Lisbon is the capital and the largest city of Portugal, with an estimated population of 505,526 within its administrative limits in an area of 100.05 km2. Its urban area extends beyond the city's administrative limits with a population of around 2.8 million people, being the 11th-most populous urban area in the European Union. About 3 million people live including the Portuguese Riviera, it is the only one along the Atlantic coast. Lisbon lies in the western Iberian Peninsula on the River Tagus; the westernmost areas of its metro area form the westernmost point of Continental Europe, known as Cabo da Roca, located in the Sintra Mountains. Lisbon is recognised as an alpha-level global city by the Globalization and World Cities Study Group because of its importance in finance, media, arts, international trade and tourism. Lisbon is the only Portuguese city besides Porto to be recognised as a global city, it is one of the major economic centres on the continent, with a growing financial sector and one of the largest container ports on Europe's Atlantic coast.
Additionally, Humberto Delgado Airport served 26.7 million passengers in 2017, being the busiest airport in Portugal, the 3rd busiest in the Iberian Peninsula and the 20th busiest in Europe, the motorway network and the high-speed rail system of Alfa Pendular links the main cities of Portugal to Lisbon. The city is the 9th-most-visited city in Southern Europe, after Rome, Barcelona, Venice, Madrid and Athens, with 3,320,300 tourists in 2017; the Lisbon region contributes with a higher GDP PPP per capita than any other region in Portugal. Its GDP amounts to thus $32,434 per capita; the city occupies the 40th place of highest gross earnings in the world. Most of the headquarters of multinational corporations in Portugal are located in the Lisbon area, it is the political centre of the country, as its seat of Government and residence of the Head of State. Lisbon is one of the oldest cities in the world, one of the oldest in Western Europe, predating other modern European capitals such as London and Rome by centuries.
Julius Caesar made it. Ruled by a series of Germanic tribes from the 5th century, it was captured by the Moors in the 8th century. In 1147, the Crusaders under Afonso Henriques reconquered the city and since it has been a major political and cultural centre of Portugal. Unlike most capital cities, Lisbon's status as the capital of Portugal has never been granted or confirmed – by statute or in written form, its position as the capital has formed through constitutional convention, making its position as de facto capital a part of the Constitution of Portugal. One claim repeated in non-academic literature is that the name of Lisbon can be traced back to Phoenician times, referring to a Phoenician term Alis-Ubo, meaning "safe harbour". Roman authors of the first century AD referred to popular legends that the city of Lisbon was founded by the mythical hero Odysseus on his journey home from Troy. Although modern archaeological excavations show a Phoenician presence at this location since 1200 BC, neither of these folk etymologies has any historical credibility.
Lisbon's origin may in fact derive from Proto-Celtic or Celtic Olisippo, Lissoppo, or a similar name which other visiting peoples like the Ancient Phoenicians and Romans adapted accordingly. The name of the settlement may be derived from the pre-Roman appellation for the Tagus River, Lisso or Lucio. Lisbon's name was written Ulyssippo in Latin by a native of Hispania, it was referred to as "Olisippo" by Pliny the Elder and by the Greeks as Olissipo or Olissipona. Lisbon's name is abbreviated to'LX' or'Lx', originating in an antiquated spelling of Lisbon as ‘’Lixbõa’’. While the old spelling has since been dropped from usage and goes against modern language standards, the abbreviation is still used. During the Neolithic period, the region was inhabited by Pre-Celtic tribes, who built religious and funerary monuments, megaliths and menhirs, which still survive in areas on the periphery of Lisbon; the Indo-European Celts invaded in the 1st millennium BC, mixing with the Pre-Indo-European population, thus giving rise to Celtic-speaking local tribes such as the Cempsi.
Although the first fortifications on Lisbon's Castelo hill are known to be no older than the 2nd century BC, recent archaeological finds have shown that Iron Age people occupied the site from the 8th to 6th centuries BC. This indigenous settlement maintained commercial relations with the Phoenicians, which would account for the recent findings of Phoenician pottery and other material objects. Archaeological excavations made near the Castle of São Jorge and Lisbon Cathedral indicate a Phoenician presence at this location since 1200 BC, it can be stated with confidence that a Phoenician trading post stood on a site now the centre of the present city, on the southern slope of the Castle hill; the sheltered harbour in the Tagus River estuary was an ideal spot for an Iberian settlement and would have provided a secure harbour for unloading and provisioning Phoenician ships. The Tagus settlement was an important centre of commercial trade with the inland tribes, providing an outlet for the valuable metals and salted-fish they collected, for the sale of the Lusitanian horses renowned in antiquity.
