JAMES PRIME
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Prime numberA prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is 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, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. 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 that is 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 {\displaystyle n} , called trial division, tests whether n {\displaystyle n} is a multiple of any integer between 2 and n {\displaystyle {\sqrt {n}}} . Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always produces the correct answer in polynomial time but is too slow to be practical. Particularly fast methods are available for numbers of special forms, such as Mersenne numbers. As of October 2024 the largest known prime number is a Mersenne prime with 41,024,320 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 roughly that the probability of a randomly chosen large 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 even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes that differ by two. 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.
In connection with: Prime number
Title combos: number Prime
Description combos: theorem the century known prime produces smaller not However
Prime Minister of the United KingdomThe prime minister of the United Kingdom is the head of government of the United Kingdom. The prime minister advises the sovereign on the exercise of much of the royal prerogative, chairs the Cabinet, and selects its ministers. Modern prime ministers hold office by virtue of their ability to command the confidence of the House of Commons, so they are invariably members of Parliament. The office of prime minister is not established by any statute or constitutional document, but exists only by long-established convention, whereby the monarch appoints as prime minister the person most likely to command the confidence of the House of Commons. In practice, this is the leader of the political party that holds the largest number of seats in the Commons. The prime minister is ex officio also First Lord of the Treasury (prior to 1905 also the official title of the position), Minister for the Civil Service, the minister responsible for national security,: p.22 and Minister for the Union. The prime minister's official residence and office is 10 Downing Street in London. Early conceptions of the office of prime minister evolved as the primus inter pares ("first among equals"); however that does not differentiate on status and responsibility upon whoever is holding office. Historically, the prime minister has never been the first among equals at any time prior to 1868. Until now, that characterisation of the prime minister is reflective of the democratic nature of their position. The power of the prime minister depends on the support of their respective party and on the popular mandate. The appointment of cabinet ministers and granting of honours are done through the prime minister's power of appointment. The prime minister alongside the cabinet proposes new legislation and decides on key policies that fit their agenda which are then passed by an act of parliament. The power of the office of prime minister has grown significantly since the first prime minister, Robert Walpole in 1721. Prime ministerial power evolved gradually alongside the office itself which have played an increasingly prominent role in British politics since the early 20th century. During the premierships of Margaret Thatcher and Tony Blair, prime ministerial power expanded substantially, and their leaderships in the office were described as "presidential" due to their personal wielding of power and tight control over the cabinet. The prime minister is one of the world's most powerful political leaders in modern times. As the leader of the world's sixth largest economy, the prime minister holds significant domestic and international leadership, being the leader of a prominent member state of NATO, the G7 and G20. As of 2025 58 people (55 men and 3 women) have served as prime minister, the first of whom was Robert Walpole taking office on 3 April 1721. The longest-serving prime minister was also Walpole, who served over 20 years, and the shortest-serving was Liz Truss, who served seven weeks. Keir Starmer succeeded Rishi Sunak as prime minister on 5 July 2024, following the 2024 general election.
In connection with: Prime Minister of the United Kingdom
Title combos: Prime Minister of Prime the Prime Minister of Kingdom
Description combos: minister as largest G20 over minister the of Parliament
Twin primeA twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (17, 19) or (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term twin prime is used for a pair of twin primes; an alternative name for this is prime twin or prime pair. Twin primes become increasingly rare as one examines larger ranges, in keeping with the general tendency of gaps between adjacent primes to become larger as the numbers themselves get larger. However, it is unknown whether there are infinitely many twin primes (the so-called twin prime conjecture) or if there is a largest pair. The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved.
In connection with: Twin prime
Title combos: prime Twin
Description combos: larger keeping number prime twin made there the Zhang
James CallaghanLeonard James Callaghan, Baron Callaghan of Cardiff ( KAL-ə-han; 27 March 1912 – 26 March 2005) was a British statesman and Labour Party politician who served as Prime Minister of the United Kingdom from 1976 to 1979 and Leader of the Labour Party from 1976 to 1980. Callaghan is the only person to have held all four Great Offices of State, having also served as Chancellor of the Exchequer from 1964 to 1967, Home Secretary from 1967 to 1970 and Foreign Secretary from 1974 to 1976. He was a Member of Parliament (MP) from 1945 to 1987. Born into a working-class family in Portsmouth, Callaghan left school early and began his career as a tax inspector, before becoming a trade union official in the 1930s. He served as a lieutenant in the Royal Navy during the Second World War. He was elected to Parliament at the 1945 election, and was regarded as being on the left wing of the Labour Party. He was appointed to the Attlee government as a parliamentary secretary in 1947, and began to move increasingly towards the right wing of the Labour Party, while maintaining his reputation as a "Keeper of the Cloth Cap" – that is, seen as maintaining close ties between Labour and the trade unions. Following Labour's defeat at the 1951 election, Callaghan increasingly became regarded as a leader of the right wing of the Labour Party, and stood for the positions of deputy leader in 1960 and for leader in 1963, but was defeated by George Brown for the former and Harold Wilson for the latter. Following Labour's victory at the 1964 election, Wilson appointed Callaghan as Chancellor of the Exchequer; this appointment coincided with a turbulent period for the British economy, during which Callaghan had to tackle both a chronic balance of payments deficit and various