91 (number)

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

← 90 92 → 91
← 90 91 92 93 94 95 96 97 98 99 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	ninety-one
Ordinal	91st (ninety-first)
Numeral system	91
Factorization	$7 \cdot 13$
Divisors	1, 7, 13, 91
Roman numeral	XCI
Binary	10110112
Octal	1338
Duodecimal	7712
Hexadecimal	5B16

In mathematics

Ninety-one is the twenty-seventh distinct semiprime and the second of the form (7.q). The aliquot sum of 91 is 21 within the aliquot sequence (91,21,11,1,0) 91 being the fourth composite number in the 11-aliquot tree.

Ninety-one is a triangular number and a hexagonal number, one of the few such numbers to also be a centered hexagonal number, and it is also a centered nonagonal number and a centered cube number. It is a square pyramidal number, being the sum of the squares of the first six integers.

It is 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 = 6³+(-5)³ = 4³+3³. (See 1729 for more details).

It is also the smallest positive integer expressible as a sum of six distinct squares: 91 = 1²+2²+3²+4²+5²+6². The only other ways to write 91 as a sum of distinct squares are: 91 = 1²+4²+5²+7² and 91 = 1²+3²+9².

It is also the smallest pseudoprime satisfying the congruence 3ⁿ = 3 mod n.^[1]

91 is a repdigit in base 9 (111). 91 is after number 90 and before number 92.

In science

• The atomic number of protactinium, an actinide.
• McCarthy 91 function, a recursive function in discrete mathematics

In astronomy,

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

The Saros number of the solar eclipse series which began on August 6, 159 BC and ended on 1175 October. The duration of Saros series 91 was 1334.2 years, and it contained 75 solar eclipses.

The Saros number of the lunar eclipse series which began on 161 May and ended on 1459 July. The duration of Saros series 91 was 1298.1 years, and it contained 73 lunar eclipses.

In other fields

Ninety-one is also:

• The year AD 91, 91 BC, or 1991.
• The designation of American Interstate 91, a freeway that runs from Connecticut to Vermont
• The designation of U.S. Route 91, a north-south highway that runs from Utah to Idaho
• 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

References

1. ^ Friedman, Erich. What's Special About This Number?

Divisibility of 91:

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