OpenLLM-France/wikimedia huggingface dataset:
# Lucas primality test

In computational number theory, the Lucas test is a primality test for a natural number n; it requires that the prime factors of n − 1 be already known. It is the basis of the Pratt certificate that gives a concise verification that n is prime.

## Concepts

Let n be a positive integer. If there exists an integer a, 1 < a < n, such that
    $a^{n-1}\ \equiv \ 1{\pmod {n}}\,$
and for every prime factor q of n − 1
    $a^{({n-1})/q}\ \not \equiv \ 1{\pmod {n}}\,$
then n is prime. If no such number a exists, then n is either 1, 2, or composite.
The reason for the correctness of this claim is as follows: if the first equivalence holds for a, we can deduce that a and n are coprime. If a also survives the second step, then the order of a in the group (Z/nZ)* is equal to n−1, which means that the order of that group is n−1 (because the order of every element of a group divides the order of the group), implying that n is prime. Conversely, if n is prime, then there exists a primitive root modulo n, or generator of the group (Z/nZ)*. Such a generator has order |(Z/nZ)*| = n−1 and both equivalences will hold for any such primitive root.
Note that if there exists an a < n such that the first equivalence fails, a is called a Fermat witness for the compositeness of n.

## Example

For example, take n = 71. Then n − 1 = 70 and the prime factors of 70 are 2, 5 and 7. We randomly select an a=17 < n. Now we compute:
    $17^{70}\ \equiv \ 1{\pmod {71}}.$
For all integers a it is known that
    $a^{n-1}\equiv 1{\pmod {n}}\ {\text{ if and only if }}{\text{ ord}}(a)|(n-1).$
Therefore, the multiplicative order of 17 (mod 71) is not necessarily 70 because some factor of 70 may also work above. So check 70 divided by its prime factors:
    $17^{35}\ \equiv \ 70\ \not \equiv \ 1{\pmod {71}}$
    $17^{14}\ \equiv \ 25\ \not \equiv \ 1{\pmod {71}}$
    $17^{10}\ \equiv \ 1\ \equiv \ 1{\pmod {71}}.$
Unfortunately, we get that 17$^{10}$≡1 (mod 71). So we still don't know if 71 is prime or not.
We try another random a, this time choosing a = 11. Now we compute:
    $11^{70}\ \equiv \ 1{\pmod {71}}.$
Again, this does not show that the multiplicative order of 11 (mod 71) is 70 because some factor of 70 may also work. So check 70 divided by its prime factors:
    $11^{35}\ \equiv \ 70\ \not \equiv \ 1{\pmod {71}}$
    $11^{14}\ \equiv \ 54\ \not \equiv \ 1{\pmod {71}}$
    $11^{10}\ \equiv \ 32\ \not \equiv \ 1{\pmod {71}}.$
So the multiplicative order of 11 (mod 71) is 70, and thus 71 is prime.
(To carry out these modular exponentiations, one could use a fast exponentiation algorithm like binary or addition-chain exponentiation).

## Algorithm

The algorithm can be written in pseudocode as follows:
# Vince Sheehan (rugby league, South Sydney)

Vince Sheehan (?–1926) was an Australian rugby league footballer who played in the 1910s and 1920s. He played for South Sydney in the New South Wales Rugby League (NSWRL) competition.

## Playing career

Sheehan made his first grade debut for South Sydney in round 9 of the 1917 season against Annandale at Wentworth Park.
In 1918, Sheehan played eight games and scored five tries as South Sydney won the premiership that year. In 1919, he was selected to play for New South Wales and made one appearance where he scored two tries against Queensland. He was selected for New South Wales to tour New Zealand but broke his collar bone on the eve of the trip.
Sheehan retired following the conclusion of the 1922 season.
# Llusca Ritti (Corani)

Llusca Ritti (possibly from Quechua llusk'a polished / slippery, rit'i snow, "polished snow" or "slippery snow") is a mountain in the Vilcanota mountain range in the Andes of Peru, about 5,200 metres (17,060 ft) high. It is located in the Puno Region, Carabaya Province, Corani District. Llusca Ritti lies southeast of the mountains Taruca Sayana and Quello Sallayoc, southwest of the mountain Riti Huasi and north of the mountain Yana Sallayoc.
Intermittent streams originates northeast and southeast of Llusca Ritti. Their waters flow to a lake named Quicho Suytococha and then to the river Lajamayu.
# Blackpool United Hebrew Congregation

The Blackpool United Hebrew Congregation is a former Orthodox Jewish congregation and synagogue, located on Leamington Road, Blackpool, Lancashire, England, in the United Kingdom. The congregation worshiped in the Ashkenazi rite. The former synagogue building was listed as a Grade II building in 1998.

