92 (number) explained

Number:	92
Divisor:	1, 2, 4, 23, 46, 92

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

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

M _{n} (collectively), as defined by permutations based on elements 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 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

n such that 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).^[1]

In other fields

Ninety-two is also:

• 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.

Notes and References

1. 2024-02-27 .