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# 229 (number)

 ← 228 229 230 →
Cardinaltwo hundred twenty-nine
Ordinal229th
(two hundred twenty-ninth)
Factorizationprime
Primeyes
Greek numeralΣΚΘ´
Roman numeralCCXXIX
Binary111001012
Ternary221113
Quaternary32114
Quinary14045
Senary10216
Octal3458
Duodecimal17112
VigesimalB920
Base 366D36

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

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]

## 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. ^
6. ^
7. ^
8. ^
9. ^
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. ^
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.