## History

The Blackpool United Hebrew Congregation was founded in about 1907 with the merger of Blackpool Hebrew Congregation which had been founded in 1898 and Blackpool New Orthodox Hebrew Congregation (founded in 1905). The synagogue was originally located in Springfield Road, North Shore. The synagogue in Leamington Road was consecrated in 1916.
It was a provincial synagogue under the aegis of the Chief Rabbi of the United Kingdom.
The synagogue building, designed by Blackpool alderman and justice of the peace Robert Butcher Mather in the Byzantine Revival style, is Grade II listed It was built between 1916 and 1926 and was later altered in 1955 and 1976.
On 8 February 2009, the synagogue hosted a visit by Jonathan Sacks, the Chief Rabbi of the United Hebrew Congregations of the United Kingdom. The visit was arranged by Eric Moonman, the president of the Zionist Federation of Great Britain and Ireland.
The synagogue closed in May 2012, as the community numbers had fallen below a viable congregation. The last service, conducted by Cantor Stephen Robins ARCM, was held on 13 May 2012 accompanied by the Shabbaton Choir. The synagogue was packed for the occasion with many former members and children and grandchildren of congregants from previous years attending. The sermon was given by Rabbi Arnold Saunders of Manchester, a previous Minister.
The last Minister of the synagogue was Rabbi David Braunold who assumed the pulpit in 1985 and departed for the St Anne's Hebrew Congregation in 2010. Rabbi Braunold gave the welcoming address at the last service.
The community merged with the one in St Annes. The building was sold in 2012, and again in 2019.
# Bob LeBlanc

Robert Leron LeBlanc (born November 5, 1962) is an American former professional football linebacker who played 4 seasons in the National Football League (NFL) for the Dallas Cowboys Buffalo Bills New York Jets. He played college football at Coffeyville Community College and Elon.

## Early life and education

LeBlanc was born on November 5, 1962, in Panama City, Florida. He attended Shawnee Mission South High School in Overland Park, Kansas, graduating in c. 1983. He first played college football for Coffeyville Community College, spending the 1981 and 1982 seasons there before transferring to Elon University. He played two years there, from 1984 to 1985, at linebacker, before graduating in 1985.

## Professional career

After going unselected in the 1985 NFL draft, LeBlanc was signed as an undrafted free agent by the Dallas Cowboys, only to be released when he failed a physical test.
LeBlanc moved to the Canadian Football League (CFL) later in the year, being signed by the Calgary Stampeders to their practice roster on August 14.
He left the Stampeders during the 1987 NFL strike to be signed by the Buffalo Bills. He was named starter for their game against the Indianapolis Colts, and made his professional debut in the 47–6 loss. He appeared in a total of three games, each as a starter, before being released.
LeBlanc was signed by the New York Jets in 1988, but was placed on season-ending injured reserve.
# Vinyl BC

Vinyl Basketball Club, also known as Vinyl BC, is an American professional basketball team. They are a member of the Unrivaled basketball league, and made their debut in 2025. The team is currently based in Miami, Florida. They are led by coach Teresa Weatherspoon.

## History

On October 24, 2024, the Unrivaled basketball league announced the names and logos of six teams joining its league, which are Laces BC, Lunar Owls BC, Mist BC, Rose BC, Phantom BC, and Vinyl BC. Vinyl BC, along with the other five teams, will be based in Miami, Florida for the inaugural 2025 season, before the teams travel more frequently during the 2026 season. The six head coaches were later hired on November 15.

