80 (number)

80 (eighty) is the natural number following 79 and preceding 81.

80 is:

• The sum of Euler's totient function φ(x) over the first sixteen integers:

1 +たす 1 +たす 2 +たす 2 +たす 4 +たす 2 +たす 6 +たす 4 +たす 6 +たす 4 +たす 10 +たす 4 +たす 12 +たす 6 +たす 8 +たす 8 =わ 80.

• A semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20, and 40) gives 80.^[1]
• A ménage number.^[2]
• Palindromic in bases 3 (2222₃), 6 (212₆), 9 (88₉), 15 (55₁₅), 19 (44₁₉), and 39 (22₃₉).
• A repdigit in bases 3, 9, 15, 19, and 39.
• The sum of the first four twin prime pairs:

(3 + 5) + (5 + 7) + (11 + 13) + (17 + 19) = 80.

The Pareto principle (also known as the 80-20 rule) states that, for many events, roughly 80% of the effects come from 20% of the causes.^{[3] [4]}

Every solvable configuration of the 15 puzzle can be solved in no more than 80 single-tile moves.^[5]

In Northern Europe, there have traditionally been words for eighty units - often eggs or herrings: Wall  [de; da; no] in German, ol in Danish, and øll in Norwegian (all cognates).

• wiktionary:eighty for 80 in other languages.

• Integers

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