80 (number)

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

In mathematics

80 is:

the sum of Euler's totient function φ(x) over the first sixteen integers.
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 4 twin prime pairs ((3 + 5) + (5 + 7) + (11 + 13) + (17 + 19)).

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]

^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
^ "Sloane's A000179 : Ménage numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
^ Bunkley, Nick (March 3, 2008). "Joseph Juran, 103, Pioneer in Quality Control, Dies". The New York Times..
^ "What is 80/20 Rule, Pareto's Law, Pareto Principle". Archived from the original on 2013-01-28. Retrieved 2017-05-20..
^ A. Brüngger, A. Marzetta, K. Fukuda and J. Nievergelt, The parallel search bench ZRAM and its applications, Annals of Operations Research 90 (1999), pp. 45–63.