31 - Revision history

Vipul: /* Properties and families */

2012-06-23T01:21:27Z

Properties and families

← Older revision		Revision as of 01:21, 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]] \|\| 11th prime number \|\| {{#lst:prime number\|list}} \|\| divide and check		\| [[satisfies property::prime number]] \|\| 11th prime number \|\| {{#lst:prime number\|list}} \|\| {{divide and check up to sqrt}} In this case, since <math>\sqrt{31}</math> is between 5 and 6, verifying primality requires checking that 31 i not divisible by any prime up to 5, i.e., it is not divisible by [[2]], [[3]], or [[5]].
	\|-		\|-
	\| [[satisfies property::Mersenne number]] <math>M_n = 2^n - 1</math> \|\| <math>n = 5</math>, i.e., <math>M_5 = 2^5 - 1</math> \|\| {{#lst:Mersenne number\|list}} \|\| plug and check		\| [[satisfies property::Mersenne number]] <math>M_n = 2^n - 1</math> \|\| <math>n = 5</math>, i.e., <math>M_5 = 2^5 - 1</math> \|\| {{#lst:Mersenne number\|list}} \|\| plug and check

Vipul: /* Properties and families */

2012-06-23T01:08:40Z

Properties and families

← Older revision		Revision as of 01:08, 23 June 2012
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	\| [[satisfies property::regular prime]] \|\| 10th regular prime (note that 2 is neither a regular nor an irregular prime) \|\| {{#lst:regular prime\|list}} \|\|		\| [[satisfies property::regular prime]] \|\| 10th regular prime (note that 2 is neither a regular nor an irregular prime) \|\| {{#lst:regular prime\|list}} \|\|
	\|-		\|-
	\| [[satisfies property::Euclid ~~prime~~]] \|\| ~~prime~~ that is of the form [[primorial]] + 1 \|\| {{#lst:Euclid ~~prime~~\|list}} \|\| [[30]] is a primorial: it is the product of the first three primes		\| [[satisfies property::Euclid number]] \|\| number that is of the form [[primorial]] + 1 \|\| {{#lst:Euclid number\|list}} \|\| [[30]] is a primorial: it is the product of the first three primes
	\|}		\|}

Vipul: /* Summary */

2012-06-23T01:07:53Z

Summary

← Older revision		Revision as of 01:07, 23 June 2012
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	\| [[satisfies property::Mersenne number]] <math>M_n = 2^n - 1</math> \|\| <math>n = 5</math>, i.e., <math>M_5 = 2^5 - 1</math> \|\| {{#lst:Mersenne number\|list}} \|\| plug and check		\| [[satisfies property::Mersenne number]] <math>M_n = 2^n - 1</math> \|\| <math>n = 5</math>, i.e., <math>M_5 = 2^5 - 1</math> \|\| {{#lst:Mersenne number\|list}} \|\| plug and check
	\|-		\|-
	\| [[satisfies property::Mersenne prime]] (both a [[Mersenne number]] and a [[prime number]]) \|\| \|\| \|\|		\| [[satisfies property::Mersenne prime]] (both a [[Mersenne number]] and a [[prime number]]) \|\| \|\| {{#lst:Mersenne prime\|list}} \|\|
	\|-		\|-
	\| [[satisfies property::regular prime]] \|\| 10th regular prime (note that 2 is neither a regular nor an irregular prime) \|\| {{#lst:regular prime\|list}} \|\|		\| [[satisfies property::regular prime]] \|\| 10th regular prime (note that 2 is neither a regular nor an irregular prime) \|\| {{#lst:regular prime\|list}} \|\|
			\|-
			\| [[satisfies property::Euclid prime]] \|\| prime that is of the form [[primorial]] + 1 \|\| {{#lst:Euclid prime\|list}} \|\| [[30]] is a primorial: it is the product of the first three primes
	\|}		\|}

Vipul: /* Prime-generating polynomials */

2012-01-15T22:42:17Z

Prime-generating polynomials

← Older revision		Revision as of 22:42, 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]]. \|\| 5		\| <math>n^2 - n + 11</math> \|\| 2 \|\| all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. \|\| 5
			\|-
			\| <math>2n^2 + 29</math> \|\| 2 \|\| all numbers 0-28 \|\| 1
	\|}		\|}

Vipul: /* Prime-generating polynomials */

2012-01-15T21:54:32Z

Prime-generating polynomials

@@ Line 29: / Line 29: @@
 |-
 | <math>n^2 - n + 11</math> || 2 || all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. || 5
 |}

Vipul: /* Prime-generating polynomials */

2012-01-15T21:53:31Z

Prime-generating polynomials

← Older revision		Revision as of 21:53, 15 January 2012
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	==Prime-generating polynomials==		==Prime-generating polynomials==

	Below are some polynomials that give prime numbers for small input values, which give the value 23 for suitable input choice.		Below are some polynomials that give prime numbers for small input values, which give the value 31 for suitable input choice.

	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Polynomial !! Degree !! Some values for which it generates primes !! Input value <math>n</math> at which it generates 23		! Polynomial !! Degree !! Some values for which it generates primes !! Input value <math>n</math> at which it generates 31
	\|-		\|-
	\| <math>n^2 - n + 11</math> \|\| 2 \|\| all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. \|\| 5		\| <math>n^2 - n + 11</math> \|\| 2 \|\| all numbers 1-10, because 11 is one of the [[lucky numbers of Euler]]. \|\| 5
	\|}		\|}

Vipul at 21:53, 15 January 2012

2012-01-15T21:53:11Z

@@ Line 19: / Line 19: @@
 |-
 | [[satisfies property::regular prime]] || 10th regular prime (note that 2 is neither a regular nor an irregular prime) || {{#lst:regular prime|list}} ||
 |}

Vipul at 21:55, 2 January 2012

2012-01-02T21:55:03Z

← Older revision		Revision as of 21:55, 2 January 2012
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	\|-		\|-
	\| [[satisfies property::Mersenne prime]] (both a [[Mersenne number]] and a [[prime number]]) \|\| \|\| \|\|		\| [[satisfies property::Mersenne prime]] (both a [[Mersenne number]] and a [[prime number]]) \|\| \|\| \|\|
			\|-
			\| [[satisfies property::regular prime]] \|\| 10th regular prime (note that 2 is neither a regular nor an irregular prime) \|\| {{#lst:regular prime\|list}} \|\|
	\|}		\|}

Vipul: Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number is a prime number. ===Properties and families=== {| class="sortable" border="1" ! Property or..."

2012-01-02T21:44:27Z

Created page with "{{particular natural number}} ==Summary== ===Factorization=== The number is a prime number. ===Properties and families=== {| class="sortable" border="1" ! Property or..."

New page

{{particular natural number}}

==Summary==

===Factorization===

The number is a [[prime number]].

===Properties and families===

{| class="sortable" border="1"
! Property or family !! Parameter values !! First few numbers !! Proof of satisfaction/membership/containment
|-
| [[satisfies property::prime number]] || 11th prime number || {{#lst:prime number|list}} || divide and check
|-
| [[satisfies property::Mersenne number]] <math>M_n = 2^n - 1</math> || <math>n = 5</math>, i.e., <math>M_5 = 2^5 - 1</math> || {{#lst:Mersenne number|list}} || plug and check
|-
| [[satisfies property::Mersenne prime]] (both a [[Mersenne number]] and a [[prime number]]) || || ||
|}