# 91 (number)

| ||||
---|---|---|---|---|

Cardinal | ninety-one | |||

Ordinal |
91st (ninety-first) | |||

Factorization | 7 × 13 | |||

Divisors | 1, 7, 13, 91 | |||

Greek numeral | ϞΑ´ | |||

Roman numeral | XCI | |||

Binary |
1011011_{2} | |||

Ternary |
10101_{3} | |||

Quaternary |
1123_{4} | |||

Quinary |
331_{5} | |||

Senary |
231_{6} | |||

Octal |
133_{8} | |||

Duodecimal |
77_{12} | |||

Hexadecimal |
5B_{16} | |||

Vigesimal |
4B_{20} | |||

Base 36 |
2J_{36} |

**91** (**ninety-one**) is the natural number following 90 and preceding 92.

Look up in Wiktionary, the free dictionary.ninety-one |

## In mathematics[edit]

91 is:

- the twenty-seventh distinct semiprime and the second of the form (7.q).
- a triangular number.
- a hexagonal number,
^{[1]}one of the few such numbers to also be a centered hexagonal number.^{[2]} - a centered nonagonal number.
^{[3]} - a centered cube number.
^{[4]} - a square pyramidal number, being the sum of the squares of the first six integers.
^{[5]} - 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): 91 = 6
^{3}+ (−5)^{3}= 4^{3}+ 3^{3}. (See 1729 for more details). This implies that 91 is the second cabtaxi number. - the smallest positive integer expressible as a sum of six distinct squares: 91 = 1
^{2}+ 2^{2}+ 3^{2}+ 4^{2}+ 5^{2}+ 6^{2}. The only other ways to write 91 as a sum of distinct squares are: 91 = 1^{2}+ 4^{2}+ 5^{2}+ 7^{2}and 91 = 1^{2}+ 3^{2}+ 9^{2}. - the smallest pseudoprime satisfying the congruence 3
^{n}≡ 3 mod*n*.^{[6]} - a repdigit in base 9 (111
_{9}). - palindromic in bases 3 (10101
_{3}), 9 (111_{9}), and 12 (77_{12}). - 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).

The decimal equivalent of the fraction ^{1}⁄_{91} can be obtained by using powers of 9.

## In science[edit]

- 91 is the atomic number of protactinium, an actinide.
- McCarthy 91 function, a recursive function in discrete mathematics
- Messier object M91, a magnitude 11.5 spiral galaxy in the constellation Coma Berenices
- The New General Catalogue object NGC 91, a single star in the constellation Andromeda

## In other fields[edit]

**Ninety-one** is also:

- The code for international direct dial phone calls to India
- In cents of a U.S. dollar, the amount of money one has if one has one each of the coins of denominations less than a dollar (penny, nickel, dime, quarter and half dollar)
- The ISBN Group Identifier for books published in Sweden.
- Psalm 91 is known as the Psalm of Protection. It is also the title of a book by Peggy Joyce Ruth
- 91 is a solitaire 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, June 2, 1998
- Swedish comic strip 91:an
- The 91st Space Wing (91 SW) is a Minuteman (missile) III unit of the United States Air Force, based at Minot Air Force Base, North Dakota
- The number of the French department Essonne
- Ninety One or 91 is a Kazakhstan Q-pop boy band formed by JUZ Entertainment in 2014

## References[edit]

**^**"Sloane's A000384 : Hexagonal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-29.**^**"Sloane's A003215 : Hex (or centered hexagonal) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-29.**^**"Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-29.**^**"Sloane's A005898 : Centered cube numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-29.**^**"Sloane's A000330 : Square pyramidal numbers".*The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-05-29.**^**Friedman, Erich. What's Special About This Number?