171 (number)

Short description: Natural number

← 170 171 172 →
← 170 171 172 173 174 175 176 177 178 179 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred seventy-one
Ordinal	171st (one hundred seventy-first)
Factorization	32 × 19
Divisors	1, 3, 9, 19, 57, 171
Greek numeral	ΡΟΑ´
Roman numeral	CLXXI
Binary	101010112
Ternary	201003
Quaternary	22234
Quinary	11415
Senary	4436
Octal	2538
Duodecimal	12312
Hexadecimal	AB16
Vigesimal	8B20
Base 36	4R36

171 (one hundred [and] seventy-one) is the natural number following 170 and preceding 172.

In mathematics

171 is a triangular number and a Jacobsthal number.

There are 171 transitive relations on three labeled elements, and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices.

The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon.

There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope.

Within moonshine theory of sporadic groups, the friendly giant $\mathbb{𝕄}$ is defined as having cyclic groups ⟨ $m$ ⟩ that are linked with the function,

$f_m(\tau )=q^{-1}+a_{1}q+a_2{q}^2+...,a_k$ ∈ $\mathbb{\mathbb{Z}},q=e^{2\pi i\tau },\tau >0;$ where $q$ is the character of $\mathbb{𝕄}$ at $m$.

This generates 171 moonshine groups within $\mathbb{𝕄}$ associated with $f_m$ that are principal moduli for different genus zero congruence groups commensurable with the projective linear group $\mathrm{P}\mathrm{S}{\mathrm{L}}_{\mathrm{2}}(\mathbb{\mathbb{Z}})$.

See also

• The year AD 171 or 171 BC
• List of highways numbered 171
• All pages with titles containing 171