In organic chemistry, the phenyl group or phenyl ring is a cyclic group of atoms with the formula C6H5. Phenyl groups are related to benzene and can be viewed as a benzene ring, minus a hydrogen, which may be replaced by some other element or compound to serve as a functional group. Phenyl groups have six carbon atoms bonded together in a hexagonal planar ring, five of which are bonded to individual hydrogen atoms, with the remaining carbon bonded to a substituent. Phenyl groups are commonplace in organic chemistry. Although depicted with alternating double and single bonds, phenyl groups are chemically aromatic and have equal bond lengths between carbon atoms in the ring. A "phenyl group" is synonymous to C6H5– and is represented by the symbol Ph or, archaically, Φ. Benzene is sometimes denoted as PhH. Phenyl groups are attached to other atoms or groups. For example, triphenylmethane has three phenyl groups attached to the same carbon center. Many or most phenyl compounds are not described with the term "phenyl".

For example, the chloro derivative C6H5Cl is called chlorobenzene, although it could be called phenyl chloride. In special cases, isolated phenyl groups are detected: the phenyl anion, the phenyl cation, the phenyl radical. Although Ph and phenyl uniquely denote C6H5, substituted derivatives are described using the phenyl terminology. For example, O2NC6H4 is nitrophenyl and F5C6 is pentafluorophenyl. Monosubstituted phenyl groups are associated with electrophilic aromatic substitution reactions and the products follow the arene substitution pattern. So, a given substituted phenyl compound has three isomers, ortho and para. A disubstituted phenyl compound 1,2,3-trisubstituted. Higher degrees of substitution, of which the pentafluorophenyl group is an example and are named according to IUPAC nomenclature. Phenyl is derived from the French word phényle, which in turn derived from Greek phaino: "shining", as the first phenyl compounds named were byproducts of making and refining various gases used for lighting.

According to McMurry, "The word is derived from the Greek pheno, commemorating the discovery of benzene by Michael Faraday in 1825 from the oily residue left by the illuminating gas used in London street lamps." Phenyl compounds are derived from benzene, at least conceptually and in terms of their production. In terms of its electronic properties, the phenyl group is related to a vinyl group, it is considered an inductively withdrawing group, because of the higher electronegativity of sp2 carbon atoms, a resonance donating group, due to the ability of its π system to donate electron density when conjugation is possible. The phenyl group is hydrophobic. Phenyl groups tend to resist reduction. Phenyl groups have enhanced stability in comparison to equivalent bonding in aliphatic groups; this increased stability is due to the unique properties of aromatic molecular orbitals. The bond lengths between carbon atoms in a phenyl group are 1.4 Å. In 1H-NMR spectroscopy, protons of a phenyl group have chemical shifts around 7.27 ppm.

These chemical shifts are influenced by aromatic ring current and may change depending on substituents. Phenyl groups are introduced using reagents that behave as sources of the phenyl anion or the phenyl cation. Representative reagents include phenylmagnesium bromide. Electrophiles attack benzene to give phenyl derivatives: C6H6 + E+ → C6H5E + H+where E+ = Cl+, NO2+, SO3; these reactions are called electrophilic aromatic substitutions. Representative compounds containing phenyl groups Phenyl groups are found in many organic compounds, both natural and synthetic. Most common among natural products is the amino acid phenylalanine, which contains a phenyl group. A major product of the petrochemical industry is "BTX" consisting of benzene and xylene - all of which are building blocks for phenyl compounds; the polymer polystyrene is derived from a phenyl-containing monomer and owes its properties to the rigidity and hydrophobicity of the phenyl groups. Many drugs as well as many pollutants contain phenyl rings.

One of the simplest phenyl-containing compounds is phenol, C6H5OH. It is said the resonance stability of phenol makes it a stronger acid than that of aliphatic alcohols such as ethanol. However, a significant contribution is the greater electronegativity of the sp2 alpha carbon in phenol compared to the sp3 alpha carbon in aliphatic alcohols. Media related to Phenyl group at Wikimedia Commons

In number theory, a Behrend sequence is an integer sequence whose multiples include all integers. The sequences are named after Felix Behrend. If A is a sequence of integers greater than one, if M denotes the set of positive integer multiples of members of A A is a Behrend sequence if M has natural density one; this means that the proportion of the integers from 1 to n that belong to M converges, in the limit of large n, to one. The prime numbers form a Behrend sequence, because every integer greater than one is a multiple of a prime number. More a subsequence A of the prime numbers forms a Behrend sequence if and only if the sum of reciprocals of A diverges; the semiprimes, the products of two prime numbers form a Behrend sequence. The only integers that are not multiples of a semiprime are the prime powers, but as the prime powers have density zero, their complement, the multiples of the semiprimes, have density one. The problem of characterizing these sequence was described as "very difficult" by Paul Erdős in 1979.

These sequences were named "Behrend sequences" in 1990 by Richard R. Hall, with a definition using logarithmic density in place of natural density. Hall chose their name in honor of Felix Behrend, who proved that for a Behrend sequence A, the sum of reciprocals of A must diverge. Hall and Gérald Tenenbaum used natural density to define Behrend sequences in place of logarithmic density; this variation in definitions makes no difference in which sequences are Behrend sequences, because the Davenport–Erdős theorem shows that, for sets of multiples, having natural density one and having logarithmic density one are equivalent. When A is a Behrend sequence, one may derive another Behrend sequence by omitting from A any finite number of elements; every Behrend sequence may be decomposed into the disjoint union of infinitely many Behrend sequences

Spirit of the Age is a 1988 compilation album by the British space rock group Hawkwind covering their Charisma Records period 1976–1979. It was issued by Virgin Records after they had acquired the Charisma catalogue, to test whether there was a viable market for the Hawkwind albums included in the deal. There was, the company re-issued each of the four albums the following year as part of the Compact price series. In 1992, Virgin wished to include a new Hawkwind compilation, Tales from Atom Henge: The Robert Calvert Years, as part of their Virgin Universal series; the band's fan club editor, Brian Tawn, was approached to compile this new release, but chose to replicate the original compilation album with the exception of two changes: the addition of the hard to find single B-sides "Honky Dorky" and "The Dream of Isis", the omission of "The Forge of Vulcan" in order to make space. "The Forge of Vulcan" – from Quark and Charm "Flying Doctor" – from 25 Years On "Steppenwolf" – from Astounding Sounds, Amazing Music "Hassan I Sabbah" – from Quark and Charm "25 Years" – from 25 Years On "Jack of Shadows" – from PXR5 "Psi Power" – from 25 Years On "Reefer Madness" – from Astounding Sounds, Amazing Music "Fable of a Failed Race" – from Quark and Charm "High Rise" – from PXR5 "Quark and Charm" – from Quark and Charm "Back on the Streets" – single A-side "Kerb Crawler" – from Astounding Sounds, Amazing Music " The Dreams of the Cold War Kid" – from 25 Years On "Spirit of the Age" – from Quark and Charm "Honky Dorky" – single B-side "Flying Doctor" "Steppenwolf" "Hassan I Sabbah" "25 Years" "Jack of Shadows" "PSI Power" "Reefer Madness" "Fable of a Failed Race" "High Rise" "Quark and Charm" "Back on the Streets" "The Dream of Isis" – single B-side "Kerb Crawler" " The Dreams of the Cold War Kid" "Spirit of the Age" Spirit of the Age: September 1988: Virgin Records, COMCD8 Tales from Atom Henge: November 1992: Virgin Universal, CDVM9008 Spirit of the Age at AllMusic.

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