## Roster

On November 20, 2024, the six head coaches collaborated on balancing and choosing the rosters for the six teams. Vinyl BC’s roster was finalized with Arike Ogunbowale, Jordin Canada, Rhyne Howard, Rae Burrell, Aliyah Boston and Dearica Hamby as its players.
Vinyl BC Roster :
| Players |||||||
| Arike Ogunbowale | Jordin Canada | Rhyne Howard | Rae Burrell | Aliyah Boston | Dearica Hamby |

## 2025 schedule
### Regular season

2025 Vinyl BC Total: 5–9 (Home: 3–4; Road: 2–5) :
January: 2–2 (Home: 1–1; Road: 1–1)
GameDateTeamScoreHigh pointsHigh reboundsHigh assistsLocationRecord
1
January 17
@ Rose BC
W 79–73
Rhyne Howard (33)
Dearica Hamby (13)
Dearica Hamby (4)
Wayfair Arena
1–0
2
January 20
Phantom BC
W 84–69
Dearica Hamby (22)
Rhyne Howard (8)
Tied – 3 players (4)
2–0
3
January 24
@ Laces BC
L 79–83
Dearica Hamby (18)
Dearica Hamby (8)
Tied – 3 players (4)
Wayfair Arena
2–1
4
January 27
Lunar Owls BC
L 57–67
Boston & Canada (14)
Arike Ogunbowale (10)
Arike Ogunbowale (7)
2–2 :
February: 3–4 (Home: 2–1; Road: 1–3)
GameDateTeamScoreHigh pointsHigh reboundsHigh assistsLocationRecord
5
February 1
@ Mist BC
L 67–77
Dearica Hamby (35)
Dearica Hamby (15)
Arike Ogunbowale (6)
Wayfair Arena
2–3
6
February 3
@ Lunar Owls BC
L 68–85
Rhyne Howard (21)
Dearica Hamby (10)
Tied – 3 players (3)
2–4
7
February 8
Laces BC
W 11–0
Game canceled – Laces forfeit
3–4
8
February 18
Rose BC
L 55–61
Rhyne Howard (24)
Dearica Hamby (11)
Burrell & Ogunbowale (3)
Wayfair Arena
3–5
9
February 21
Mist BC
W 72–65
Rhyne Howard (26)
Dearica Hamby (9)
Jordin Canada (5)
Wayfair Arena
4–5
10
February 22
@ Phantom BC
L 72-79
Rhyne Howard (28)
Jordin Canada (10)
Jordin Canada (8)
Wayfair Arena
4-6
11
February 28
@ Laces BC
W 64-63
Rhyne Howard (24)
Aliyah Boston (10)
Jordin Canada (6)
Wayfair Arena
5-6 :
March: 0–3 (Home: 0–2; Road: 0–1)
GameDateTeamScoreHigh pointsHigh reboundsHigh assistsLocationRecord
12
March 1
Lunar Owls BC
L 72-78
Dearica Hamby (31)
Dearica Hamby (11)
Jordin Canada (8)
Wayfair Arena
5-7
13
March 8
Phantom BC
L 74-80
Rhyne Howard (37)
Rhyne Howard (12)
Rhyne Howard (5)
5-8
14
March 10
@ Rose BC
L 46-74
Hamby & Howard (12)
Dearica Hamby (13)
Jordin Canada (3)
5-9 :

## 2025

Rhyne Howard was named to the All-Unrivaled Second Team.
# Anne Boleyn in the Tower of London

Anne Boleyn in the Tower of London or Anne Boleyn in the Tower of London Early in her Imprisonment is an oil on canvas painting by Édouard Cibot, from 1835. It was exhibited at that the Paris Salon of 1835. It is now held in the Musée Rolin, in Autun.
In 2014 it was lent to the Museum of Fine Arts of Lyon for the exhibition L'invention du Passé. Histoires de cœur et d'épée 1802-1850, then in 2015 to the musée du Luxembourg for Les Tudors.
# Con Sullivan

Cornelius Patrick Sullivan (31 July 1883 – 31 October 1964) was a New Zealand-born rugby league footballer who played in the 1900s and 1910s and represented New Zealand, Australia, and Australasia.

