30 (number) - Wikiwand

In mathematics

Summarize

Perspective

30 is an even, composite, pronic number. With 2, 3, and 5 as its prime factors, it is a regular number and the first sphenic number, the smallest of the form $2\times 3\times r$ , where $r$ is a prime greater than 3. It has an aliquot sum of 42; within an aliquot sequence of thirteen composite numbers (30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0) to the Prime in the 3-aliquot tree. From 1 to the number 30, this is the longest Aliquot Sequence.

It is also:

A semiperfect number, since adding some subsets of its divisors (e.g., 5, 10 and 15) equals 30.^[1]
A primorial.^[2]
A Harshad number in decimal.^[3]
Divisible by the number of prime numbers (10) below it.
The largest number such that all coprimes smaller than itself, except for 1, are prime.
The sum of the first four squares, making it a square pyramidal number.^[4]
The number of vertices in the Tutte–Coxeter graph.
The measure of the central angle and exterior angle of a dodecagon, which is the petrie polygon of the 24-cell.
The number of sides of a triacontagon, which in turn is the petrie polygon of the 120-cell and 600-cell.
The number of edges of a dodecahedron and icosahedron, of vertices of an icosidodecahedron, and of faces of a rhombic triacontahedron.
The sum of the number of elements of a 5-cell: 5 vertices, 10 edges, 10 faces, and 5 cells.
The Coxeter number of E₈.
A largely composite number,^[5] as it has 8 divisors and no smaller number has more than 8 divisors

Furthermore,

In a group $G$ , such that $|G|=p^{n}\times m$ , where $p$ does not divide $m$ , and has a subgroup of order $p^{n}$ , 30 is the only number less than 60 that is neither a prime nor of the aforementioned form. Therefore, 30 is the only candidate for the order of a simple group less than 60, in which one needs other methods to specifically reject to eventually deduce said order.^{[citation needed]}

The SI prefix for 10³⁰ is Quetta- (Q), and for 10⁻³⁰ (i.e., the reciprocal of 10³⁰) quecto (q). These numbers are the largest and smallest number to receive an SI prefix to date.

Look up thirty in Wiktionary, the free dictionary.

In other fields

Thirty is:

Used (as –30–) to indicate the end of a newspaper (or broadcast) story, a copy editor's typographical notation
The number of days in the months April, June, September and November (and in unusual circumstances February—see February 30). Although the number of days in a month vary, 30 is used to estimate months elapsing.
In years of marriage, the pearl wedding anniversary

History and literature

Age 30 is when Jewish priests traditionally start their service (according to Numbers 4:3).
One of the rallying cries of the 1960s student/youth protest movement was the slogan, "Don't trust anyone over thirty".
In The Myth of Sisyphus the French existentialist Albert Camus comments that the age of thirty is a crucial period in the life of a man, for at that age he gains a new awareness of the meaning of time.

References