It is the fiftiethprime number, and aregular prime.[1]It is also afull reptend prime, meaning that the decimal expansion of theunit fraction 1/229 repeats periodically with as long a period as possible.[2]With227 it is the larger of a pair oftwin primes,[3]and it is also the start of a sequence of three consecutivesquarefree 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 229cyclic permutations of the numbers from 1 to 7 in which none of the numbers is mapped to its successor (mod 7),[6]229rooted tree structures formed from ninecarbon atoms,[7]and 229triangulations of a polygon formed by adding three vertices to each side of a triangle.[8]There are also 229 differentprojective 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 theEuclidean plane.[10][11]
^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,MR2264046.
