hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Furstenberg's proof of the infinitude of primes
In mathematics, particularly in number theory, Hillel Furstenberg's proof of the infinitude of primes is a topological proof that the integers contain infinitely many prime numbers.  When examined closely, the proof is less a statement about topology than a statement about certain properties of arithmetic sequences.  Unlike Euclid's classical proof, Furstenberg's proof is a proof by contradiction.  The proof was published in 1955 in the American Mathematical Monthly while he was still an undergraduate student at Yeshiva University.

Arithmetic progression
An arithmetic progression, arithmetic sequence or linear sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13, 15, ... is an arithmetic progression with a common difference of 2.

If the initial term of an arithmetic progression is  and the common difference of successive members is , then the -th term of the sequence () is given by

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.
Ilince
Ilince (Serbian Cyrillic: Илинце; Albanian: Ilincë) is a village in the municipality of Preševo, Serbia. According to the 2002 census, the village has a population of 136 people. Of these, 134 (98,52 %) were ethnic Albanians, and 2 (1,47 %) were Hungarians.

Municipalities and cities of Serbia
The municipalities and cities (Serbian: општине и градови / opštine i gradovi) are the first-level administrative division and the basic level of local government of Serbia. The country is divided into 145 municipalities and 29 cities.

Municipalities and cities form 29 administrative districts, except the City of Belgrade which is not part of any district.
Andraca melli
Andraca melli is a moth of the family Endromidae. It is found in China (Zhejiang, Jiangxi, Fujian, Guangdong, Hainan), Vietnam and Thailand.

The wingspan is 37–39 millimetres (1.5–1.5 in). The head is thinly covered with brown-green hairs. The forewings are bluntly pointed apically and the outer edge is smooth and straight. The tornus is nearly rectangular.

The larvae feed on Camellia sinensis, Camellia oleifera, Fraxinus pennsylvanica, Ternstroemia japonica and Pentaphylax euryoides.

Fraxinus pennsylvanica
Fraxinus pennsylvanica, the green ash or red ash, is a species of ash native to eastern and central North America, from Nova Scotia west to southeastern Alberta and eastern Colorado, south to northern Florida, and southwest to Oklahoma and eastern Texas. It has spread and become naturalized in much of the western United States and also in Argentina and Europe, from Spain to Russia.

Other names more rarely used include downy ash, swamp ash, and water ash.
Winberri
Winberri (c.1820 – 11 October 1840) was an Indigenous Australian resistance leader who, in 1840, led an armed group of Taungurung men in a campaign against British colonists in what is now called central Victoria. Also known as Winberry, Tinbury, or Windberry, he was shot dead in October 1840 by the New South Wales Mounted Police while they were arresting him during the Lettsom raid.

New South Wales Mounted Police
The New South Wales Mounted Police Unit is a mounted section of the New South Wales Police Force.

Founded by Governor Sir Thomas Brisbane on 7 September 1825, the Mounted Police were recruited from the 3rd Regiment of Foot, stationed in New South Wales at the time, to protect travellers, recaptured escaped convicts and suppress Indigenous resistance to colonisation. The force remained the mounted division of the colonial military force in the colony of New South Wales until 1850, when it took on a more civilian role.

The New South Wales Mounted Police Unit is the oldest continuous mounted group in the world.
Nana Oti Akenten
Nana Oti Akenten (ruled from 1630 – 1660) was the ruler of the Asante Oyoko clan which occupied parts of what is now Ghana. Nana Oti was the brother of Nana Kobia Antwi and their mother was Antwiwaa Nyame. Nana Oti sent his hunter called Bofoo Nyame on a trip and he discovered that the Agona family has already settled in a place called Kwaebrem which was later called Kwaabre. When the hunter learned that the area was productive, he went to tell Nana Oti. The settlement was then given the name Kumasi after the monarch, his family, and some of his followers opted to purchase that portion of the land from Agonaba Obaapanyin Adwoa Wiri. It was under his regime that a series of military operations against other Akan states came into alliance with the Ashanti. During his reign, there was a trend towards Ashanti military unification.

