Seventeen
Introduction
Seventeen is a natural number following sixteen and preceding eighteen. It is a prime number, and holds significance in various mathematical, scientific, and cultural contexts. This article delves into the properties, significance, and applications of the number seventeen.
Mathematical Properties
Seventeen is a prime number, specifically the 7th prime number in the sequence. It is also a Chen prime, meaning it is a prime number that is two less than another prime number.
In the realm of algebraic number theory, seventeen is a Heegner number, indicating that the ring of integers of the field Q(√-d) has unique factorization.
Seventeen is also a Fermat prime, which means it is of the form 2^n + 1, where n itself is a power of 2. Fermat primes are named after Pierre de Fermat, who first studied these numbers.
Scientific Significance
In the field of physics, group 17 of the periodic table consists of the halogens, which are particularly reactive due to having seven electrons in their outermost shell.
In biology, the Brood X of the seventeen-year cicada is one of the most well-known examples of periodicity in nature.
In chemistry, the atomic number of chlorine is seventeen, making it the seventeenth element in the periodic table.
Cultural Significance
Seventeen holds various cultural and religious significances across the world. In Ancient Roman culture, the number was considered unlucky. This belief stemmed from the Roman numeral XVII, which can be rearranged to spell 'VIXI', a Latin word meaning 'I have lived' and often found on tombstones.
In Japanese culture, the number is considered unlucky because it can be pronounced as 'shichi', which sounds similar to the words for 'death' and 'pain'.
In contrast, in Norse mythology, the god Odin received the runes in a self-sacrificial ritual involving hanging from the World Tree for nine days and nights and injuring himself with his spear, which is often interpreted as a symbolic death and rebirth. After this, he was able to see the runes, of which there were seventeen, signifying wisdom and knowledge.
In Popular Culture
Seventeen often appears in literature, music, and other forms of popular culture. For instance, it is the age of the protagonist in many coming-of-age novels, such as J.D. Salinger's 'The Catcher in the Rye'.
In music, the number is frequently used in song titles and lyrics, such as 'Edge of Seventeen' by Stevie Nicks and 'Seventeen' by Janis Ian.