5 (number)

5 (five /ˈfaɪv/) is a number, numeral, and glyph. It is the natural number following 4 and preceding 6.

In mathematics

Five is the third prime number. Because it can be written as 2²¹ + 1, five is classified as a Fermat prime; therefore a regular polygon with 5 sides (a regular pentagon) is constructible with compass and unmarked straightedge. 5 is the third Sophie Germain prime, the first safe prime, the third Catalan number, and the third Mersenne prime exponent. Five is the first Wilson prime and the third factorial prime, also an alternating factorial. Five is the first good prime. It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. It is also the only number that is part of more than one pair of twin primes. Five is a congruent number.

Five is conjectured to be the only odd untouchable number and if this is the case then five will be the only odd prime number that is not the base of an aliquot tree.

The number 5 is the fifth Fibonacci number, being 2 plus 3. 5 is also a Pell number and a Markov number, appearing in solutions to the Markov Diophantine equation: (1, 2, 5), (1, 5, 13), (2, 5, 29), (5, 13, 194), (5, 29, 433), ... ( A030452 lists Markov numbers that appear in solutions where one of the other two terms is 5). Whereas 5 is unique in the Fibonacci sequence, in the Perrin sequence 5 is both the fifth and sixth Perrin numbers.

Piano sonata

A piano sonata is a sonata written for a solo piano. Piano sonatas are usually written in three or four movements, although some piano sonatas have been written with a single movement (Scarlatti, Scriabin, Medtner), two movements (Haydn), five (Brahms' Third Piano Sonata) or even more movements. The first movement is generally composed in sonata form.

The Baroque keyboard sonata

In the Baroque era, the use of the term "sonata" generally referred to either the sonata da chiesa (church sonata) or sonata da camera (chamber sonata), both of which were sonatas for various instruments (usually one or more violins plus basso continuo). The keyboard sonata was relatively neglected by most composers.

The sonatas of Domenico Scarlatti (of which there are over 500) were the hallmark of the Baroque keyboard sonata, though they were for the most part unpublished during Scarlatti's lifetime. The majority of these sonatas are in one-movement binary form, both sections being in the same tempo and utilizing the same thematic material. These sonatas are prized for both their technical difficulty and their musical and formal ingenuity. The influence of Spanish folk music is evident in Scarlatti's sonatas.

Daniel Barenboim

Daniel Barenboim (German: [baːrənboim], Hebrew: דניאל ברנבוים; born 15 November 1942) is an Argentine-Israeli pianist and conductor, who also is a citizen of Palestine and Spain. He is general music director of the Berlin State Opera, and the Staatskapelle Berlin; he previously served as Music Director of the Chicago Symphony Orchestra, the Orchestre de Paris and La Scala in Milan. Barenboim is known for his work with the West–Eastern Divan Orchestra, a Seville-based orchestra of young Arab and Israeli musicians, and as a resolute critic of the Israeli occupation of Palestinian territories.

Barenboim has received many awards and prizes, including an honorary Knight Commander of the Order of the British Empire, France's Légion d'honneur both as a Commander and Grand Officier, and the German Großes Bundesverdienstkreuz and Willy Brandt Award. Together with the Palestinian-American scholar Edward Said, he was given Spain's Prince of Asturias Concord Award. He has won seven Grammy awards for his work and discography. Barenboim is a polyglot, fluent in Spanish, Hebrew, English, French, Italian, and German.