Kwabre District
Kwabre District is a former district that was located in Ashanti Region of Ghana.  Originally created as an ordinary district assembly in 1988, which it was created from the former Kwabre-Sekyere District Council; until the western part of the district was split off to become the southern portion of Afigya-Kwabre District on 1 November 2007 (effectively 29 February 2008); while the remaining portion has since then been officially renamed as Kwabre East District, which it was elevated to municipal district assembly status to become Kwabre East Municipal District on 1 November 2017 (effectively 15 March 2018). The district assembly was located in the northern part of Ashanti Region and had Mamponteng as its capital town.
Himesh Ramanayake
Himesh Ramanayake (born 5 October 1997) is a Sri Lankan cricketer. He made his first-class debut for Burgher Recreation Club in the 2017–18 Premier League Tournament on 8 December 2017. He made his Twenty20 debut for Burgher Recreation Club in the 2017–18 SLC Twenty20 Tournament on 25 February 2018. He made his List A debut for Burgher Recreation Club in the 2017–18 Premier Limited Overs Tournament on 10 March 2018.

In March 2018, he was named in Dambulla's squad for the 2017–18 Super Four Provincial Tournament. In October 2020, he was drafted by the Colombo Kings for the inaugural edition of the Lanka Premier League.

In March 2021, he was part of the Sinhalese Sports Club team that won the 2020–21 SLC Twenty20 Tournament, the first time they had won the tournament since 2005. In August 2021, he was named in the SLC Reds team for the 2021 SLC Invitational T20 League tournament.

Singhalese Sports Club
The Singhalese Sports Club (SSC) is a first-class cricket club in Colombo, Sri Lanka till 2025 when they were relegated after enduring a horrendous 2024-25 version of the  Major Club 3 day tournament in which they could only muster a single victory and lost two of their eight matches. Singhalese is the most successful club in Sri Lankan domestic cricket, having won the Premier Trophy a record 32 times to 2017. Although the name is correctly spelt with the old spelling "Singhalese", the name is sometimes misspelt with the modern spelling "Sinhalese". Three former Prime Ministers of Sri Lanka have been presidents of the club.
BAP1
BRCA1 associated protein-1 (ubiquitin carboxy-terminal hydrolase) is a deubiquitinating enzyme that in humans is encoded by the BAP1 gene. BAP1 encodes an 80.4 kDa nuclear-localizing protein with a ubiquitin carboxy-terminal hydrolase (UCH) domain that gives BAP1 its deubiquitinase activity.  Recent studies have shown that BAP1 and its fruit fly homolog, Calypso, are members of the polycomb-group proteins (PcG) of highly conserved transcriptional repressors required for long-term silencing of genes that regulate cell fate determination, stem cell pluripotency, and other developmental processes.

Cell potency
Cell potency is a cell's ability to differentiate into other cell types.
The more cell types a cell can differentiate into, the greater its potency. Potency is also described as the gene activation potential within a cell, which like a continuum, begins with totipotency to designate a cell with the most differentiation potential, pluripotency, multipotency, oligopotency, and finally unipotency.
Philip Moffat
Philip John Moffat (born 29 May 1975) is an English former first-class cricketer.

Moffat was born at Lancaster in May 1975. He was educated at Lancaster Royal Grammar School, before matriculating to the University of Leeds. From there he proceeded to Hughes Hall at the University of Cambridge. While studying at Cambridge, he played first-class cricket for Cambridge University Cricket Club in 1998, making five appearances. Playing as a medium pace bowler in the Cambridge side, he took 7 wickets at an average of 33.14, with best figures of 3 for 25. As a lower order batsman, he scored 34 runs with a highest score of 12. His brother, Gavin, was also a first-class cricketer.

Hughes Hall, Cambridge
Hughes Hall is a constituent college of the University of Cambridge in England. The majority of students are postgraduate, although nearly one-fifth of the student population comprises individuals aged 21 and above who are studying undergraduate degree courses. Hughes Hall was founded in the 19th century as the Cambridge Training College for Women with the purpose of providing a college dedicated to training women graduates for the teaching profession. Since then it has enlarged and expanded to support a community of students and researchers, both male and female, working in all the academic areas of the university.

The college is housed in a number of 19th- and 20th-century buildings at a main site adjacent to Fenner's, the Cambridge University Cricket Club ground, and between the City Centre and the railway station.
Network SouthEast
Network SouthEast (NSE) was one of the three passenger sectors of British Rail created in 1982. NSE mainly operated commuter rail trains within Greater London and inter-urban services in densely populated South East England, although the network went as far west as Exeter and also covered the inner East of England. Before 1986, the sector was originally known as London & South Eastern. During the privatisation of British Rail, it was gradually divided into a number of franchises.

