091313, 9560171091112
6枚出し7桁四つ子素数

概要
--

絵札を1枚用いる6枚出し7桁四つ子素数について記す。

例

* 116824x(いいロバ西)
* 123343x(ひふみんの刺身)
* 165310x(歩こう佐藤)
* 165910x(歩こう工藤)
* 171181x(いないいっぱい)
* 210766x(ニートな六浪)
* 256126x(煮込むアフロ)
* 310327x(里見ニーナ)
* 451048x(仕事しや)
* 538210x(ゴミはニート)
* 548413x(小柴死刑)
* 610291x(武藤憎い)
* 610648x(武藤虫歯)
* 651019x(婿TOEIC)
* 781336x(ナンパキング三郎)
* 786103x(悩む父さん)
* 810853x(ハトはゴミ)
* 831241x(野菜強い)
* 987610x

一覧
--

[101536, 102238, 102394, 102775, 104359, 106396, 106825, 109126, 109399, 111781, 111886, 112183, 112213, 112666, 113788, 114679, 115561, 115783, 116371, 116824, 117253, 117358, 118228, 121087, 122839, 123343, 124624, 124636, 127228, 128551, 129811, 132217, 132259, 132457, 133726, 135124, 136846, 138127, 141097, 163105, 165310, 165910, 171181, 191026, 191245, 210766, 211657, 213613, 238108, 241342, 253510, 255211, 256126, 271237, 276412, 310147, 310327, 312961, 351223, 351298, 371344, 374116, 383713, 385411, 411034, 413824, 441358, 451048, 483313, 538210, 548413, 561046, 610291, 610648, 613621, 621379, 626137, 637813, 647113, 651019, 656101, 661333, 662128, 664135, 715114, 761092, 764137, 768136, 781336, 786103, 791323, 810178, 810853, 831241, 831391, 838510, 843106, 851317, 865810, 874114, 912763, 913813, 951142, 954910, 987610, 991075]
13111211

概要
--

13111211は素数である。4枚出し最強素数。

通称KJQJ（ケージェーキュージェー）

## 13111211を含む素数

213111211

513111211

3313111211

4713111211

4813111211

6913111211(ロックKJQJ)

7113111211

7513111211

8113111211

8613111211

8913111211

21213111211

22213111211

41113111211

44313111211(しじみKJQJ)

52413111211(小西KJQJ)

56713111211

64213111211(虫にKJQJ)

67813111211

71113111211(セブンイレブンKJQJ)

75813111211(名古屋KJQJ)

87313111211(花見KJQJ)

88413111211(林KJQJ)

121213111211

122413111211(クリスマスイブKJQJ)

910113111211(くどいKJQJ)

4101013111211

4121013111211

4121313111211

6101113111211

7121013111211

8121213111211

9131013111211

12121213111211

## 13111211の戦略

4枚出し最大素数なので、手札にKJQJがそろっている場合はそれを切り札と考えて戦略を組む。

初期手札11枚の場合、（4枚の小さい素数）→（KJQJ）→（3枚出し素数）と手札分けすることで、先手の場合にかなり確実に勝つことができる。
66105四つ子素数

概要
--

66105四つ子素数は66105を含む四つ子素数である。

例

443566105, 536610511, 1847866105, 2660566105, 2816610511, 5299366105, 6913066105, 7300066105, 7456610512, 7866610510, 59346610510, 93726610510, 107056610512, 164176610512, 316976610511, 429126610510, 467396610511, 500316610510, 501661051111, 503886610510, 571726610512, 609746610511, 685606610512, 711776610511, 889686610513, 945486610510, 2194661051110, 2330661051010, 3069661051012, 4458661051213, 6020661051112, 6853661051011, 10677661051312, 10890661051210, 11609661051313, 12677661051310, 17244661051012, 18974661051013, 20171661051013, 21069661051213, 21299661051112, 22774661051311, 25140661051213, 28669661051113, 28733661051310, 29366661051010, 30434661051313, 32708661051013, 34675661051011, 36969661051312, 38158661051110, 39214661051011, 41100661051213, 44777661051310, 45819661051312, 46004661051310, 49429661051011, 54277661051113, 56232661051012, 57825661051012, 59193661051012, 60250661051110, 61399661051011, 62237661051310, 63643661051113, 65791661051110, 65904661051213, 66199661051011, 66830661051211, 68874661051213, 72552661051111, 72869661051010, 74618661051313, 75523661051212, 75618661051312, 80193661051213, 84625661051212, 85060661051311, 85179661051012, 90038661051211, 90821661051313, 93301661051110, 95180661051211
344161

