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Other integer data types are implemented with a fixed size, usually a number of bits which is a power of 2 (4, 8, 16, etc.) or a memorable number of decimal digits (e.g., 9 or 10). Cardinality The set of integers is countably infinite , meaning it is possible to pair each integer with a unique natural number.
Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
Name First elements Short description OEIS Natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... The natural numbers (positive integers) n ∈ . A000027: Triangular ...
The integers consist of 0, the natural numbers (1, 2, 3, ...), and their negatives (−1, −2, −3, ...). The set of all integers is usually denoted by Z (or Z in blackboard bold, ), which stands for Zahlen (German for "numbers"). Articles about integers are automatically sorted in numerical order.
It is also the first number that is the sum of its proper divisors, making it the smallest perfect number. [2] 6 is the first unitary perfect number, since it is the sum of its positive proper unitary divisors, without including itself. Only five such numbers are known to exist. [3] 6 is the largest of the four all-Harshad numbers. [4]
[2] The internal representation of this datum is the way the value is stored in the computer's memory. Unlike mathematical integers, a typical datum in a computer has some minimal and maximum possible value. The most common representation of a positive integer is a string of bits, using the binary numeral system.
Cuisenaire rods: 5 (yellow) cannot be evenly divided in 2 (red) by any 2 rods of the same color/length, while 6 (dark green) can be evenly divided in 2 by 3 (lime green). In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. [1]
An integer is determined to be even if it is divisible by two. When written in base 10, all multiples of 2 will end in 0, 2, 4, 6, or 8. [3] 2 is the smallest and the only even prime number, and the first Ramanujan prime. [4] It is also the first superior highly composite number, [5] and the first colossally abundant number. [6]