91 (number)

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

In mathematics
91 is:


 * the twenty-seventh distinct semiprime and the second of the form (7.q), where q is a higher prime.
 * the aliquot sum of 91 is 21 33; itself a semiprime, within an aliquot sequence of two composite numbers (91,21,11, 1,0) to the prime in the 11-aliquot tree. 91 is the fourth composite number in the 11-aliquot tree.(91,51,21,18).
 * a triangular number.
 * a hexagonal number, one of the few such numbers to also be a centered hexagonal number.
 * a centered nonagonal number.
 * a centered cube number.
 * a square pyramidal number, being the sum of the squares of the first six integers.
 * 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). This implies that 91 is the second cabtaxi number.
 * 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.
 * the smallest pseudoprime satisfying the congruence 3n ≡ 3 mod n.
 * a repdigit in base 9 (1119).
 * palindromic in bases 3 (101013), 9 (1119), and 12 (7712).
 * a Riordan number.
 * the smallest number that looks prime but isn't, proven using the Rotten Theorem by John Conway.

The decimal equivalent of the fraction $1/undefined$ can be obtained by using powers of 9.

In science

 * 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
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.
 * STS-91 Space Shuttle Discovery mission to the International Space Station, June 2, 1998
 * Swedish comic strip 91:an
 * The 91st Missile 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