229 (number)

← 228 229 230 →
Cardinaltwo hundred twenty-nine
Ordinal229th
(two hundred twenty-ninth)
Factorizationprime
Primeyes
Greek numeralΣΚΘ´
Roman numeralCCXXIX, ccxxix
Binary111001012
Ternary221113
Senary10216
Octal3458
Duodecimal17112
HexadecimalE516

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

In mathematics

It is the fiftieth 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]

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A007703 (Regular primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A001913 (Full reptend primes: primes with primitive root 10)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A006512 (Greater of twin primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A007675 (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.). "Sequence A061783 (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.). "Sequence A000757 (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.). "Sequence A000678 (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.). "Sequence A087809 (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.). "Sequence A001403 (Number of combinatorial configurations of type (n_3))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ Sloane, N. J. A. (ed.). "Sequence A099999 (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.). "Sequence A014540 (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.

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