229 (two hundred ndtwenty-nine) is the

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 ...

following 228 and preceding 230.

In mathematics

It is the fiftieth

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 ...

, and a regular prime. It is also a

full reptend prime In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat ...

, meaning that the decimal expansion of the

unit fraction A unit fraction is a positive fraction with one as its numerator, 1/. It is the multiplicative inverse (reciprocal) of the denominator of the fraction, which must be a positive natural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When a ...

1/229 repeats periodically with as long a period as possible. With 227 it is the larger of a pair of twin primes, and it is also the start of a sequence of three consecutive squarefree numbers. It is the smallest prime that, when added to the reverse of its decimal representation, yields another prime: 229 + 922 = 1151. There are 229

cyclic permutation In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has ''k'' elements, it may be called a ''k ...

s of the numbers from 1 to 7 in which none of the numbers is mapped to its successor (mod 7), 229 rooted tree structures formed from nine

carbon Carbon () is a chemical element; it has chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetravalent—meaning that its atoms are able to form up to four covalent bonds due to its valence shell exhibiting 4 ...

atoms, and 229 triangulations of a polygon formed by adding three vertices to each side of a triangle. There are also 229 different projective configurations of type (12₃12₃), in which twelve points and twelve lines meet with three lines through each of the points and three points on each of the lines, all of which may be realized by straight lines in the

Euclidean plane In mathematics, a Euclidean plane is a Euclidean space of Two-dimensional space, dimension two, denoted \textbf^2 or \mathbb^2. It is a geometric space in which two real numbers are required to determine the position (geometry), position of eac ...

. The

complete graph In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices i ...

''K''₁₃ has 229 crossings in its straight-line drawing with the fewest possible crossings..

In mathematics

References

See also