Kamieniec Ząbkowicki is a village in Ząbkowice Śląskie County, Lower Silesian Voivodeship, in south-western Poland. It is the seat of the administrative district called Gmina Kamieniec Ząbkowicki; the village is an important railroad junction, located on the main line which links Wrocław with Kłodzko and Prague. In Kamieniec, this route crosses with the west-east connection from Jaworzyna Śląska to Kędzierzyn-Koźle, it lies 8 kilometres south-east of Ząbkowice Śląskie, 68 kilometres south of the regional capital Wrocław. The village has a population of 4,200; the place is known for the former Kamieniec Abbey, established in 1209 as an Augustinian college by Bishop Wawrzyniec of Wrocław at the site of a former castle of Bretislaus II of Bohemia. In 1247 it became a filial monastery of the Cistercian Lubiąż Abbey. King Frederick II of Prussia hid here from Habsburg troops on February 27, 1741 during the First Silesian War. Secularized in 1810 by order of King Frederick William III of Prussia, the estates of Kamenz were acquired by Wilhelmine of Prussia, wife of King William I of the Netherlands.
Between 1838 and 1873 their daughter Princess Marianne of the Netherlands and her husband Prince Albert of Prussia had a new palace built in a Neogothic style according to the plans of Karl Friedrich Schinkel. Prior to 1945 it was in Germany under the name of Kamenz; the Palace was plundered and set on fire by the occupying Soviet Red Army during World War II. After World War II the region was placed under Polish administration by the Potsdam Agreement under territorial changes demanded by the Soviet Union; the village was renamed Kamieniec Ząbkowicki, most Germans fled or were expelled and replaced with Poles expelled from the Polish areas annexed by the Soviet Union. Kamieniec Ząbkowicki Palace Gola Dzierżoniowska Castle Medieval town of Niemcza Cistercian monastery at Henryków Wojsławice Arboretum Kamieniec Palace
Duchies of Silesia
The Duchies of Silesia were the more than twenty divisions of the region of Silesia formed between the 12th and 14th centuries by the breakup of the Duchy of Silesia part of the Kingdom of Poland. In 1335, the duchies were ceded to the Kingdom of Bohemia under the Treaty of Trentschin. Thereafter until 1742, Silesia was one of the Bohemian crown lands and lay within the Holy Roman Empire. Most of Silesia was annexed by the King of Prussia under the Treaty of Berlin in 1742. Only the Duchy of Teschen, the Duchy of Troppau and the Duchy of Nysa remained under the control of the Bohemian crown and as such were known as the Duchy of Upper and Lower Silesia until 1918. In the hope to prevent an inheritance dispute, the Piast prince Bolesław III Wrymouth by his last will and testament had divided Poland into hereditary provinces distributed among his four sons: Masovia, Greater Poland and Silesia. Beside which, the Seniorate Province with the residence of Kraków was reserved for the eldest, who according to the principle of agnatic seniority was to be High Duke of all Poland.
This act inadvertently started the process known as Fragmentation of Poland. Bolesław's son Władysław II received the Duchy of Silesia and, as the eldest, was granted the title of a High Duke among with the Seniorate Province. After he had tried to gain control over all Poland, he was banned and expelled by his younger half-brothers in 1146. Bolesław's second eldest son Bolesław IV the Curly, Duke of Masovia, became Polish High Duke. When, in 1163, Władysław's three sons, backed by Emperor Frederick I Barbarossa returned to Poland, Bolesław IV had to restore their heritage. After ten years of joint rule, Władysław's sons divided Silesia in 1173: Bolesław I the Tall, the eldest, received the core territory around the residences of Wrocław, Legnica and Opole. In 1180, he granted the Duchy of Opole to his son Jarosław, who ruled until his death in March 1201. Upon Bolesław's death in December 1201, his lands were inherited by his only remaining son Henry I the Bearded Mieszko I Tanglefoot became Duke of Racibórz and received Bytom and Oświęcim in 1177.
