91 (ninety-one) is the

natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

following 90 and preceding 92.

In mathematics

91 is: * the twenty-seventh distinct

semiprime In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers. Because there are infinitely many prime ...

and the second of the form (7×q). * a

triangular number A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...

. * a hexagonal number, one of the few such numbers to also be a

centered hexagonal number In mathematics and combinatorics, a centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The following ...

. * a

centered nonagonal number A centered nonagonal number (or centered enneagonal number) is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal ...

. * a centered cube number. * a

square pyramidal number In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the number of stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci. They are part of a bro ...

, being the sum of the squares of the first six

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...

s. * the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes):
. (See

1729 Events January–March * January 8 – Frederick, the eldest son of King George II of Great Britain is made Prince of Wales at the age of 21, a few months after he comes to Britain for the first time after growing up in Hano ...

for more details).
This implies that 91 is the second cabtaxi number. * the smallest positive integer expressible as a sum of six distinct squares:
. * The only other ways to write 91 as a sum of distinct squares are:
and * . * the smallest pseudoprime satisfying the congruence .Friedman, Erich
What's Special About This Number?
* a repdigit in base 9 (111₉). * palindromic in bases 3 (10101₃), 9 (111₉), and 12 (77₁₂). * the fourth composite number in the 11-aliquot tree. The aliquot sum of 91 is 21 within the aliquot sequence (91,21,11,1,0). * a Riordan number. The decimal equivalent of the fraction can be obtained by using powers of 9.

In science

* 91 is the

atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...

of protactinium, an actinide. *

McCarthy 91 function The McCarthy 91 function is a recursive function, defined by the computer scientist John McCarthy as a test case for formal verification within computer science. The McCarthy 91 function is defined as :M(n)=\begin n - 10, & \mboxn > 100\mbox ...

, a recursive function in

discrete mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuou ...

* Messier object M91, a magnitude 11.5

spiral galaxy Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''constellation A constellation is an area on the celestial sphere in which a group of visible stars forms a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the earliest constellation ...

Coma Berenices Coma Berenices is an ancient asterism in the northern sky, which has been defined as one of the 88 modern constellations. It is in the direction of the fourth galactic quadrant, between Leo and Boötes, and it is visible in both hemisphe ...

* The

New General Catalogue The ''New General Catalogue of Nebulae and Clusters of Stars'' (abbreviated NGC) is an astronomical catalogue of deep-sky objects compiled by John Louis Emil Dreyer in 1888. The NGC contains 7,840 objects, including galaxies, star clusters and ...

br>object
NGC 91, a single

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

in the constellation Andromeda

In other fields

Ninety-one is also: * The code for international direct dial phone calls to

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area, the List of countries and dependencies by population, second-most populous ...

* In cents of a

U.S. dollar The United States dollar ( symbol: $; code: USD; also abbreviated US$ or U.S. Dollar, to distinguish it from other dollar-denominated currencies; referred to as the dollar, U.S. dollar, American dollar, or colloquially buck) is the official ...

, the amount of money one has if one has one each of the coins of denominations less than a dollar (

penny A penny is a coin ( pennies) or a unit of currency (pl. pence) in various countries. Borrowed from the Carolingian denarius (hence its former abbreviation d.), it is usually the smallest denomination within a currency system. Presently, it is t ...

nickel Nickel is a chemical element with symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel is a hard and ductile transition metal. Pure nickel is chemically reactive but large pieces are slow t ...

, dime, quarter and half dollar) * The

ISBN The International Standard Book Number (ISBN) is a numeric commercial book identifier that is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency. An ISBN is assigned to each separate edition a ...

Group Identifier for books published in

Sweden Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic countries, Nordic c ...

. * Psalm 91 is known as the Psalm of Protection. * 91 is a

solitaire Solitaire is any tabletop game which one can play by oneself, usually with cards, but also with dominoes. The term "solitaire" is also used for single-player games of concentration and skill using a set layout tiles, pegs or stones. These game ...

card game where the object is to move cards, so the top cards total 91. * STS-91 Space Shuttle ''Discovery'' mission to the

International Space Station The International Space Station (ISS) is the largest Modular design, modular space station currently in low Earth orbit. It is a multinational collaborative project involving five participating space agencies: NASA (United States), Roscosmos ( ...

, June 2, 1998 * Swedish comic strip '' 91:an'' * The

91st Missile Wing The 91st Missile Wing is a United States Air Force unit assigned to the Air Force Global Strike Command Twentieth Air Force. It is stationed at Minot Air Force Base, North Dakota as a tenant unit. The 91 MW is one of the Air Force's three inte ...

(91 SW) is a

Minuteman (missile) The LGM-30 Minuteman is an American land-based intercontinental ballistic missile (ICBM) in service with the Air Force Global Strike Command. , the LGM-30G Minuteman III version is the only land-based ICBM in service in the United States and ...

III unit of the

United States Air Force The United States Air Force (USAF) is the air service branch of the United States Armed Forces, and is one of the eight uniformed services of the United States. Originally created on 1 August 1907, as a part of the United States Army Si ...

, based at Minot Air Force Base,

North Dakota North Dakota () is a U.S. state in the Upper Midwest, named after the indigenous Dakota Sioux. North Dakota is bordered by the Canadian provinces of Saskatchewan and Manitoba to the north and by the U.S. states of Minnesota to the east, ...

* The number of the French department

Essonne Essonne () is a department of France in the southern Île-de-France region. It is named after the river Essonne. In 2019, it had a population of 1,301,659 across 194 communes.Integers