## Playing career

Sullivan started his career playing rugby in Wellington where he was a representative player. In 1909 he switched codes and was selected to tour Australia, winning an international cap for New Zealand against Australia in 1909. He played 5 other tour matches, scoring 2 tries. In 1910 he started playing for North Sydney in the NSWRFL Premiership. Later in the year he played 2 matches for the Wellington rugby league team against Taranaki and Auckland.
In his first year at the club he was selected to play for New South Wales, Australia (including the first Ashes test on Australian soil) and a combined "Australasia" team against the first Great Britain Lions tourists. The following year he was selected to go on the 1911–12 Kangaroo tour of Great Britain, and played in 16 matches, for Australasia, including the third Test. Sullivan toured New Zealand with the New South Wales side in 1912-13 and played his last Test series against England in 1914 in teams captained by his clubmate and brother-in-law Sid Deane.

## Later years

Sullivan later married Deane's sister with their son Bob Sullivan continuing the family link with the club. Bob Sullivan made a Test appearance for Australia in 1954. His younger brother John also played for Norths in the 1950s as a versatile back.
Con Sullivan died in October 1964.
# Frank Storie

Frank Storie (1883-1960) was an Australian rugby league footballer who played in the 1900s. He played for South Sydney in the New South Wales Rugby League (NSWRL) competition. Storie was a foundation player for South Sydney playing in the club's first ever game.

## Playing career

Storie made his first grade debut for Souths against North Sydney at Birchgrove Oval in Round 1 1908 which was the opening week of the NSWRL competition in Australia. Souths won the match 11–7 with Storie playing at centre.
Souths went on to claim the inaugural minor premiership in 1908 and reach the first NSWRL grand final against rivals Eastern Suburbs. Storie played at on the wing as Souths claimed their first premiership winning 14–12 at the Royal Agricultural Society Grounds in front of 4000 spectators.
In 1909, Storie played 5 times for the club as Souths claimed their second premiership in a row against Balmain in controversial circumstances. Balmain were furious that the 1909 NSWRL grand final was to be played as the under card to the Wallabies v Kangaroos match. Balmain attempted to stop the match being played and refused to take the field. Storie and the other South Sydney players attended the ground and then ran on the field, kicked off and scored a try after which they were declared premiers. Storie retired from rugby league after the conclusion of this match.
# Pariwana

Pariwana (Quechua for flamingo, Hispanicized spelling Parihuana) is a 5,022-metre-high (16,476 ft) mountain in the Andes of Peru. It is located in the Puno Region, Lampa Province, on the border of the districts of Palca and Vilavila. Pariwana lies north of Qillqa.
# Palomani

Palomani (possibly from Aymara, urpi, paluma dove, "the one with a dove (or doves)") is a mountain in the Apolobamba mountain range on the border of Bolivia and Peru. It reaches a height of about 5,723 metres (18,776 ft). On the Bolivian side it is located in the La Paz Department, Franz Tamayo Province, Pelechuco Municipality, and on the Peruvian side it lies in the Puno Region, Putina Province, Ananea District. It is situated north of Suches Lake. Palomani is south of Chaupi Orco (or Viscachani), Salluyu and Jichu Qullu, near Chocñacota in the west.
Adventure travel companies have offered guided tours to the area, including Andes Tours UK.
# Pomanota

Pomanota (possibly from Aymara puma cougar, puma, -n(i) a suffix, uta house, "house of the puma") is a mountain in the Vilcanota mountain range in the Andes of Peru, about 5,516 metres (18,097 ft) high. It is situated in the Cusco Region, Canchis Province, San Pablo District and in the Puno Region, Carabaya Province, Corani District as well as in the Melgar Province, Nuñoa District. Pomanota lies southeast of the Joyllor Puñuna, the highest elevation in the glaciated area of Quelccaya (Quechua for "snow plain"), and northwest of the Jonorana.
# Pucaparina

Pucaparina (possibly from Aymara puka colored, Quechua puka red, Aymara parina flamingo, "colored flamingo" or "red flamingo") is a mountain in the Vilcanota mountain range in the Andes of Peru, about 4,800 metres (15,748 ft) high. It lies in the Puno Region, Melgar Province, Nuñoa District.
# Pukara (Sandia)

