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]

According to Exodus 7:7, Moses was 80 years old when he initially spoke to Pharaoh on behalf of his people. Today, 80 years of age is the upper age limit for cardinals to vote in papal elections.

Eighty is also:

used in the classic book title Around the World in Eighty Days
the length of the Eighty Years' War or Dutch revolt (1568–1648)
the standard TCP/IP port number for HTTP connections
the 80A, 80B and 80C photographic filters correct for excessive redness under tungsten lighting
The year AD 80, 80 BC, or 1980
Eighty shilling ale
The older four-pin-base version of the 5Y3GT rectifier tube
A common limit for the characters per line, in computing, derived from the number of columns in IBM cards
American band Green Day has a song called "80"
A fictional alien superhero named Ultraman 80
On the Réaumur scale, 80 degrees is the boiling temperature of pure water at sea level

^ "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.