Banbury railway station
Banbury railway station serves the historic market town of Banbury in Oxfordshire, England. The station is a stop on the Chiltern Main Line; it is operated by Chiltern Railways and has four platforms in use.
Tamara Shaverzashvili
Tamara Antonovna Shaverzashvili (Georgian: თამარ შავერზაშვილი; 14 October 1891 – 18 September 1955) was a Georgian composer, pianist, and teacher who composed many children's songs and received an title Honored Worker in Art of the Georgian SSR. She published her music under the name Tamara Shaverzashvili.

Shaverzashvili was born in Kutaisi. She graduated from the Tiflis Music School, where she studied piano and composition with Vladimir Shcherbachov and Iona Tuskia. Later, she studied with Pyotr Ryazanov.

Shaverzashvili taught piano privately, and from 1935 to 1938, lived in Tbilisi and taught at the Z. Paliashvili Central Music School. In 1938, she began teaching at the Tbilisi Conservatory and during her tenure there was awarded the Honored Worker in Art award in 1946. Baritone David Gamrekeli and pianist T. Dunenko recorded at least one of her songs commercially in 1938.

Shaverzashvili's compositions included:

Vladimir Shcherbachov
Vladimir Vladimirovich Shcherbachov (Shcherbachyov, Shcherbachev)  (Russian: Влади́мир Влади́мирович Щербачёв; 25 January 1889, in Warsaw – 5 March 1952, in Leningrad) was a Soviet composer.

He studied with Maximilian Steinberg, Anatoly Lyadov, and Jāzeps Vītols (Joseph Wihtol) at the St. Petersburg Conservatory from 1908 to 1914. While there he also worked as a pianist for Sergey Diaghilev and taught theory. He served in World War I and then worked in Soviet government music positions. In 1918-1923 he worked as a lecturer and ran the musical department of the Narkompros. He later became a professor at the Leningrad Conservatory (1923-1931 and 1944-1948) and the Tbilisi Conservatory. He counted Boris Arapov, Vasily Velikanov, Evgeny Mravinsky, Valery Zhelobinsky, Gavriil Popov, Valerian Bogdanov-Berezovsky, Pyotr Ryazanov, and Mikhail Chulaki among his pupils, as well as various others.
Catapyrenium
Catapyrenium is a genus of squamulose lichens in the family Verrucariaceae. These small lichens grow as clusters of tiny scales (squamules that lie flat against rocks and soil, often in dry or disturbed habitats. The genus includes about 18 species found worldwide, particularly in arid and semi-arid regions where they help stabilize soil surfaces.

Aridity
Aridity is the condition of geographical regions which make up approximately 43% of total global available land area, characterized by low annual precipitation, increased temperatures, and limited water availability. These areas tend to fall upon degraded soils, and their health and functioning are key necessities of regulating ecosystems’ atmospheric components.
Mallam Aminu Kano International Airport
Mallam Aminu Kano International Airport (Hausa: Filin Jirgin Saman Mallami Aminu Kano, IATA: KAN, ICAO: DNKN) is an international airport serving Kano, the capital city of Kano State in Nigeria. It was a Royal Air Force station before the country became independent. It is the main airport serving northern Nigeria and was named after the 20th-century politician Aminu Kano. The airport has an international and a domestic terminal. Construction started on a new domestic terminal and was commissioned on 23 May 2011. In 2009, the airport handled 323,482 passengers. The bulk of international flights cater to the large Sudanese community in Kano and Muslim pilgrimages to Mecca.

International flight
An international flight is a form of commercial flight within civil aviation where the departure and the arrival take place in different countries.

Since its origins, international commercial flights have taken place with a variety of aircraft types including airplanes and airships. Modern international flight typically takes place on wide-body aircraft and involves immigration and customs formalities through international airports.
Stade Canac
Stade Canac is a baseball stadium in Quebec City, Quebec that is currently the home of the Québec Capitales of the Frontier League (FL). Originally opened in 1939, it has a seating capacity of 4,297 and is located within the boundaries of Parc Victoria, a municipal park and recreation area located between the St-Roch district of Quebec City and the south shore of the Saint-Charles River.