概要
--

344161は素数である。語呂はミシシッピロイ。左に3,6,9,39,63,96を付けて素数になる裏弥勒オロチ数。

## 344161を含む素数

* 3344161
* 6344161
* 9344161
* 39344161
* 63344161
* 96344161
* 3441611
* 3441617
* 6183441197(ロイはミシシッピ行くな)

## 344161と合わせて覚えたい素数

* 41641(よいロシア)
* 41x41(x=1,3,6,9,12)
* 33442x(x=1,3,7,9)

余談
--

* 3441611と3441617が素数なので実質四つ子素数。
* 3と4の処理に困ったら使える。

## 関連項目

* 1151
* 未分類素数
* https://ja.m.wikipedia.org/wiki/ミシシッピ州
1110291

概要
--

1110291は合成数である(3 \* 7^3 \* 13 \* 83)。

## 1110291を含む素数

* 素数と1110291の組み合わせシリーズ(33個)

311110291, 471110291, 711110291, 971110291, 1071110291, 1091110291, 1131110291, 1791110291, 1911110291, 1991110291, 2111110291, 2771110291, 2831110291, 3591110291, 3671110291, 3791110291, 4091110291, 4211110291, 4611110291, 4671110291, 4871110291, 5631110291, 6411110291, 6731110291, 7091110291, 7731110291, 7971110291, 8211110291, 8271110291, 8591110291, 8871110291, 9111110291, 9971110291

## 1110291を含む語呂素数

* 4211110291(しずえJT憎い)
* 7731110291(ななみJT憎い)

余談
--

* 1110291の素因数分解から1001チェックは容易である。
* 3桁以下の素数と1110291の組み合わせが素数になる確率は33/168 ≒ 0.2である。

## 関連項目

* 合成数
* ブースター
40009

**40009**は、素数大富豪で出すことのできない最小の素数である。素数大富豪で出すことのできない素数をエデンの園素数または非素数大富豪素数と呼ぶこともある。

## 40009が素数大富豪で出すことのできない最小の素数であることの証明

定理1：4桁以下の素数に含まれる0は高々2個である。

証明：1桁、2桁の場合は自明。3桁の場合は、百の位は0でないので十の位と一の位が0となるが、このような数は明らかに100の倍数であり、素数ではない。4桁の場合は、百、十、一の位が0となりえるが、一の位が0の場合は10の倍数となり素数ではない。したがって0は百の位と十の位にしか入らない。2つの桁に0が入る可能性があるので、4桁以下の素数に含まれる0は高々2個である。

定理2：4桁以下の素数はすべて素数大富豪素数である。

証明：各桁の数を表すカードを並べることにより、4桁以下の全ての数を出すことができる。使うカードは高々4枚なので、すべての桁が同じ数となってもそのカードが足りなくなることはない。また、定理1より0の数は最大2個なので、0のためのジョーカーが足りなくなることはなく、4桁以下の素数はすべて素数大富豪で出すことができる。素数大富豪で出すことができる素数は素数大富豪素数と呼ぶので、4桁以下の素数はすべて素数大富豪素数である。

定理3：同じ0以外の数字が5個並んだ5桁の数は、素数ではない。

証明：並ぶ数字をnとすると、nが5個並んだ数は10000n+1000n+100n+10n+nと表すことができ、11111nに等しい。n>2のときは11111nはnを約数に持つので、素数ではない。n=1のときは11111n=11111となり、11111は41\*271と素因数分解できるので素数ではない。したがって、同じ0以外の数字が5個並んだ5桁の数は、素数ではない。

