13 - Revision history

Vipul: /* Polynomials */

2012-07-03T18:12:33Z

Polynomials

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 |-
 | <math>n^2 - n + 11</math> || 2 || all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. || 2
 |}

2012-07-03T18:09:48Z

Properties and families

← Older revision		Revision as of 18:09, 3 July 2012
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	! Property or family !! Parameter values !! First few numbers !! Proof of satisfaction/membership/containment		! Property or family !! Parameter values !! First few numbers !! Proof of satisfaction/membership/containment
	\|-		\|-
	\| [[satisfies property::prime number]] \|\| it is the 6th prime number \|\| {{#lst:prime number\|list}} \|\| divide and check		\| [[satisfies property::prime number]] \|\| it is the 6th prime number \|\| {{#lst:prime number\|list}} \|\| {{divide and check up to sqrt}} Since <math>\sqrt{13}</math> is between [[3]] and [[4]], we only need to check divisibility by primes less than or equal to 3, i.e., we need to verify that 13 is not divisible by the primes [[2]] and [[3]].
	\|-		\|-
	\| [[satisfies property::Proth prime]]: prime of the form <math>k \cdot 2^n + 1</math> with <math>2^n > k</math> \|\| <math>n = 2, k = 3</math> \|\| {{#lst:Proth prime\|list}} \|\|		\| [[satisfies property::Proth prime]]: prime of the form <math>k \cdot 2^n + 1</math> with <math>2^n > k</math> \|\| <math>n = 2, k = 3</math> \|\| {{#lst:Proth prime\|list}} \|\|

2012-07-03T18:08:41Z

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 The number 13 is a [[satisfies property::prime number]].
-==Prime-generating polynomials==
+===Properties and families===
 Below are some polynomials that give prime numbers for small input values, which give the value 13 for suitable input choice.

2012-01-15T22:02:33Z

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 |-
 | <math>n^2 - n + 11</math> || 2 || all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. || 2
 |}

2012-01-15T21:59:30Z

← Older revision		Revision as of 21:59, 15 January 2012
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	The number 13 is a [[satisfies property::prime number]].		The number 13 is a [[satisfies property::prime number]].

			==Prime-generating polynomials==

			Below are some polynomials that give prime numbers for small input values, which give the value 13 for suitable input choice.

			{\| class="sortable" border="1"
			! Polynomial !! Degree !! Some values for which it generates primes !! Input value <math>n</math> at which it generates 13
			\|-
			\| <math>n^2 - n + 11</math> \|\| 2 \|\| all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. \|\| 2
			\|}

2012-01-02T22:51:31Z

Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 13 is a satisfies property::prime number."

New page

{{particular natural number}}

==Summary==

===Factorization===

The number 13 is a [[satisfies property::prime number]].