Konrad Spindleshanks, the youngest, in 1177 claimed his rights and received the Duchy of Głogów from his brother Bolesław, who after Konrad's death about 1180/90 again inherited it. After his brother Bolesław I had died, Miezsko I Tanglefoot conquered and took the Duchy of Opole from his nephew Henry I the Bearded, he ruled over the Racibórz and Opole duchies, which emerged as Upper Silesia, until his death in 1211. Henry I the Bearded remained sovereign of the Lower Silesian Duchy of Wrocław, he acquired the Greater Polish lands of Kalisz in 1206, which he granted to his Piast cousin Władysław Odonic, as well as Lubusz Land in 1210. High Duke of Poland from 1232, he conquered further Greater Polish territories around Santok in 1234. Mieszko's heir was Duke Casimir I of Opole, who died in 1230. Thereupon, Henry I managed to reunite whole Silesia under his reign, he was succeeded by his son Henry II the Pious in 1238, while Upper Silesia was inherited by Casimir's son Mieszko II the Fat in 1239.
He and his younger brother, Władysław Opolski, had received Greater Polish Kalisz in 1234. Henry II was killed at the Battle of Legnica in 1241, his eldest son and heir, Duke Bolesław II the Bald temporarily gave Lubusz Land to his younger brother Mieszko. He reconciled with his Greater Polish cousin Duke Przemysł I and returned Santok in 1247 and remained sole ruler of Lower Silesia until 1248. Mieszko II the Fat, of Upper Silesia, in 1244, returned Kalisz to Duke Przemysł I of Greater Poland, he died in 1246 and his possessions were inherited by his brother Władysław Opolski. In 1327, King John I of Bohemia began accepting the fealty of the Silesian dukes as part of his claim on the Polish crown. At the Congress of Visegrád in 1335 it was agreed that John would abandon his claim and in return receive the suzerainty of the Silesian duchies and a one-time payment; this was finalized in the Treaty of Trentschin on 24 August 1335. Under the Bohemian crown, the duchies continued to be ruled by branches of the Piast dynasty known as the Silesian Piasts until their lineages died out in 1675.
When a ducal lineage died out, the duchy became a state country. The Bohemian Crown passed to the House of Habsburg in 1526. In 1742, most of Silesia was annexed by Prussia following the First Silesian War; this was confirmed following the Second Silesian War in 1745 and the Third Silesian War in 1763. Following the dissolution of the Holy Roman Empire, Bohemian Silesia remained a part of the Austrian Empire and Austro-Hungarian Empire down to its dissolution in 1918. Note: this list may not be complete. Duchy of Bielsko Duchy of Brzeg Duchy of Bytom Duchy of Głogów Duchy of Głubczyce Duchy of Jawor Duchy of Krnov Duchy of Legnica Duchy of Löwenberg Duchy of Münsterberg Duchy of Nysa Duchy of Oleśnica Duchy of Opole Duchy of Oświęcim D
Austria the Republic of Austria, is a country in Central Europe comprising 9 federated states. Its capital, largest city and one of nine states is Vienna. Austria has an area of 83,879 km2, a population of nearly 9 million people and a nominal GDP of $477 billion, it is bordered by the Czech Republic and Germany to the north and Slovakia to the east and Italy to the south, Switzerland and Liechtenstein to the west. The terrain is mountainous, lying within the Alps; the majority of the population speaks local Bavarian dialects as their native language, German in its standard form is the country's official language. Other regional languages are Hungarian, Burgenland Croatian, Slovene. Austria played a central role in European History from the late 18th to the early 20th century, it emerged as a margraviate around 976 and developed into a duchy and archduchy. In the 16th century, Austria started serving as the heart of the Habsburg Monarchy and the junior branch of the House of Habsburg – one of the most influential royal houses in history.