定理4：5桁の素数のうち素数大富豪素数でないものは、千、百と十の位が0であり、万の位が1でなく、一の位は1、3、7か9のうちのどれかである。

証明：各桁の数表すカードを並べることにより、5桁のほとんどの素数を出すことができるが、同じ数のカードを5枚必要とするものやジョーカーを3枚必要とするものは出すことができない。同じ数のカードを5枚必要とするものは、定理3より素数ではない。ジョーカーを３つ必要とするとはすなわち０を３つ含むということであり、万の位と一の位は0となりえないので、千、百と十の位は0となる。また、万の位が1であるものは、万の位と千の位を合わせて10のカードを使って出すことができるので、素数大富豪素数である。一の位が5や0である数は5の倍数、一の位が2、4、6か8である数は2の倍数であり、素数ではない。よって、5桁の素数のうち素数大富豪素数でないものは、千、百と十の位が0であり、万の位が1でなく、一の位は1、3、7か9のうちのどれかである。

5桁の数のうち、千、百と十の位が0であり、万の位が1でなく、一の位が1、3、7か9のうちのどれかであるような数の集合をSと定義する。Sの要素は、20001、20003、20007、20009、30001、30003、30007、30009、40001、40003、40007、40009、50001、50003、50007、50009、60001、60003、60007、60009、70001、70003、70007、70009、80001、80003、80007、80009、90001、90003、90007、90009である。

定理5：Sの要素である最小の素数は40009である。

証明：20001は3×59×113、20003は83×241、20007は3^4×13×19、20009は11×17×107、30001は19×1579、30003は3×73×137、30007は37×811、30009は3×7×1429、40001は13×17×181、40003は109×367、40007は11×3637と素因数分解できるため、すべて素数ではない。40009は素数である。よって、Sの要素である最小の素数は40009である。

定理6：素数大富豪で出すことのできない最小の素数は40009である。

証明：素数大富豪で出すことのできない最小の素数をpと置く。定理2より、p>10000である。また、定理4より、p<100000ならばp∈Sである。よって、Sの要素である最小の素数をpSと置くと、pSが存在するならばp=pSである。定理5よりpS=40009なので、p=40009である。したがって、素数大富豪で出すことのできない最小の素数は40009である。

## 関連項目

* 素数大富豪素数
* エデンの園素数
* 非素数大富豪素数
* 128
* 307
* 2003
* 70001
* 70003
* 70009
* 90001
* 90007

出典
--

1. ↑ http://integers.hatenablog.com/entry/2016/02/21/235655
2. ↑ http://nisei.hatenablog.com/entry/40009
24103四つ子素数

概要
--

24103四つ子素数は24103を含む四つ子素数である。

例

75324103, 84924103, 313241038, 692410318, 812410345, 813624103, 1267241032, 1641241036, 1762410331, 1852241032, 1998241036, 2393241037, 2535241033, 2536241032, 3245241037, 3292410385, 4229241031, 4527241036, 6343241038, 7018241032, 7024103119, 9277241032, 10442410357, 10892410366, 11332410388, 12122410396, 14042410348, 14642410315, 15322410349, 15652410397, 18842410345, 19972410319, 21012410392, 21122410342, 21782410324, 23712410389, 25812410338, 27272410357, 27824103109, 29532410314, 32222410384, 33922410394, 34362410335, 37152410338, 37952410399, 39162410386, 39672410338, 40852410343, 40924103137, 41562410377, 44902410337, 46462410394, 46562410375, 49172410339, 49382410369, 50062410382, 50082410383, 52882410367, 53122410358, 53222410312, 53442410353, 54232410331, 54862410319, 57252410314, 59872410316, 60712410358, 61152410338, 61624103413, 62062410352, 62542410337, 65552410318, 66262410385, 66522410398, 68632410346, 69982410310, 70512410344, 75492410383, 79442410339, 81002410315, 81992410351, 83072410324, 85922410348, 88252410373, 93702410329, 94622410396, 96092410354, 97072410382, 97072410391, 97712410351, 99632410363, 99722410369, 151824103411, 164824103113, 234924103510, 258024103510, 314124103123, 379924103413, 387024103210, 446124103612, 447724103107, 455824103311, 459924103126, 461124103912, 470424103105, 477624103129, 478224103117, 524324103511, 548324103412, 549524103913, 597224103124, 644624103310, 661124103811, 711724103107, 725324103913, 757224103123, 800324103106, 807724103812, 817824103111, 831224103610, 831424103413, 980424103510, 986524103125, 2135241031213, 4471241031010, 6598241031310, 7902241031011