Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example, 5 is prime because 1 and 5 are its only positive integer factors, whereas 6 is composite because it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. The uniqueness in this theorem requires excluding 1 as a prime because one can include arbitrarily many instances of 1 in any factorization, e.g., 3, 1 · 3, 1 · 1 · 3, etc. are all valid factorizations of 3.

The property of being prime (or not) is called primality. A simple but slow method of verifying the primality of a given number n is known as trial division. It consists of testing whether n is a multiple of any integer between 2 and . Algorithms much more efficient than trial division have been devised to test the primality of large numbers. These include the Miller–Rabin primality test, which is fast but has a small probability 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 January 2016, the largest known prime number has 22,338,618 decimal digits.

Prime (liturgy)

Prime, or the First Hour, is a fixed time of prayer of the traditional Divine Office (Canonical Hours), said at the first hour of daylight (approximately 7:00 a.m.), between the morning Hour of Lauds and the 9 a.m. Hour of Terce. It is part of the Christian liturgies of Eastern Christianity, but in the Latin Rite it was suppressed by the liturgical reforms following the Second Vatican Council. However, clergy who have an obligation to celebrate the Liturgy of the Hours may still fulfil their obligation by using the Roman Breviary promulgated by Pope John XXIII in 1962, which contains the Hour of Prime. Like all the liturgical hours, except the Office of Readings, it consists primarily of Psalms. It is one of the Little Hours.

Name

The word "Prime" comes from Latin and refers to the first hour of daylight (i.e., dawn). Originally, in the West, Prime was called matitutina (hora), "morning hour". Later, in order to distinguish it from the nocturnal offices of Matins and Lauds, and to include it among hours of the day, it was called prima. The name is first met with in the Rule of St. Benedict. In the Antiphonary of Bangor it is called secunda.

Prime (film)

Prime is a 2005 American romantic comedy film starring Uma Thurman, Meryl Streep and Bryan Greenberg. It was written and directed by Ben Younger. The film grossed $67,937,503 worldwide.

Plot

Rafi (Uma Thurman) is a recently divorced, 37-year-old career woman from Manhattan who becomes romantically involved with David (Bryan Greenberg), a talented 23-year-old Jewish painter from the Upper West Side. Rafi shares all her secrets with her therapist Lisa (Meryl Streep) who, unbeknownst to Rafi, is David's mother. Lisa, supportive of Rafi's relationship with a younger man, discovers the connection and finds herself not only faced with the ethical and moral dilemma of counseling David's girlfriend, but also the reality that she feels differently about the relationship now that she knows her son is involved. Lisa consults her own therapist, and they decide that it is in the best interest of her patient Rafi for Lisa to continue treatment, as long as the relationship remains the "fling" it appears to be.

AMT

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AMT Genova

The AMT Genova, formally known as the Azienda Mobilità e Trasporti and formerly as the Azienda Municipalizzata Trasporti, is a joint stock company that holds the concession for public transport in the Italian city of Genoa.

History

The first public transport in Genoa was provided by a horse bus service linking the city centre and Sampierdarena, that started in 1873. In 1878, the French company Compagnia Generale Francese dei Tramways (CGFT) began to build a horse tram system. The city subsequently granted further concessions to two other companies, the Swiss backed Società di Ferrovie Elettriche e Funicolari (FEF) and the Belgian/Italian Società Tramways Orientali (TO). However by 1894, the FEF had achieved no more than a single short electric tram line between Piazza Manin and Piazza Corvetto, whilst the TO had not progressed beyond the planning stage. The CGFT system had extended through the city and the Val Polcevera, but was still horse operated.

In 1894, the German company Allgemeine Elektrizitäts Gesellschaft (AEG) bought both the FEF and TO companies. The following year AEG created the company Officine Electrical Genovesi (OEG), which took over the city's existing electricity supply company, and the Società Unione Italiana Tramways Elettrici (UITE), which purchased the CGFT's concession. By the end of 1895, AEG has a monopoly of both electricity supply and public transport provision in the city. Under their new ownership, the FEF and the TO developed a tram network of more than 53 kilometres (33 mi) reaching Nervi and Prato, whilst UITE electrified their lines to Voltri and Pontedecimo. Finally in December 1901, AEG merged the FEF and TO into an enlarged UITE.