As archduchy, it was a major component and administrative centre of the Holy Roman Empire. Following the Holy Roman Empire's dissolution, Austria founded its own empire in the 19th century, which became a great power and the leading force of the German Confederation. Subsequent to the Austro-Prussian War and the establishment of a union with Hungary, the Austro-Hungarian Empire was created. Austria was involved in both world wars. Austria is a parliamentary representative democracy with a President as head of state and a Chancellor as head of government. Major urban areas of Austria include Graz, Linz and Innsbruck. Austria is ranked as one of the richest countries in the world by per capita GDP terms; the country has developed a high standard of living and in 2018 was ranked 20th in the world for its Human Development Index. The republic declared its perpetual neutrality in foreign political affairs in 1955. Austria has been a member of the United Nations since 1955 and joined the European Union in 1995.
It is a founding member of the OECD and Interpol. Austria signed the Schengen Agreement in 1995, adopted the euro currency in 1999; the German name for Austria, Österreich, derives from the Old High German Ostarrîchi, which meant "eastern realm" and which first appeared in the "Ostarrîchi document" of 996. This word is a translation of Medieval Latin Marchia orientalis into a local dialect. Another theory says that this name comes from the local name of the mountain whose original Slovenian name is "Ostravica" - because it is steep on both sides. Austria was a prefecture of Bavaria created in 976; the word "Austria" was first recorded in the 12th century. At the time, the Danube basin of Austria was the easternmost extent of Bavaria; the Central European land, now Austria was settled in pre-Roman times by various Celtic tribes. The Celtic kingdom of Noricum was claimed by the Roman Empire and made a province. Present-day Petronell-Carnuntum in eastern Austria was an important army camp turned capital city in what became known as the Upper Pannonia province.
Carnuntum was home for 50,000 people for nearly 400 years. After the fall of the Roman Empire, the area was invaded by Bavarians and Avars. Charlemagne, King of the Franks, conquered the area in AD 788, encouraged colonization, introduced Christianity; as part of Eastern Francia, the core areas that now encompass Austria were bequeathed to the house of Babenberg. The area was known as the marchia Orientalis and was given to Leopold of Babenberg in 976; the first record showing the name Austria is from 996, where it is written as Ostarrîchi, referring to the territory of the Babenberg March. In 1156, the Privilegium Minus elevated Austria to the status of a duchy. In 1192, the Babenbergs acquired the Duchy of Styria. With the death of Frederick II in 1246, the line of the Babenbergs was extinguished; as a result, Ottokar II of Bohemia assumed control of the duchies of Austria and Carinthia. His reign came to an end with his defeat at Dürnkrut at the hands of Rudolph I of Germany in 1278. Thereafter, until World War I, Austria's history was that of its ruling dynasty, the Habsburgs.
In the 14th and 15th centuries, the Habsburgs began to accumulate other provinces in the vicinity of the Duchy of Austria. In 1438, Duke Albert V of Austria was chosen as the successor to his father-in-law, Emperor Sigismund. Although Albert himself only reigned for a year, henceforth every emperor of the Holy Roman Empire was a Habsburg, with only one exception; the Habsburgs began to accumulate territory far from the hereditary lands. In 1477, Archduke Maximilian, only son of Emperor Frederick III, married the heiress Maria of Burgundy, thus acquiring most of the Netherlands for the family. In 1496, his son Philip the Fair married Joanna the Mad, the heiress of Castile and Aragon, thus acquiring Spain and its Italian and New World appendages for the Habsburgs. In 1526, following the Battle of Mohács, Bohemia and the part of Hungary not occupied by the Ottomans came under Austrian rule. Ottoman expansion into Hungary led to frequent conflicts between the two empires evident in the Long War of 1593 to 1606.
The Turks made incursions into Styria nearly 20 times, of which some are c
Portugal the Portuguese Republic, is a country located on the Iberian Peninsula in southwestern Europe. It is the westernmost sovereign state of mainland Europe, being bordered to the west and south by the Atlantic Ocean and to the north and east by Spain, its territory includes the Atlantic archipelagos of the Azores and Madeira, both autonomous regions with their own regional governments. Portugal is the oldest state on the Iberian Peninsula and one of the oldest in Europe, its territory having been continuously settled and fought over since prehistoric times; the pre-Celtic people, Celts and Romans were followed by the invasions of the Visigoths and Suebi Germanic peoples. Portugal as a country was established during the Christian Reconquista against the Moors who had invaded the Iberian Peninsula in 711 AD. Founded in 868, the County of Portugal gained prominence after the Battle of São Mamede in 1128; the Kingdom of Portugal was proclaimed following the Battle of Ourique in 1139, independence from León was recognised by the Treaty of Zamora in 1143.