Pukara (Quechua for fortress, Hispanicized spelling Pucara) is a mountain in the Andes of Peru, about 4,200-metre (13,800 ft) high, with an archaeological site on top. It is located in the Puno Region, Sandia Province, Patambuco District, southwest of Patambuco. The pre-Inca funerary site is also known as Trinchera (Spanish for trench). The place was declared a National Cultural Heritage by Resolución Directoral Nacional No. 296/INC-2003 by the National Institute of Culture. It consists of tombs, walls, houses, squares and tunnels.
# Pumajolluni

Pumajolluni (possibly from Aymara puma cougar, puma, qullu mountain, -ni a suffix to indicate ownership, "the one with a cougar mountain") is a mountain in the Carabaya mountain range in the Andes of Peru at a lake of the same name. The mountain is about 5,200 metres (17,060 ft) high. It is located in the Puno Region, Carabaya Province, on the border of the districts Ajoyani, Coasa and Ituata. It lies southwest of the mountain Chullumpirini.
The lake named Pumajolluni is situated south of the mountain at 14°04′40″S 70°12′20″W﻿ / ﻿14.07778°S 70.20556°W﻿ / -14.07778; -70.20556 between the lakes Vilacota in the northwest and Pampacocha and Ajojajota in the southeast.
# Qillqa (Melgar)

Qillqa (Quechua for writing (the act and art of writing) Hispanicized spelling Quilca) is a mountain in the Andes of Peru, about 4,900.9 metres (16,079 ft) high. It is located in the Puno Region, Melgar Province, Macari District, near the border with the Cusco Region, Espinar Province, Alto Pichigua District.
# Quellhuacotarriti

Quellhuacotarriti (Aymara qillwa, qiwña, qiwlla Andean gull, quta lake, Quechua rit'i snow, "gull lake snow (mountain)") is a mountain in the Carabaya mountain range in the Andes of Peru, about 5,200 m (17,100 ft) high. It is located in the Puno Region, Carabaya Province, Macusani District. Quellhuacotarriti lies southwest of Allincapac and south of Vela Cunca.
# Puxin railway station

25°00′15″N 121°26′41″E﻿ / ﻿25.004203°N 121.444693°E﻿ / 25.004203; 121.444693
Puxin station (traditional Chinese: 埔心車站; simplified Chinese: 埔心车站; pinyin: Bùxīn Chēzhàn) is a railway station on the Taiwan Railways Administration West Coast line located in Yangmei District, Taoyuan City, Taiwan.

## History

The station was opened in 1900 as Anpinzhen (Hetin) station (安平鎮招呼站). It changed its name to the current name on 1 March 1955. The station building on the south entrance was built on 31 January 1986 and an expansion on the north entrance was completed on 9 December 2002. It is only served by local trains. The station building caught fire on 5 May 2016, and the fire damage was repaired by August 2016.

## Around the station

* Kuo Yuan Ye Museum of Cake and Pastry (2,500 meters; 8,200 ft northwest of the station)
* Puxin Night Market (next to the station)
* Puxin Ranch (1,300 meters; 4,300 ft northwest of the station)
# 7-Chlorotryptamine

7-Chlorotryptamine (7-chloro-T, 7-CT, or 7-Cl-T; code name PAL-532) is a serotonin receptor agonist and monoamine releasing agent (MRA) of the tryptamine family. It is a pale yellow solid. It is a full agonist of the serotonin 5-HT$_{2A}$ receptor, with an EC$_{50}$Tooltip half-maximal effective concentration of 18.8 nM and an E$_{max}$Tooltip maximal efficacy of 102%. In addition, it is a serotonin releasing agent (SRA), with EC$_{50}$ values of 8.03 nM for serotonin, 656 nM for norepinephrine, and 1,330 nM for dopamine in rat brain synaptosomes. The drug is one of the most potent SRAs in vitro known, after 6-fluorotryptamine (6-FT) and naphthylaminopropane (NAP; PAL-287). 7-CT was first described in the scientific literature by 2014.
# Sumpiruni

Sumpiruni (possibly from Aymara sumpiru hat (a borrowing from Spanish sombrero), -ni a suffix to indicate ownership, "the one with a hat") is a 5,063-metre-high (16,611 ft) mountain in the Vilcanota mountain range in the Andes of Peru. It is situated in the Puno Region, Carabaya Province, Macusani District. Sumpiruni lies west of Catautira. This is where the Ninahuisa River originates. It flows along the southern slopes of Catautira before it turns to the northeast.
# Sagittarius Window Eclipsing Extrasolar Planet Search

g Extrasolar Planet Search, or SWEEPS, was a 2006 astronomical survey project using the Hubble Space Telescope's Advanced Camera for Surveys - Wide Field Channel to monitor 180,000 stars for seven days to detect extrasolar planets via the transit method.