The ballpark is often informally referred to as simply "Parc Victoria" by local residents even though the field only occupies about a quarter of the park's total area. Modest in capacity relative to the size of the city's population, it has been well-attended during Capitales home games.

Ballpark
A ballpark, or baseball park, is a type of sports venue where baseball is played. The playing field is divided into two field sections called the infield and the outfield. The infield is an area whose dimensions are rigidly defined in part based on the placement of bases, and the outfield is where dimensions can vary widely from ballpark to ballpark. A larger ballpark may also be called a baseball stadium because it shares characteristics of other stadiums.
Qızıloba, Aghdara
Gyzyloba (Azerbaijani: Qızıloba) or Karmiravan (Armenian: Կարմիրավան) is a village in the Aghdara District of Azerbaijan, in the disputed region of Nagorno-Karabakh. The village was on the ceasefire line between the armed forces of the breakaway Republic of Artsakh and those of Azerbaijan. There have been allegations of ceasefire violations in the village's vicinity. The village had an ethnic Armenian-majority population in 1989.

Aghdara District
Aghdara District (Azerbaijani: Ağdərə rayonu) is one of the 67 districts of Azerbaijan. It is located in the west of the country in the Karabakh Economic Region. The district borders the districts of Goranboy, Tartar, Aghdam, Khojaly and Kalbajar. Its capital and largest city is Aghdara. As of 2024, the district had a nominal population of 12,100.

The district was officially abolished in 1992 and was only reestablished in 2023.
Axel Elveljung
Erik Axel Rickard Elveljung (born Erik Axel Rickard Johansson; 6 March 1989) is a Swedish footballer who plays as a striker for Rasbo IK. He has previously played for IF Brommapojkarna and Östers IF, as well as represented the Sweden U17 and U19 teams.

Sweden men's national under-17 football team
The Sweden men's national under-17 football team (Swedish: svenska pojklandslaget i fotboll) is the football team representing Sweden in competitions for under-17-year-old players. Primarily, it competes to qualify for the annual UEFA European Under-17 Championship.

In the 2013 UEFA European Under-17 Championship, Sweden reached the semi-finals where they were knocked out on penalties by Russia. In the 2013 FIFA U-17 World Cup they finished in third place after beating Argentina with 4–1 in the third-place match. Valmir Berisha scored three goals in the match and thus became the top scorer of the tournament.
Huay Pu Keng
Huay Pu Keng (Thai: ห้วยปูแกง) is a village located in the Mae Hong Son province, in the northwest of Thailand. The village is inhabited by the Tai Yai, a Thai ethnic community and four subgroups of the Karenni people, namely the Kayan, Kayaw, Red Karen and Pakayor. The Kayan women in particular became famous because tourists began to find interest in their long necks with brass rings.

Brass ring
A brass ring is a small, grabbable ring that a dispenser presents to a carousel rider during the course of a ride. These dispensers are filled with a large number of iron or steel rings and a single or a few brass rings. The rings can then be tossed at a target as the carousel rotates. Typically, a brass ring can be traded for a prize, which is often a free repeat ride. Although they were standard features for carousels during their heyday in the late 19th and early 20th centuries, brass ring dispensers are now rare. The figurative phrase to grab the brass ring is derived from this device.
Congo barb
The Congo barb (Clypeobarbus congicus) is a species of ray-finned fish belonging to the family Cyprinidae, the family which includes the carps, barbs and related fishes. This species is found in the basin of the Congo River in the Democratic Republic of Congo; and in the Ruzizi River in Burundi and the Malagarasi River in western Tanzania in East Africa.

Cyprinidae
Cyprinidae is a family of cyprinoid freshwater fishes commonly referred to as the carp family, which includes the carps, barbs, and barbels, among others. These cyprinids also share sister taxa with the danionins and minnows under the suborder Cyprinoidei. Cyprinidae is the largest and most diverse fish family, and the largest family of vertebrates overall, with roughly 1,780 species split into 166 valid genera.

