35 (thirty-five) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
34 and preceding
36.
In mathematics
35 is the sum of the first five
triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
s, making it a
tetrahedral number
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron. The th tetrahedral number, , is the sum of the first triangular numbers, that is,
...
.
35 is the number of ways that three things can be selected from a set of seven unique things, also known as the "
combination
In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are th ...
of seven things taken three at a time".
35 is a
centered cube number
A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equival ...
, a
centered tetrahedral number
A centered tetrahedral number is a centered figurate number that represents a tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, ...
, a
pentagonal number
A pentagonal number is a figurate number that extends the concept of triangular and square numbers to the pentagon, but, unlike the first two, the patterns involved in the construction of pentagonal numbers are not rotationally symmetrical. The ...
, and a
pentatope number
A pentatope number is a number in the fifth cell of any row of Pascal's triangle starting with the 5-term row , either from left to right or from right to left.
The first few numbers of this kind are:
: 1, 5, 15, 35, 70, 126, 210, 330, 4 ...
.
35 is a
highly cototient number In number theory, a branch of mathematics, a highly cototient number is a positive integer k which is above 1 and has more solutions to the equation
:x - \phi(x) = k
than any other integer below k and above 1. Here, \phi is Euler's totient fun ...
, since there are more solutions to the equation
than there are for any other integers below it except 1.
There are 35 free
hexomino
A hexomino (or 6-omino) is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex(a)-. When rotations and reflections are not c ...
es, the
polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling.
Polyominoes have been used in pop ...
es made from six squares.
Since the greatest prime factor of
is 613, which is more than 35 twice, 35 is a
Størmer number In mathematics, a Størmer number or arc-cotangent irreducible number is a positive integer n for which the greatest prime factor of n^2+1 is greater than or equal to 2n. They are named after Carl Størmer.
Sequence
The first few Størmer numbers ...
.
35 is the tenth discrete
semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime nu ...
(
) and the first with 5 as the lowest non-unitary factor. The aliquot sum of 35 is 13, this being the second
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...
with such an aliquot sum; the first being the cube
27. 35 is the last member of the first triple cluster of semiprimes 33, 34, 35. The second such triple discrete semiprime cluster is 85, 86, 87.
35 is the highest number one can count to on one's fingers using
senary
A senary () numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two con ...
.
35 is the number of quasigroups of order 4.
35 is the smallest
composite number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...
of the form
, where is a non-negative integer.
In science
*The
atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of
bromine
Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table (halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simila ...
In other fields
*
35 mm film 35 mm may refer to:
* 135 film, a type of still photography format commonly referred to as 35 mm film
* 35 mm movie film
35 mm film is a film gauge used in filmmaking, and the film standard. In motion pictures that record on f ...
is the basic film gauge most commonly used for both analog
photography
Photography is the art, application, and practice of creating durable images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film. It is employed ...
and
motion pictures
A film also called a movie, motion picture, moving picture, picture, photoplay or (slang) flick is a work of visual art that simulates experiences and otherwise communicates ideas, stories, perceptions, feelings, beauty, or atmosphere ...
.
* The minimum age of presidential candidates for election to the
United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...
,
Ireland
Ireland ( ; ga, Éire ; Ulster Scots dialect, Ulster-Scots: ) is an island in the Atlantic Ocean, North Atlantic Ocean, in Northwestern Europe, north-western Europe. It is separated from Great Britain to its east by the North Channel (Grea ...
,
Russia
Russia (, , ), or the Russian Federation, is a List of transcontinental countries, transcontinental country spanning Eastern Europe and North Asia, Northern Asia. It is the List of countries and dependencies by area, largest country in the ...
,
Trinidad and Tobago
Trinidad and Tobago (, ), officially the Republic of Trinidad and Tobago, is the southernmost island country in the Caribbean. Consisting of the main islands Trinidad and Tobago, and numerous much smaller islands, it is situated south of ...
, and
Uruguay
Uruguay (; ), officially the Oriental Republic of Uruguay ( es, República Oriental del Uruguay), is a country in South America. It shares borders with Argentina to its west and southwest and Brazil to its north and northeast; while bordering ...
.
* For
Social Security in the United States
Social organisms, including human(s), live collectively in interacting populations. This interaction is considered social whether they are aware of it or not, and whether the exchange is voluntary or not.
Etymology
The word "social" derives from ...
, the 35 highest years of earnings are used to calculate retirement benefits.
See also
*
List of highways numbered 35
References
{{Integers, zero
Integers