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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.
An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers.
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").
Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are in bold and superior highly composite numbers are starred. ... 5, 15, 25, 75 6 ...
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. 89
A Lychrel number is a positive integer that never yields a palindromic number when subjected to the iterative process of being added to itself with digits reversed. [23] The question of whether there are any Lychrel numbers in base 10 is an open problem in recreational mathematics ; the smallest candidate is 196 .
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The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers