53 - Revision history

Vipul: /* Summary */

2012-06-23T01:22:57Z

Summary

← Older revision		Revision as of 01:22, 23 June 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]] \|\| \|\| {{#lst:prime number\|list}} \|\| divide and check		\| [[satisfies property::prime number]] \|\| \|\| {{#lst:prime number\|list}} \|\| {{divide and check up to sqrt}} In this case, since <math>\sqrt{53}</math> is between 7 and 8, verifying primality requires checking that 53 is not divisible by any prime up to 7, i.e., it is not divisible by [[2]], [[3]], [[5]], or [[7]].
	\|-		\|-
	\| [[satisfies property::regular prime]] \|\| \|\| {{#lst:regular prime\|list}} \|\|		\| [[satisfies property::regular prime]] \|\| \|\| {{#lst:regular prime\|list}} \|\|

Vipul: /* Properties and families */

2012-01-16T04:19:06Z

Properties and families

@@ Line 9: / Line 9: @@
 ===Properties and families===
-{{fillin}}
+{| class="sortable" border="1"
 ==Prime-generating polynomials==

Vipul: /* Prime-generating polynomials */

2012-01-15T22:14:22Z

Prime-generating polynomials

← Older revision		Revision as of 22:14, 15 January 2012
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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]]. \|\| 7		\| <math>n^2 - n + 11</math> \|\| 2 \|\| all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. \|\| 7
	\|-		\|-
	\| <math>n^2 - n + 41</math> \|\| 2 \|\| all numbers 1-40, because 41 is one of the [[lucky numbers of Euler]]. \|\| 5		\| <math>n^2 - n + 41</math> \|\| 2 \|\| all numbers 1-40, because 41 is one of the [[lucky numbers of Euler]]. \|\| 4
	\|}		\|}

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 53 is a prime number. ===Properties and families=== {{fillin}} ==Prime-generating polynomial..."

2012-01-15T22:14:10Z

Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number 53 is a prime number. ===Properties and families=== {{fillin}} ==Prime-generating polynomial..."

New page

{{particular natural number}}

==Summary==

===Factorization===

The number 53 is a [[prime number]].

===Properties and families===

{{fillin}}

==Prime-generating polynomials==

Below are some polynomials that give prime numbers for small input values, which give the value 53 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 53
|-
| <math>n^2 - n + 11</math> || 2 || all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. || 7
|-
| <math>n^2 - n + 41</math> || 2 || all numbers 1-40, because 41 is one of the [[lucky numbers of Euler]]. || 5
|}