All articles starting with P
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Prime element
A prime element is a nonzero, noninvertible element of a commutative ring such that when it divides a product ab, it divides a or b, the ring-theoretic generalization of ordinary prime numbers.
Prime Focus Spectrograph
The Prime Focus Spectrograph (PFS, Hawaiian Onohi'ula) is a fiber-fed spectrograph at the Subaru Telescope on Maunakea, capturing about 2,400 objects per exposure since 2025.
Prime gap
A prime gap is the difference between two successive prime numbers, such as the seven composites between 89 and 97. Gaps grow arbitrarily large and average about ln x near x.
Prime Head
Prime Head is the snow-covered northernmost headland of Trinity Peninsula and the Antarctic Peninsula at 63°13'S 57°17'W, named by the UK-APC in 1963; Argentina and Chile call it Cabo Siffrey.
Prime ideal
A prime ideal is a proper ideal in a commutative ring such that whenever a product ab lies in it, one factor lies in it.
Prime k-tuple
A prime k-tuple is a set of k linear forms one asks to be prime simultaneously; the Hardy–Littlewood conjecture (1923) predicts every admissible tuple is all-prime infinitely often.
Prime labeling
Prime labeling is a graph labeling technique assigning the integers 1 through n to a graph's vertices so every pair of adjacent vertices receives coprime labels.
Prime lens
A prime lens is a photographic or cine lens with a fixed focal length, common at 24, 35, 50, and 85 mm; reframing requires moving the camera rather than zooming.
Prime meridian
The prime meridian, known as the Greenwich Meridian, is the internationally agreed line of 0° longitude at the Royal Observatory Greenwich, chosen by 25 nations in 1884.
Prime Minister Internship Scheme
The Prime Minister Internship Scheme (PMIS), also known as the PM Internship Scheme, is an Indian government program announced in 2024 offering 12-month paid internships in 500 top companies.
Prime Minister of Afghanistan
Prime Minister of Afghanistan: head of government under the 1964 monarchy, the 1987 and 1990 republics, absent from the 2004 presidential constitution, and since 2021 the acting head of the Taliban caretaker cabinet, Mohammad Hassan Akhund, under supreme leader Hibatullah Akhundzada.
Prime Minister of Australia
Prime Minister of Australia: head of the Australian Government, an office created by convention rather than the Constitution. Chairs Cabinet, advises the Governor-General, first held by Edmund Barton in 1901; Anthony Albanese incumbent since 2022.
Prime Minister of Bangladesh
Prime Minister of Bangladesh (প্রধানমন্ত্রী), head of government under the 1972 constitution's articles 55–58; executive power vested in the PM, first held by Sheikh Mujibur Rahman, currently Tarique Rahman since February 2026.
Prime Minister of Belgium
Prime Minister of Belgium (Eerste minister, Premier ministre): head of the federal government, chairs the Council of Ministers. Title official since 1920, constitutional mention 1970, constructive no-confidence under Article 96; current PM Bart De Wever.
Prime Minister of Canada
Prime Minister of Canada: head of government in Canada's constitutional monarchy, first held by John A. Macdonald in 1867; controls appointments, Cabinet, and Crown prerogatives, supported by PMO and PCO; current holder Mark Carney.
Prime Minister of Denmark
Prime Minister of Denmark (statsminister): head of government appointed by the monarch under negative parliamentarism. Established in practice by the 1901 system change, constitutionalized 1953; incumbent Mette Frederiksen since 2019.
Prime Minister of Estonia
Prime Minister of Estonia (peaminister): head of government under the 1992 Constitution, currently Kristen Michal (Reform Party) since 23 July 2024, leading a Reform–Eesti 200–Social Democrat coalition after Kaja Kallas's departure to the EU.
Prime Minister of Finland
Prime Minister of Finland (pääministeri, statsminister): head of government, elected by Parliament and appointed by the President. Current holder Petteri Orpo since June 2023 leads the 77th government; the 2000 Constitution made Finland effectively parliamentary.
Prime Minister of France
Prime Minister of France (Premier ministre): head of the French Government under the 1958 Fifth Republic Constitution, appointed by the President, accountable to the National Assembly, wielding Article 49.3; current holder Sébastien Lecornu, residing at Matignon.
Prime Minister of Greece
Prime Minister of Greece (Πρωθυπουργός της Ελληνικής Δημοκρατίας): head of government, chairs the Cabinet and KYSEA, appointed by the President under Article 37; current incumbent Kyriakos Mitsotakis of New Democracy.
Prime Minister of India
Prime Minister of India (Pradhan Mantri): head of the Union Council of Ministers under Articles 74-75, appointed by the President, first held by Nehru in 1947; Narendra Modi is the 14th and current PM, in a third term since 9 June 2024.
Prime Minister of Israel (רֹאשׁ הַמֶּמְשָׁלָה)
The Prime Minister of Israel, in Hebrew Rosh HaMemshala, is the head of the executive branch, first held by David Ben-Gurion in 1948 and currently Benjamin Netanyahu, its longest-serving holder.
Prime Minister of Italy
Prime Minister of Italy (Presidente del Consiglio dei Ministri), head of government under Article 95 of the Constitution; Giorgia Meloni incumbent since 22 October 2022; office defined by Law 400/1988 powers, bicameral confidence, decree-laws, and the proposed premierato direct-election reform.
Prime Minister of Jamaica
Prime Minister of Jamaica: head of government under the 1962 Westminster constitution, appointed by the Governor-General as the House member commanding majority confidence; first held by Bustamante (1962), currently Andrew Holness, ninth holder, with a republic transition pending.
Prime Minister of Japan (内閣総理大臣)
Prime Minister of Japan (内閣総理大臣, Naikaku Sōri Daijin), head of the Cabinet and government, Diet-designated under the parliamentary cabinet system; created 1885 with Itō Hirobumi, restructured 1947; current incumbent Takaichi Sanae, the 105th and first female holder.
Prime Minister of Malaysia
The Prime Minister of Malaysia (Perdana Menteri Malaysia) is Malaysia's head of government, appointed by the Yang di-Pertuan Agong; the incumbent is Anwar Ibrahim, the tenth holder since 2022.
Prime Minister of Nepal
Prime Minister of Nepal (प्रधानमन्त्री): head of government under the 2015 constitution, first held by Bhimsen Thapa in 1806; incumbent Balendra Shah, appointed 27 March 2026 after Sushila Karki's interim premiership following the 2025 Gen Z protests.
Prime Minister of New Zealand
Prime Minister of New Zealand: head of government and Cabinet chair, appointed by the Governor-General by convention, no statutory definition; 42 holders since Henry Sewell in 1856; current PM Christopher Luxon.
Prime Minister of Norway
Prime Minister of Norway (statsminister): head of government in Norway's constitutional monarchy, appointed by King Harald V; incumbent Jonas Gahr Støre (Labour), appointed 14 October 2021, leading a Labour-only government of 20 ministers since February 2025.
Prime Minister of Pakistan (وزیراعظم)
Prime Minister of Pakistan (وزیراعظم), head of government under the 1973 Constitution, first held by Liaquat Ali Khan in 1947; removable by National Assembly no-confidence vote under Article 95; no holder has completed a full term.