In the 15th and 16th centuries, Portugal established the first global empire, becoming one of the world's major economic and military powers. During this period, today referred to as the Age of Discovery, Portuguese explorers pioneered maritime exploration, notably under royal patronage of Prince Henry the Navigator and King John II, with such notable voyages as Bartolomeu Dias' sailing beyond the Cape of Good Hope, Vasco da Gama's discovery of the sea route to India and the European discovery of Brazil. During this time Portugal monopolized the spice trade, divided the world into hemispheres of dominion with Castille, the empire expanded with military campaigns in Asia. However, events such as the 1755 Lisbon earthquake, the country's occupation during the Napoleonic Wars, the independence of Brazil, a late industrialization compared to other European powers, erased to a great extent Portugal's prior opulence. After the 1910 revolution deposed the monarchy, the democratic but unstable Portuguese First Republic was established being superseded by the Estado Novo right-wing authoritarian regime.
Democracy was restored after the Carnation Revolution in 1974. Shortly after, independence was granted to all its overseas territories; the handover of Macau to China in 1999 marked the end of what can be considered the longest-lived colonial empire. Portugal has left a profound cultural and architectural influence across the globe, a legacy of around 250 million Portuguese speakers, many Portuguese-based creoles, it is a developed country with a high-income advanced economy and high living standards. Additionally, it is placed in rankings of moral freedom, democracy, press freedom, social progress, LGBT rights. A member of the United Nations and the European Union, Portugal was one of the founding members of NATO, the eurozone, the OECD, the Community of Portuguese Language Countries; the word Portugal derives from the Roman-Celtic place name Portus Cale. Portus, the Latin word for port or harbour, Cala or Cailleach was the name of a Celtic goddess – in Scotland she is known as Beira – and the name of an early settlement located at the mouth of the Douro River which flows into the Atlantic Ocean in the north of what is now Portugal.
At the time the land of a specific people was named after its deity. Those names are the origins of the - gal in Galicia. Incidentally, the meaning of Cale or Calle is a derivation of the Celtic word for port which would confirm old links to pre-Roman, Celtic languages which compare to today's Irish caladh or Scottish cala, both meaning port; some French scholars believe it may have come from ` Portus Gallus', the port of the Celts. Around 200 BC, the Romans took the Iberian Peninsula from the Carthaginians during the Second Punic War, in the process conquered Cale and renamed it Portus Cale incorporating it to the province of Gaellicia with capital in Bracara Augusta. During the Middle Ages, the region around Portus Cale became known by the Suebi and Visigoths as Portucale; the name Portucale evolved into Portugale during the 7th and 8th centuries, by the 9th century, that term was used extensively to refer to the region between the rivers Douro and Minho. By the 11th and 12th centuries, Portugallia or Portvgalliae was referred to as Portugal.
The early history of Portugal is shared with the rest of the Iberian Peninsula located in South Western Europe. The name of Portugal derives from the joined Romano-Celtic name Portus Cale; the region was settled by Pre-Celts and Celts, giving origin to peoples like the Gallaeci, Lusitanians and Cynetes, visited by Phoenicians, Ancient Greeks and Carthaginians, incorporated in the Roman Republic dominions as Lusitania and part of Gallaecia, after 45 BC until 298 AD. The region of present-day Portugal was inhabited by Neanderthals and by Homo sapiens, who roamed the border-less region of the northern Iberian peninsula; these were subsistence societies that, although they did not establish prosperous settlements, did form organized societies. Neolithic Portugal experimented with domestication of herding animals, the raising of some cereal crops and fluvial or marine fishing, it is believed by some scholars that early in the first millennium BC, several waves of Celts invaded Portugal from Central Europe and inter-married with the local populations, forming differe
Integrated Authority File
The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used for documentation in libraries and also by archives and museums; the GND is managed by the German National Library in cooperation with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero licence; the GND specification provides a hierarchy of high-level entities and sub-classes, useful in library classification, an approach to unambiguous identification of single elements. It comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format; the Integrated Authority File became operational in April 2012 and integrates the content of the following authority files, which have since been discontinued: Name Authority File Corporate Bodies Authority File Subject Headings Authority File Uniform Title File of the Deutsches Musikarchiv At the time of its introduction on 5 April 2012, the GND held 9,493,860 files, including 2,650,000 personalised names.