## Area examined

The stars that were monitored in this astronomical survey were all located in the Sagittarius-I Window. The Sagittarius Window is a rare view to the Milky Way's central bulge stars: our view to most of the galaxy's central stars is generally blocked by lanes of dust. These stars in the galaxy's central bulge region are approximately 27,000 light years from Earth.

## Planets discovered

Sixteen candidate planets were discovered with orbital periods ranging from 0.6 to 4.2 days. Planets with orbital periods less than 1.2 days have not previously been detected, and have been dubbed "ultra-short period planets" (USPPs) by the search team. USPPs were discovered only around low-mass stars, suggesting that larger stars destroyed any planets orbiting so closely or that planets were unable to migrate as far inward around larger stars.
Planets were found with roughly the same frequency of occurrence as in the local neighborhood of Earth.
SWEEPS-4 and SWEEPS-11 orbited stars that were sufficiently visually distinct from their neighbors that follow-up observations using the radial velocity method were possible, allowing their masses to be determined.
This table is constructed from information obtained from the Extrasolar Planets Encyclopedia and SIMBAD databases that reference the Nature article as their source.
# Arundel Mill and Castle

Arundel Mill and Castle is an 1837 landscape painting by the English artist John Constable. Produced the year of his death, it depicts a scene on the River Arun in Sussex. In the foreground is a mill, while Arundel Castle is shown in the distance. Today it is in the Toledo Museum of Art in Toledo, Ohio, described as Constable's last painting. Constable had viewed the scene while visiting George Constable, a friend and brewer. He was working on the painting in 1836, but shelved it to complete Cenotaph to the Memory of Sir Joshua Reynolds in time for that year's Summer Exhibition at the Royal Academy. He resumed work on it the following year but died before its completion. His friend Charles Robert Leslie felt it was far enough advanced to exhibit posthumously at that year's Royal Academy Exhibition. Leslie believed that the scene had reminded Constable of the Stour Valley in his native Suffolk.
# Flagship Airlines

Flagship Airlines was an American regional airline headquartered on the grounds of Nashville International Airport in Nashville, Tennessee, United States.

## History

Flagship Airlines traced its origins to Air Virginia, a commuter and regional feeder air carrier, which later changed names to AVAir. AVAir had rapidly declined into bankruptcy following the AVAir Flight 3378 tragedy. AMR Corporation founded Nashville Eagle out of the assets of AVAir and Air Midwest. Flagship Airlines was formed by the merger of Command Airways into Nashville Eagle on June 1, 1991.
Flagship operated code sharing flights for American Airlines under the American Eagle brand name. The airline served the East Coast and the Bahamas from hubs at Miami, Nashville, New York-JFK, and Raleigh/Durham. The Raleigh/Durham based closed on December 28, 1994.
Ultimately, Flagship Airlines merged with Simmons Airlines and Wings West Airlines to form American Eagle Airlines in 1998. The former Simmons IATA two letter code of MQ became the surviving identifier for the unified airlines. In 2014, the airline was renamed Envoy Air.

## Fleet

Flagship Airlines fleet in 1994 :
| Aircraft | Total | Passengers |
| ATR-42 | 14 | 46 |
| BAe Jetstream 32 | 48 | 19 |
| Saab 340 | 53 | 34 |
| Shorts 360 | 20 | 36 |

## Accident

On 13 December 1994, Flagship Airlines Flight 3379, operating for American Eagle, entered an aerodynamic stall and crashed into a wooded area during a missed approach to Raleigh–Durham International Airport in North Carolina. The two pilots and 13 of the 18 passengers were killed.