92 (number)

← 91 92 93 →
← 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-two
Ordinal	92nd (ninety-second)
Factorization	2^2 × 23
Divisors	1, 2, 4, 23, 46, 92
Greek numeral	ϞΒ´
Roman numeral	XCII
Binary	10111002
Ternary	101023
Senary	2326
Octal	1348
Duodecimal	7812
Hexadecimal	5C16

92 (ninety-two) is the natural number following 91 and preceding 93

In mathematics

Form

92 is a composite number of the general form p²q, where q is a higher prime (23). It is the tenth of this form and the eighth of the form 2²q.

Properties

• 92 has an aliquot sum of 76, within an aliquot sequence of five numbers (92, 76, 64, 63, 41) before reaching 1. 44, the totient of 92, is also the composite index of 63,^[1] where the reduced totient of 92 is 22.^[2] 41 is the thirteenth prime number and sixth super-prime.
• Its arithmetic mean of its six divisors^[3] is twenty-eight,^[4][5] where (6, 28) represent the first two perfect numbers.^[6] It is the sixtieth arithmetic number, where 60 is the second unitary perfect number (the next such number is 90).
• For ${\displaystyle n=8}$, there are 92 solutions in the n-Queens Problem.
• 92 is the eighth pentagonal number.^[7]
• 92 is an Erdős–Woods number, since it is possible to find sequences of 92 consecutive integers such that each inner member shares a factor with either the first or the last member.^[8]

There are 92 "atomic elements" in John Conway's look-and-say sequence, corresponding to the 92 non-transuranic elements in the chemist's periodic table.

Solids

The most faces or vertices an Archimedean or Catalan solid can have is 92: the snub dodecahedron has 92 faces while its dual polyhedron, the pentagonal hexecontahedron, has 92 vertices. On the other hand, as a simple polyhedron, the final stellation of the icosahedron has 92 vertices.

There are 92 Johnson solids.

Abstract algebra

92 is the total number of objects that are permuted by the series of five finite, simple Mathieu groups ${\displaystyle \mathbb {M} _{n}}$ (collectively), as defined by permutations based on elements ${\displaystyle n\in \{11,12,22,23,24\}}$. Half of 92 is 46 (the largest even number that is not the sum of two abundant numbers), which is the number of maximal subgroups of the friendly giant ${\displaystyle \mathbb {F} _{1}}$, the largest "sporadic" finite simple group.

In different bases

92 is palindromic in other bases, where it is represented as 232₆, 161₇, 44₂₂, and 22₄₅.

There are 92 numbers ${\displaystyle n}$ such that ${\displaystyle 2^{n}}$ does not contain all digits in base ten (the largest such number is 168, where 68 is the smallest number with such a representation containing all digits, followed by 70 and 79).^[9]

In science

• The atomic number of uranium, an actinide.
• Messier object M92, a magnitude 7.5 globular cluster in the constellation Hercules
• The New General Catalogue object NGC 92, a magnitude 13.1 peculiar spiral galaxy in the constellation Phoenix, and a member of Robert's Quartet

In other fields

Ninety-two is also:

• The code for international direct dial phone calls to Pakistan.
• The numeric code for the Hauts-de-Seine department of France. The number is reflected in the department's postal code, plus the names of at least three local sports clubs, specifically Racing 92 in rugby union and Metropolitans 92 and Nanterre 92 in basketball.
• In the title of the book Ninety-two in the Shade, by Thomas McGuane.
• The 92nd Tiger book by Michael Gilbert.
• The House on 92nd Street, a 1945 film.
• The model number of the gray Texas Instruments TI-92 graphing calculator.
• The Beretta 92 series of semi-automatic pistols.
• The "Illustrious 92" or "Glorious 92": Massachusetts legislators who refused to rescind the Massachusetts Circular Letter soliciting other British colonies' support in resistance to the Townshend Acts prior to the American Revolution. Analogous to the number 45 in reference to the protests of John Wilkes against British corruption.
• The ISBN Group Identifier for books published by international publishers such as UNESCO.
• The number which runs through almost every single of British film-maker Peter Greenaway's films. This number has special association with the fictional character of Greenaway's creation, Tulse Luper. It is said the number itself is based on a mathematical error in calculations concerning John Cage's work Indeterminacy. See The Falls for extensive use of this number.
• "92", a song by Avail from their 1996 album 4am Friday.
• STS-92 Space Shuttle Discovery mission, on October 11, 2000, to the International Space Station.
• According to Guinness World Records, Taumatawhakatangihangakoauauotamateaurehaeaturipukakapikimaungahoronukupokaiwhenuakitanatahu is the longer version of the longest place name in the world, with 92 letters.
• The 92nd Street Y in Manhattan.

Vehicles

• The Saab 92 automobile
• The USS Tacoma (PG-92) gunboat

In sports

• The 92 Club is a society of association football fans who have attended a home match of all 92 current member clubs of the Premier League and English Football League in England and Wales.

See also

• List of highways numbered 92

References

1. Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
2. Sloane, N. J. A. (ed.). "Sequence A002322 (Reduced totient function psi(n): least k such that x^k congruent 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
3. Sloane, N. J. A. (ed.). "Sequence A000005 (d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
4. Sloane, N. J. A. (ed.). "Sequence A003601". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
5. Sloane, N. J. A. (ed.). "Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
6. Sloane, N. J. A. (ed.). "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
7. "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
8. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
9. Sloane, N. J. A. (ed.). "Sequence A130696 (Numbers k such that 2^k does not contain all ten decimal digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-27.