229 (number)

Last updated
228 229 230
Cardinal two hundred twenty-nine
Ordinal 229th
(two hundred twenty-ninth)
Factorization prime
Prime yes
Greek numeral ΣΚΘ´
Roman numeral CCXXIX
Binary 111001012
Ternary 221113
Senary 10216
Octal 3458
Duodecimal 17112
Hexadecimal E516

229 (two hundred [and] twenty-nine) is the natural number following 228 and preceding 230.

Contents

In mathematics

It is a prime number, and a regular prime. [1] It is also a full reptend prime, meaning that the decimal expansion of the unit fraction 1/229 repeats periodically with as long a period as possible. [2] With 227 it is the larger of a pair of twin primes, [3] and it is also the start of a sequence of three consecutive squarefree numbers. [4] It is the smallest prime that, when added to the reverse of its decimal representation, yields another prime: 229 + 922 = 1151. [5]

There are 229 cyclic permutations of the numbers from 1 to 7 in which none of the numbers is mapped to its successor (mod 7), [6] 229 rooted tree structures formed from nine carbon atoms, [7] and 229 triangulations of a polygon formed by adding three vertices to each side of a triangle. [8] 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, [9] all of which may be realized by straight lines in the Euclidean plane. [10] [11]

The complete graph K13 has 229 crossings in its straight-line drawing with the fewest possible crossings. [12] [13]

Related Research Articles

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

19 (nineteen) is the natural number following 18 and preceding 20. It is a prime number.

68 (sixty-eight) is the natural number following 67 and preceding 69. It is an even number.

109 is the natural number following 108 and preceding 110.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

400 is the natural number following 399 and preceding 401.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

900 is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10 it is a Harshad number. It is also the first number to be the square of a sphenic number.

135 is the natural number following 134 and preceding 136.

213 is the number following 212 and preceding 214.

185 is the natural number following 184 and preceding 186.

313 is the natural number following 312 and preceding 314.

10,000,000 is the natural number following 9,999,999 and preceding 10,000,001.

100,000,000 is the natural number following 99,999,999 and preceding 100,000,001.

233 is the natural number following 232 and preceding 234.

290 is the natural number following 289 and preceding 291.

204 is the natural number following 203 and preceding 205.

20,000 is the natural number that comes after 19,999 and before 20,001.

References

  1. Sloane, N. J. A. (ed.). "SequenceA007703(Regular primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. Sloane, N. J. A. (ed.). "SequenceA001913(Full reptend primes: primes with primitive root 10)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "SequenceA006512(Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. Sloane, N. J. A. (ed.). "SequenceA007675(Numbers n such that n, n+1 and n+2 are squarefree)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. Sloane, N. J. A. (ed.). "SequenceA061783(Primes p such that p + (p reversed) is also a prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. Sloane, N. J. A. (ed.). "SequenceA000757(Number of cyclic permutations of [n] with no i->i+1 (mod n))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  7. Sloane, N. J. A. (ed.). "SequenceA000678(Number of carbon (rooted) trees with n carbon atoms = unordered 4-tuples of ternary trees)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  8. Sloane, N. J. A. (ed.). "SequenceA087809(Number of triangulations (by Euclidean triangles) having 3+3n vertices of a triangle with each side subdivided by n additional points)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  9. Sloane, N. J. A. (ed.). "SequenceA001403(Number of combinatorial configurations of type (n_3))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  10. Sloane, N. J. A. (ed.). "SequenceA099999(Number of geometrical configurations of type (n_3))". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  11. Gropp, Harald (1997), "Configurations and their realization", Discrete Mathematics , 174 (1–3): 137–151, doi: 10.1016/S0012-365X(96)00327-5 .
  12. Sloane, N. J. A. (ed.). "SequenceA014540(Rectilinear crossing number of complete graph on n nodes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  13. Aichholzer, Oswin; Krasser, Hannes (2007), "Abstract order type extension and new results on the rectilinear crossing number", Computational Geometry, 36 (1): 2–15, doi: 10.1016/j.comgeo.2005.07.005 , MR   2264046 .

See also