speculative attacks on the pound sterling, with its exchange rate to other currencies being fixed by the Bretton Woods system. On 18 November 1967, having initially denied that it would do so, the Government devalued the pound sterling. In the wake of the decision, Wilson moved Callaghan to the role of Home Secretary. During this time, Callaghan was responsible for overseeing the operations of the British Army to support the police in Northern Ireland, following a request from the Northern Ireland government. Callaghan remained in the Shadow Cabinet during Labour's period in Opposition from 1970 to 1974; upon Labour's victory at the 1974 election, Wilson appointed Callaghan as Foreign Secretary. Callaghan was responsible for renegotiating the terms of Britain's membership of the European Communities (EC), and strongly supported the successful "Yes" vote campaign in the 1975 referendum, which confirmed the UK's membership of the EC. When Wilson suddenly announced his retirement in March 1976, Callaghan defeated five other candidates to be elected Leader of the Labour Party; he was appointed prime minister on 5 April 1976. Labour had won a narrow majority in the House of Commons at the October 1974 election but, through by-election defeats, had lost this by the time Callaghan became prime minister; and several by-election defeats and defections in his early months of power forced him to strike a confidence and supply agreement with the Liberal Party. This had ended by the time of significant industrial disputes and widespread strikes in the 1978–79 "Winter of Discontent" – which, followed by the defeat of the referendum on devolution for Scotland, led to minor parties joining with the Conservative Party to pass a motion of no-confidence in Callaghan on 28 March 1979. Although remaining personally popular in opinion polls, he led Labour to defeat at the 1979 election and was replaced by Conservative Margaret Thatcher. The 1979 defeat marked the beginning of 18 years in opposition for the Labour Party, the longest in its history. Callaghan served as Labour leader and Leader of the Opposition until November 1980. He attempted to reform the process by which Labour elected its leader. After leaving the leadership he returned to the backbenches, and between 1983 and 1987 was Father of the House of Commons. On retiring from the Commons in 1987, he was elevated to the House of Lords as Baron Callaghan of Cardiff. He died in 2005 at the age of 92, and remains to date the UK's longest-lived former prime minister. He is the most recent prime minister to have served in the British Armed Forces and the only prime minister to have served in the Royal Navy. He is also the only person, to date, to have held all four of the Great Offices of State.
In connection with: James Callaghan
Title combos: James Callaghan
Description combos: for and responsible on March 1980 minister Conservative to
Deacon BlueDeacon Blue are a Scottish pop rock band formed in Glasgow in 1985. The line-up of the band consists of vocalists Ricky Ross and Lorraine McIntosh, keyboard player James Prime, drummer Dougie Vipond, guitarist Gregor Philp and bassist Lewis Gordon. In 2013, their estimated album sales stood at six million, and by 2020 were estimated to have risen to in excess of seven million, with twelve UK top 40 singles, along with two number one albums in both the United Kingdom and their native Scotland. The band released their debut album, Raintown (1987) to critical and commercial success, with their second album, When the World Knows Your Name (1989), topping the UK Albums Chart for two weeks. The single "Real Gone Kid" became their first top ten single in the UK Singles Chart and reached number one in Spain. Deacon Blue followed up the success of their first two albums with Fellow Hoodlums (1991) and Whatever You Say, Say Nothing (1993). The band split in 1994 until five years later, holding a reunion gig which led on to a new album, Walking Back Home (1999). The band released another album, Homesick (2001), the last to feature guitarist Graeme Kelling following his death from pancreatic cancer in 2004. In 2006, the band recorded three new songs for a Singles album – including the single "Bigger than Dynamite". Deacon Blue returned after a period of absence to release The Hipsters (2012), their first studio album since Homesick in 2001. The band released a further four albums following their reunion – A New House, (2014), Believers (2016), City of Love (2020) and Riding on the Tide of Love (2021) to commercial success. In 2024, they released "Late 88" as the lead single from their eleventh studio album The Great Western Road (2025).
In connection with: Deacon Blue
Title combos: Deacon Blue
Description combos: UK The Singles six James Dynamite 1989 band In
List of prime ministers of the United KingdomThe prime minister of the United Kingdom is the principal minister of the crown of His Majesty's Government, and the head of the British Cabinet. There is no specific date for when the office of prime minister first appeared, as the role was not created but rather evolved over time through a merger of duties. The term was regularly, if informally, used by Robert Walpole by the 1730s. It was used in the House of Commons as early as 1805, and it was certainly in parliamentary use by the 1880s, although did not become the official title until 1905, when Arthur Balfour was prime minister. Historians generally consider Robert Walpole, who led the government of the Kingdom of Great Britain for over twenty years from 1721, to be the first prime minister. Walpole is also the longest-serving British prime minister by this definition. The first prime minister of the United Kingdom of Great Britain and Ireland was William Pitt the Younger at its creation on 1 January 1801. The first to use the title in an official act was Benjamin Disraeli who signed the 1878 Treaty of Berlin as "Prime Minister of Her Britannic Majesty". In 1905, the post of prime minister was officially given recognition in the order of precedence, with the incumbent Henry Campbell-Bannerman the first officially referred to as "prime minister". The first prime minister of the current United Kingdom of Great Britain and Northern Ireland upon its creation in 1922 (when 26 Irish counties seceded and created the Irish Free State) was Andrew Bonar Law, although the country was not renamed officially until 1927, when Stanley Baldwin was the serving prime minister. The current prime minister is Keir Starmer, who assumed the office on 5 July 2024.
In connection with: List of prime ministers of the United Kingdom
Title combos: Kingdom List of ministers the ministers of United prime
Description combos: prime renamed Cabinet is was 1801 by not government
James PrimeJames Prime (born 3 November 1960) is a Scottish musician best known as the keyboard player for rock band Deacon Blue. Prime also lectures at the University of the West of Scotland.
In connection with: James Prime
Title combos: James Prime
Description combos: of is the best Blue known for Blue James
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