84 (number)

84 (eighty-four) is the natural number following 83 and preceding 85. It is seven dozens.

In mathematics
84 is a semiperfect number, being thrice a perfect number, and the sum of the sixth pair of twin primes $$(41 + 43)$$. It is the number of four-digit perfect powers in decimal.

It is the third (or second) dodecahedral number, and the sum of the first seven triangular numbers (1, 3, 6, 10, 15, 21, 28), which makes it the seventh tetrahedral number.

The twenty-second unique prime in decimal, with notably different digits than its preceding (and known following) terms in the same sequence, contains a total of 84 digits.

A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.

84 is the limit superior of the largest finite subgroup of the mapping class group of a genus $$g$$ surface divided by $$g$$.

Under Hurwitz's automorphisms theorem, a smooth connected Riemann surface $$X$$ of genus $$g > 1$$ will contain an automorphism group $$\mathrm{Aut}(X) = G$$ whose order is classically bound to $$|G| \le 84 \text { } (g - 1)$$.

84 is the thirtieth and largest $$n$$ for which the cyclotomic field $$\mathrm {Q}(\zeta_{n})$$ has class number $$1$$ (or unique factorization), preceding 60 (that is the composite index of 84), and 48.

There are 84 zero divisors in the 16-dimensional sedenions $$\mathbb S$$.

In astronomy

 * Messier object M84, a magnitude 11.0 lenticular galaxy in the constellation Virgo
 * The New General Catalogue object NGC 84, a single star in the constellation Andromeda

In other fields


Eighty-four is also:


 * The year AD 84, 84 BC, or 1984.
 * The number of years in the Insular latercus, a cycle used in the past by Celtic peoples, equal to 3 cycles of the Julian Calendar and to 4 Metonic cycles and 1 octaeteris
 * The atomic number of polonium
 * The model number of Harpoon missile
 * WGS 84 - The latest revision of the World Geodetic System, a fixed global reference frame for the Earth.
 * The house number of 84 Avenue Foch
 * The number of the French department Vaucluse
 * The code for international direct dial phone calls to Vietnam
 * The town of Eighty Four, Pennsylvania
 * The company 84 Lumber
 * The ISBN Group Identifier for books published in Spain
 * A variation of the game 42 played with two sets of dominoes.
 * The film 84 Charing Cross Road (1987) starring Anne Bancroft and Anthony Hopkins
 * KKNX Radio 84 in Eugene, Oregon
 * The B-Side to "Up All Night" (Take That song)
 * British Army term for the 84mm Carl Gustav recoilless rifle.
 * How many Earth years it takes Uranus to orbit the Sun once