Editing Number (section)

==Subclasses of the integers==

===Even and odd numbers===
{{main|Even and odd numbers}}
An '''even number''' is an integer that is "evenly divisible" by two, that is [[Euclidean division|divisible by two without remainder]]; an '''odd number''' is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "[[divisibility|divisible]]".) Any odd number ''n'' may be constructed by the formula {{nowrap|''n'' {{=}} 2''k'' + 1,}} for a suitable integer ''k''. Starting with {{nowrap|''k'' {{=}} 0,}} the first non-negative odd numbers are {1, 3, 5, 7, ...}. Any even number ''m'' has the form {{nowrap|''m'' {{=}} 2''k''}} where ''k'' is again an [[integer]]. Similarly, the first non-negative even numbers are {0, 2, 4, 6, ...}.

===Prime numbers===
{{main|Prime number}}
A '''prime number''', often shortened to just '''prime''', is an integer greater than 1 that is not the product of two smaller positive integers. The first few prime numbers are 2, 3, 5, 7, and 11. There is no such simple formula as for odd and even numbers to generate the prime numbers. The primes have been widely studied for more than 2000 years and have led to many questions, only some of which have been answered. The study of these questions belongs to [[number theory]]. [[Goldbach's conjecture]] is an example of a still unanswered question: "Is every even number the sum of two primes?"

One answered question, as to whether every integer greater than one is a product of primes in only one way, except for a rearrangement of the primes, was confirmed; this proven claim is called the [[fundamental theorem of arithmetic]]. A proof appears in [[Euclid's Elements]].

===Other classes of integers===
Many subsets of the natural numbers have been the subject of specific studies and have been named, often after the first mathematician that has studied them. Example of such sets of integers are [[Fibonacci number]]s and [[perfect number]]s. For more examples, see [[Integer sequence]].