30 (number)
30 is the natural number following 29 and preceding 31.
In mathematics
30 is an even, composite, and 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, where is a prime greater than 3. It has an aliquot sum of 42; within an aliquot sequence of thirteen composite numbers 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 equals 30.
- A primorial.
- A Harshad number in decimal.
- Divisible by the number of prime numbers 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.
- 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, as it has 8 divisors and no smaller number has more than 8 divisors
In a group, such that, where does not divide, and has a subgroup of order, 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.
The SI prefix for 1030 is Quetta-, and for 10−30 quecto. These numbers are the largest and smallest number to receive an SI prefix to date.
In other fields
Thirty is:- Used to indicate the end of a newspaper story, a copy editor's typographical notation
- The number of days in the months April, June, September and November. Although the number of days in a month vary, 30 is used to estimate months elapsing.
- In years of marriage, the pearl wedding anniversary
- The international calling code for Greece
History and literature
- Age 30 is when Jewish priests traditionally start their service.
- 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.