Sophie Germain prime - Revision history

Vipul: /* Occurrence */

2012-01-02T22:08:27Z

Occurrence

← Older revision		Revision as of 22:08, 2 January 2012
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	===Initial values===		===Initial values===

	~~{{oeis\|A005384}}~~

	The first few Sophie Germain primes are:		The first few Sophie Germain primes are:

Vipul: /* Initial values */

2012-01-02T22:07:57Z

Initial values

← Older revision		Revision as of 22:07, 2 January 2012
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	{{oeis\|A005384}}		{{oeis\|A005384}}

	The first few Sophie Germain primes are: 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559.		The first few Sophie Germain primes are:

			<section begin="list"/>[[2]], [[3]], [[5]], [[11]], [[23]], [[29]], [[41]], [[53]], [[83]], [[89]], <toggledisplay>113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559 </toggledisplay>[[Oeis:A005384\|View list on OEIS]]<section end="list"/>

	The first few primes that are ''not'' Sophie Germain primes are: 7, 13, 17, 19, 31.		The first few primes that are ''not'' Sophie Germain primes are: 7, 13, 17, 19, 31.

Vipul: /* Density in primes */

2010-05-03T20:15:00Z

Density in primes

← Older revision		Revision as of 20:15, 3 May 2010
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	! Cutoff <math>n</math> !! Number of primes <math>\le n</math> !! Number of Sophie Germain primes <math>\le n</math> !! Proportion of primes that are Sophie Germain primes !! Number of Sophie Germain primes divided by <math>n/(\ln n)^2</math>		! Cutoff <math>n</math> !! Number of primes <math>\le n</math> !! Number of Sophie Germain primes <math>\le n</math> !! Proportion of primes that are Sophie Germain primes !! Number of Sophie Germain primes divided by <math>n/(\ln n)^2</math>
	\|-		\|-
	\| 10 \|\| 4 \|\| 3 \|\| <math>3/4 = 0.75</math> \|\|		\| 10 \|\| 4 \|\| 3 \|\| <math>3/4 = 0.75</math> \|\| <math>1.59057</math>
	\|-		\|-
	\| 100 \|\| 25 \|\| 10 \|\| <math>2/5 = 0.4</math> \|\|		\| 100 \|\| 25 \|\| 10 \|\| <math>2/5 = 0.4</math> \|\| <math>2.12076</math>
	\|-		\|-
	\| 1000 \|\| 168 \|\| 37 \|\| <math>37/168 \approx 0.22</math> \|\|		\| 1000 \|\| 168 \|\| 37 \|\| <math>37/168 \approx 0.22</math> \|\| <math>1.76553</math>
	\|}		\|}

Vipul at 20:11, 3 May 2010

2010-05-03T20:11:20Z

@@ Line 7: / Line 7: @@
 ==Occurrence==
-===Initial examples===
+===Initial values===
-The first few Sophie Germain primes are <math>2,3,5,11,23,29</math>. The first prime that is ''not'' a Sophie Germain prime is <math>7</math>.
+{{oeis|A005384}}
 ===Infinitude conjecture===

Vipul: /* Occurrence */

2009-04-21T23:52:32Z

Occurrence

← Older revision		Revision as of 23:52, 21 April 2009
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	where <math>\pi_{SG}(n)</math> denotes the number of Sophie Germain primes less than or equal to <math>n</math>.		where <math>\pi_{SG}(n)</math> denotes the number of Sophie Germain primes less than or equal to <math>n</math>.

			Other related conjectures to the existence of Sophie Germain primes are:

			* [[Conjecture on existence of Cunningham chains of the first kind of arbitrary length]]
			* [[Conjecture on existence of bitwin chains of arbitrary length]]

	===Infinitude of complement===		===Infinitude of complement===

Vipul: /* Occurrence */

2009-04-21T23:51:30Z

Occurrence

← Older revision		Revision as of 23:51, 21 April 2009
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	==Occurrence==		==Occurrence==

			===Initial examples===

			The first few Sophie Germain primes are <math>2,3,5,11,23,29</math>. The first prime that is ''not'' a Sophie Germain prime is <math>7</math>.

	===Infinitude conjecture===		===Infinitude conjecture===

Vipul at 23:49, 21 April 2009

2009-04-21T23:49:55Z

@@ Line 5: / Line 5: @@
 A '''Sophie Germain prime''' is a [[prime number]] <math>p</math> such that <math>2p + 1</math> is also prime. The corresponding prime <math>2p + 1</math> is termed a [[safe prime]].
 ==Testing==
 {{oeis|A005384}}

Vipul at 15:49, 20 April 2009

2009-04-20T15:49:48Z

← Older revision		Revision as of 15:49, 20 April 2009
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	==Definition==		==Definition==

	A '''Sophie Germain prime''' is a [[prime number]] <math>p</math> such that <math>2p + 1</math> is also prime.		A '''Sophie Germain prime''' is a [[prime number]] <math>p</math> such that <math>2p + 1</math> is also prime. The corresponding prime <math>2p + 1</math> is termed a [[safe prime]].


	==Testing==		==Testing==

	{{oeis\|A005384}}		{{oeis\|A005384}}

Vipul at 15:46, 20 April 2009

2009-04-20T15:46:46Z

← Older revision		Revision as of 15:46, 20 April 2009
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	A '''Sophie Germain prime''' is a [[prime number]] <math>p</math> such that <math>2p + 1</math> is also prime.		A '''Sophie Germain prime''' is a [[prime number]] <math>p</math> such that <math>2p + 1</math> is also prime.

			==Testing==

			{{oeis\|A005384}}

Vipul: Created page with '{{prime number property}} ==Definition== A '''Sophie Germain prime''' is a prime number $p$ such that $2p + 1$ is also prime.'

2009-03-21T22:49:05Z

Created page with '{{prime number property}} ==Definition== A '''Sophie Germain prime''' is a prime number <math>p</math> such that <math>2p + 1</math> is also prime.'

New page

{{prime number property}}

==Definition==

A '''Sophie Germain prime''' is a [[prime number]] <math>p</math> such that <math>2p + 1</math> is also prime.

Sophie Germain prime - Revision history

Vipul: /* Occurrence */

Vipul: /* Initial values */

Vipul: /* Density in primes */

Vipul at 20:11, 3 May 2010

Vipul: /* Occurrence */

Vipul: /* Occurrence */

Vipul at 23:49, 21 April 2009

Vipul at 15:49, 20 April 2009

Vipul at 15:46, 20 April 2009

Vipul: Created page with '{{prime number property}} ==Definition== A '''Sophie Germain prime''' is a prime number p such that 2p + 1 is also prime.'

Vipul: Created page with '{{prime number property}} ==Definition== A '''Sophie Germain prime''' is a prime number $p$ such that $2p + 1$ is also prime.'