Primality
1 is by convention neither a prime number nor a composite number, but a unit (meaning of ring theory) like −1 and, in the Gaussian integers, i and −i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units. For example, 4 = 22, but if units are included, is also equal to, say, (−1)6 × 123 × 22, among infinitely many similar "factorizations". 1 appears to meet the naïve definition of a prime number, being evenly divisible only by 1 and itself (also 1). As such, some mathematicians considered it a prime number as late as the middle of the 20th century, but mathematical consensus has generally and since then universally been to exclude it for a variety of reasons (such as complicating the fundamental theorem of arithmetic and other theorems related to prime numbers). 1 is the only positive integer divisible by exactly one positive integer, whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers. Table of basic calculations
In technology
The resin identification code used in recycling to identify polyethylene terephthalate. The ITU country code for the North American Numbering Plan area, which includes the United States, Canada, and parts of the Caribbean. A binary code is a sequence of 1 and 0 that is used in computers for representing any kind of data. In many physical devices, 1 represents the value for "on", which means that electricity is flowing.
The numerical value of true in many programming languages. 1 is the ASCII code of "Start of Header". In science
Dimensionless quantities are also known as quantities of dimension one. 1 is the atomic number of hydrogen. +1 is the electric charge of positrons and protons. Group 1 of the periodic table consists of the alkali metals. Period 1 of the periodic table consists of just two elements, hydrogen and helium. The dwarf planet Ceres has the minor-planet designation 1 Ceres because it was the first asteroid to be discovered. The Roman numeral I often stands for the first-discovered satellite of a planet or minor planet (such as Neptune I, a.k.a. Triton). For some earlier discoveries, the Roman numerals originally reflected the increasing distance from the primary instead. In philosophy
In the philosophy of Plotinus (and that of other neoplatonists), The One is the ultimate reality and source of all existence. Philo of Alexandria (20 BC – AD 50) regarded the number one as Gods number, and the basis for all numbers ("De Allegoriis Legum," ii.12 [i.66]). The Neopythagorean philosopher Nicomachus of Gerasa affirmed that one is not a number, but the source of number. He also believed the number two is the embodiment of the origin of otherness. His number theory was recovered by Boethius in his Latin translation of Nicomachuss treatise Introduction to Arithmetic.