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168 (number)

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168

← 160 161 162 163 164 165 166 167 168 169 →

← 0 100 200 300 400 500 600 700 800 900 →

one hundred sixty-eight

168th
(one hundred sixty-eighth)

2³ × 3 × 7

1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168

ΡΞΗ´

CLXVIII, clxviii

10101000₂

20020₃

440₆

250₈

120₁₂

A8₁₆

168 (one hundred [and] sixty-eight) is the natural number following 167 and preceding 169.

Mathematics

168 is a Dedekind number,^[1] and an idoneal numbers, and a Cunningham number,.^[2]

Abstract algebra

168 is the order of the second smallest nonabelian simple group $\mathrm {PSL} (2,7).$ From Hurwitz's automorphisms theorem, 168 is the maximum possible number of automorphisms of a genus 3 Riemann surface, this maximum being achieved by the Klein quartic, whose symmetry group is $\mathrm {PSL} (2,7)$ .^[3]

In other fields

Numerology

Some Chinese consider 168 a lucky number, because 一六八 ("168") Mandarin pinyin: yīliùbā is roughly homophonous with the phrase "一路發" Mandarin pinyin: yīlùfā which means "fortune all the way", or, as the United States Mint claims, "Prosperity Forever".^[4]

References

^ Sloane, N. J. A. (ed.). "Sequence A000372 (Dedekind numbers: number of monotone Boolean functions of n variables, number of antichains of subsets of an n-set, number of elements in a free distributive lattice on n generators, number of Sperner families.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-04-01.
^ "Sloane's A000926 : Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
^ "week214". math.ucr.edu. Retrieved 9 April 2023.
^ "$1 Prosperity Forever 168 Note - US Mint". Retrieved 9 April 2023.

External links

Wikimedia Commons has media related to 168 (number).

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400s, 500s, and 600s	700s, 800s, and 900s
400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693	700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999

1000s and 10,000s
1000s	1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2016 2520 3000 3511 4000 4104 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999
10,000s	10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000

100,000s to 10,000,000,000,000s
100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000

Large numbers

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Integers

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