Prime number: Difference between revisions
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* It is a [[prime element]] in the [[ring of integers]]. | * It is a [[prime element]] in the [[ring of integers]]. | ||
* It is relatively prime to all the numbers less than itself. | * It is relatively prime to all the numbers less than itself. | ||
==Occurrence== | |||
===Initial values=== | |||
<section begin="list"/>[[2]], [[3]], [[5]], [[7]], [[11]], [[13]], [[17]], [[19]], [[23]], [[29]], [[31]], [[37]], [[41]], [[43]], [[47]], [[53]], [[59]], [[61]], [[67]], [[71]], [[73]], [[79]], [[83]], [[89]], [[97]], <toggledisplay>[[101]], [[103]], [[107]], [[109]], [[113]], [[127]], [[131]], [[137]], [[139]], [[149]], [[151]], [[157]], [[163]], 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, [[257]], 263, 269, 271</toggledisplay>[[Oeis:A000040|View list on OEIS]]<section end="list"/> | |||
Latest revision as of 22:35, 15 January 2012
This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers
Definition
A prime number is a natural number greater than satisfying the following equivalent conditions:
- It has exactly two positive divisors: itself and .
- It is a prime element in the ring of integers.
- It is relatively prime to all the numbers less than itself.
Occurrence
Initial values
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, [SHOW MORE]