Cyprinids range from the 12 mm (0.5 in)-long glassfishes, to the 3 m (9.8 ft) giant barb (Catlocarpio siamensis). The family name is derived from the Greek word kyprînos (κυπρῖνος 'carp').
Allied Boat Company
Allied Boat Company was a small manufacturer of fiberglass sailboats built in Catskill, New York.  The first design was by Thomas Gillmer in 1960, the 30-foot Seawind.  The first hull, Apogee became the first fiberglass boat to circumnavigate the globe in 1968.  The company officially formed on February 9, 1962.  Until 1981, they built various designs from 30 to 42 feet by naval architects such as Sparkman & Stephens, Bill Luders, and Frank Maclear/Robert Harris.  The company went out business four times during the later years.  The level of finish below was known to vary in quality.  Poor management contributed to their economic woes.

Catskill (town), New York
Catskill is a town in the southeastern section of Greene County, New York, United States, and is the county seat of Greene County. The population was 11,298 at the 2020 census, the largest town in the county. The western part of the town is in the Catskill Park. The town contains a village, also called Catskill. The village of Catskill has a well-defined Main Street. There is a public boat launch on the Hudson River called Dutchman's Landing.
Voluptas
In Roman mythology, Voluptas or Volupta is the daughter born from the union of Cupid and Psyche, according to Apuleius. The Latin word voluptas means 'pleasure' or 'delight'; Voluptas is known as the goddess of "sensual pleasures". She is often found in the company of the Gratiae, or Three Graces.

Some Roman authors mention a goddess named Volupia, a name which appears to signify "willingness". She had a temple, the Sacellum Volupiae, on the Via Nova, by the Porta Romana. Sacrifices were offered to the Diva Angerona there.

The corresponding goddess in Greek mythology is Hedone.

Charites
The Charites (/ˈkærɪtiːz/; Ancient Greek: Χάριτες; singular Charis (Χάρις), also called by the English translation the "Graces") are goddesses of Greek mythology who personify beauty and grace. According to Hesiod, their names were Aglaea, Euphrosyne, and Thalia and were the daughters of Zeus and Eurynome, the daughter of Oceanus. However, their names, number and parentage varied across accounts. They have little independent mythology, and are usually described as attending various gods and goddesses, particularly Aphrodite.

In Roman mythology, they were known by the Latin equivalent of the Greek: the Gratiae. In Roman and later art, they were generally depicted nude in an interlaced group, but during the Greek Archaic and Classical periods, they were typically depicted as fully clothed, in a line, and in dance poses.
Chestnut Grove (Glendale, Kentucky)
The Chestnut Grove, in Hardin County, Kentucky near Glendale, Kentucky, was built in 1876.  It was listed on the National Register of Historic Places in 1988.

It is a two-story, brick Italianate house, with brick laid in common bond, built upon a brick foundation.  Its front facade has four bays and a one-story porch with milled posts and dentils.  The south facade has another one-story porch with a shed roof, milled posts, and vergeboard decoration.  It has a two-story rear wing.

The interior includes original cast iron mantles and an Italianate-style staircase.

It is located off Kentucky Route 222 about 1 mile (1.6 km) west of Glendale.

Bargeboard
A bargeboard or rake fascia is a board fastened to each projecting gable of a roof to give it strength and protection, and to conceal the otherwise exposed end grain of the horizontal timbers or purlins of the roof. The word bargeboard is probably from the Medieval Latin bargus, or barcus, a scaffold, and not from the now obsolete synonym vergeboard.
Colin Tibbett
Colin John Tibbett (born 18 March 1951) is a former English cricketer. Tibbett was a right-handed batsman. He was born at Luton, Bedfordshire.

Tibbett made his debut for Bedfordshire against Shropshire in the 1971 Minor Counties Championship. He played minor counties cricket for Bedfordshire from 1971 to 1979, making eighteen appearances, the last of which came against Suffolk in the 1979 Minor Counties Championship. In 1979, he was selected to play for Minor Counties South in the Benson & Hedges Cup, making a single List A appearance against Worcestershire at London Road, High Wycombe. Worcestershire won the toss and elected to bat, making 197/9 in their 55 overs. Minor Counties South were then dismissed for just 94 in their innings, with Rudd making a single run before he was dismissed by Norman Gifford.

Bedfordshire County Cricket Club
Bedfordshire County Cricket Club is one of 20 Minor County clubs within the domestic cricket structure of England and Wales. It represents the historic county of Bedfordshire.

The team is currently a member of the Minor Counties Championship Eastern Division and plays in the MCCA Knockout Trophy. Bedfordshire played List A matches occasionally from 1967 until 2005 but is not classified as a List A team.