185 (number)

There are 185 different directed graphs on four unlabeled vertices that have at least one sink vertex, with no outgoing edges,^[1] 185 ways of permuting the squares of a ${\displaystyle 2\times 4}$ grid of squares in such a way that each square is one unit away from its original position horizontally, vertically, or diagonally,^[2] and 185 matroids on five labeled elements in which each element participates in at least one basis.^[3]

The Spiral of Theodorus is formed by unit-length line segments that, together with the center point of the spiral, form right triangles. 185 of these right triangles fit within the first four turns of this spiral.^[4]

185 is the smallest base b without algebraic factorisation of generalized repunits for which no generalized repunit primes are known.^[5] It is known that the generalized repunit number ${\displaystyle {\frac {185^{p}-1}{184}}}$ is composite for all prime p < 350,000.^[5]

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