There are seven main types of GND entities: LIBRIS Virtual International Authority File Information pages about the GND from the German National Library Search via OGND Bereitstellung des ersten GND-Grundbestandes DNB, 19 April 2012 From Authority Control to Linked Authority Data Presentation given by Reinhold Heuvelmann to the ALA MARC Formats Interest Group, June 2012
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. A natural number greater than 1, not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 6 is composite because it is the product of two numbers that are both smaller than 6. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes, unique up to their order; the property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and n. Faster algorithms include the Miller–Rabin primality test, fast but has a small chance of error, the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical.
Fast methods are available for numbers of special forms, such as Mersenne numbers. As of December 2018 the largest known prime number has 24,862,048 decimal digits. There are infinitely many primes, as demonstrated by Euclid around 300 BC. No known simple formula separates prime numbers from composite numbers. However, the distribution of primes within the natural numbers in the large can be statistically modelled; the first result in that direction is the prime number theorem, proven at the end of the 19th century, which says that the probability of a randomly chosen number being prime is inversely proportional to its number of digits, that is, to its logarithm. Several historical questions regarding prime numbers are still unsolved; these include Goldbach's conjecture, that every integer greater than 2 can be expressed as the sum of two primes, the twin prime conjecture, that there are infinitely many pairs of primes having just one number between them. Such questions spurred the development of various branches of number theory, focusing on analytic or algebraic aspects of numbers.
Primes are used in several routines in information technology, such as public-key cryptography, which relies on the difficulty of factoring large numbers into their prime factors. In abstract algebra, objects that behave in a generalized way like prime numbers include prime elements and prime ideals. A natural number is called a prime number if it is greater than 1 and cannot be written as a product of two natural numbers that are both smaller than it; the numbers greater than 1 that are not prime are called composite numbers. In other words, n is prime if n items cannot be divided up into smaller equal-size groups of more than one item, or if it is not possible to arrange n dots into a rectangular grid, more than one dot wide and more than one dot high. For example, among the numbers 1 through 6, the numbers 2, 3, 5 are the prime numbers, as there are no other numbers that divide them evenly. 1 is not prime, as it is excluded in the definition. 4 = 2 × 2 and 6 = 2 × 3 are both composite. The divisors of a natural number n are the numbers.
Every natural number has both itself as a divisor. If it has any other divisor, it cannot be prime; this idea leads to a different but equivalent definition of the primes: they are the numbers with two positive divisors, 1 and the number itself. Yet another way to express the same thing is that a number n is prime if it is greater than one and if none of the numbers 2, 3, …, n − 1 divides n evenly; the first 25 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. No number n greater than 2 is prime because any such number can be expressed as the product 2 × n / 2. Therefore, every prime number other than 2 is an odd number, is called an odd prime; when written in the usual decimal system, all prime numbers larger than 5 end in 1, 3, 7, or 9. The numbers that end with other digits are all composite: decimal numbers that end in 0, 2, 4, 6, or 8 are and decimal numbers that end in 0 or 5 are divisible by 5; the set of all primes is sometimes denoted by P or by P.
The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptian fraction expansions of different forms for prime and composite numbers. However, the earliest surviving records of the explicit study of prime numbers come from Ancient Greek mathematics. Euclid's Elements proves the infinitude of primes and the fundamental theorem of arithmetic, shows how to construct a perfect number from a Mersenne prime. Another Greek invention, the Sieve of Eratosthenes, is still used to construct lists of primes. Around 1000 AD, the Islamic mathematician Alhazen found Wilson's theorem, characterizing the prime numbers as the numbers n that evenly divide