151 (one hundred
ndfifty-one) is a
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
. It follows
150 and precedes
152.
In mathematics
151 is the 36th
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
, the previous is
149, with which it comprises a
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
. 151 is also a
palindromic prime
In mathematics, a palindromic prime (sometimes called a palprime) is a prime number that is also a palindromic number. Palindromicity depends on the base of the number system and its notational conventions, while primality is independent of such ...
, a
centered decagonal number, and a
lucky number
In number theory, a lucky number is a natural number in a set which is generated by a certain " sieve". This sieve is similar to the sieve of Eratosthenes that generates the primes, but it eliminates numbers based on their position in the rema ...
.
151 appears in the
Padovan sequence, preceded by the terms
65,
86,
114 114 may refer to:
*114 (number)
*AD 114
*114 BC
*114 (1st London) Army Engineer Regiment, Royal Engineers, an English military unit
*114 (Antrim Artillery) Field Squadron, Royal Engineers, a Northern Irish military unit
*114 (MBTA bus)
*114 (New Je ...
; it is the sum of the first two of these.
151 is a
unique prime in
base 2, since it is the only prime with period 15 in base 2.
There are 151
4-uniform tilings, such that the symmetry of tilings with regular polygons have four
orbits
In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificia ...
of vertices.
151 is the number of
uniform paracompact honeycombs with infinite
facets and
vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a general -polytope is sliced off.
Definitions
Take some corner or Vertex (geometry), vertex of a polyhedron. Mark a point somewhere along each connected ed ...
s in the
third dimension
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (''coordinates'') are required to determine the position of a point. Most commonly, it is the three-dim ...
, which stem from
23 different
Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean ref ...
s. Split into two
whole numbers, 151 is the sum of 75 and 76, both relevant numbers in
Euclidean and
hyperbolic
Hyperbolic may refer to:
* of or pertaining to a hyperbola, a type of smooth curve lying in a plane in mathematics
** Hyperbolic geometry, a non-Euclidean geometry
** Hyperbolic functions, analogues of ordinary trigonometric functions, defined u ...
3-space:
*
75 is the total number of non-
prismatic
An optical prism is a transparent optics, optical element with flat, polished surfaces that are designed to refraction, refract light. At least one surface must be angled—elements with two parallel surfaces are ''not'' prisms. The most fami ...
uniform polyhedra
In geometry, a uniform polyhedron has regular polygons as faces and is vertex-transitive—there is an isometry mapping any vertex onto any other. It follows that all vertices are congruent. Uniform polyhedra may be regular (if also fac ...
, which incorporate
regular polyhedra
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different eq ...
,
semiregular polyhedra
In geometry, the term semiregular polyhedron (or semiregular polytope) is used variously by different authors.
Definitions
In its original definition, it is a polyhedron with regular polygonal faces, and a symmetry group which is transitive on ...
, and
star polyhedra,
*75
uniform compound polyhedra, inclusive of seven types of families of
prisms and
antiprisms,
* 76 is the number of unique
uniform compact hyperbolic honeycombs that are solely generated from
Wythoff constructions.
While 151 is the 36th indexed prime, its
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
149 has a
reciprocal whose
repeating decimal
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that i ...
expansion has a
digit sum
In mathematics, the digit sum of a natural number in a given radix, number base is the sum of all its numerical digit, digits. For example, the digit sum of the decimal number 9045 would be 9 + 0 + 4 + 5 = 18.
Definition
Let n be a natural number. ...
of
666, which is the
magic constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is ...
in a
prime reciprocal magic square equal to the sum of the first 36 non-zero
integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative in ...
s, or equivalently the 36th
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 ...
.
Furthermore, the sum between twin primes (149, 151) is
300
__NOTOC__
Year 300 ( CCC) was a leap year starting on Monday of the Julian calendar. At the time, it was known as the Year of the Consulship of Constantius and Valerius (or, less frequently, year 1053 ''Ab urbe condita''). The denomination 300 ...
, which in turn is the 24th triangular number.
References
{{DEFAULTSORT:151 (Number)
Integers