Safe prime - Revision history

Vipul: /* Occurrence */

2012-01-02T22:11:10Z

Occurrence

← Older revision		Revision as of 22:11, 2 January 2012
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	{{oeis\|A005385}}		{{oeis\|A005385}}

	The first few safe primes are: 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903.		The first few safe primes are:

			<section begin="list"/>[[5]], [[7]], [[11]], [[23]], [[47]], [[59]], [[83]], [[107]], [[167]], <toggledisplay>179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903</toggledisplay>[[Oeis:A005385\|View list on OEIS]]<section end="list"/>

	The first few primes that are ''not'' safe primes are: 2, 3, 13, 17, 19.		The first few primes that are ''not'' safe primes are: 2, 3, 13, 17, 19.

Vipul at 21:26, 29 May 2010

2010-05-29T21:26:14Z

← Older revision		Revision as of 21:26, 29 May 2010
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	The corresponding prime <math>(p-1)/2</math> is termed a [[defining ingredient::Sophie Germain prime]].		The corresponding prime <math>(p-1)/2</math> is termed a [[defining ingredient::Sophie Germain prime]].

			==Occurrence==

			===Initial values===

			{{oeis\|A005385}}

			The first few safe primes are: 5, 7, 11, 23, 47, 59, 83, 107, 167, 179, 227, 263, 347, 359, 383, 467, 479, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207, 2447, 2459, 2579, 2819, 2879, 2903.

			The first few primes that are ''not'' safe primes are: 2, 3, 13, 17, 19.

			===Density in primes===

			{\| class="wikitable" border="1"
			! Cutoff <math>n</math> !! Number of primes <math>\le n</math> !! Number of safe primes <math>\le n</math> !! Proportion of primes that are safe primes
			\|-
			\| 10 \|\| 4 \|\| 2 \|\| <math>1/2 = 0.5</math>
			\|-
			\| 100 \|\| 25 \|\| 7 \|\| <math>7/25 = 0.28</math>
			\|-
			\| 1000 \|\| 168 \|\| 24 \|\| <math>25/168 \approx 0.15</math>
			\|}

	==Relation with other properties==		==Relation with other properties==

Vipul: /* Related properties of longer chains of primes */

2009-04-21T22:14:17Z

Related properties of longer chains of primes

← Older revision		Revision as of 22:14, 21 April 2009
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	===Related properties of longer chains of primes===		===Related properties of longer chains of primes===

	* [[Cunningham chain]] is a chain of primes <math>q_1 < q_2 < \dots < q_k</math> such that <math>q_{i+1} = 2q_i + 1</math>.		* [[Cunningham chain of the first kind]] is a chain of primes <math>q_1 < q_2 < \dots < q_k</math> such that <math>q_{i+1} = 2q_i + 1</math>.
	* [[Bitwin chain]] is a collection of multiple pairs of twin primes, each pair being double the previous one.		* [[Bitwin chain]] is a collection of multiple pairs of twin primes, each pair being double the previous one.

Vipul at 22:13, 21 April 2009

2009-04-21T22:13:55Z

← Older revision		Revision as of 22:13, 21 April 2009
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	The corresponding prime <math>(p-1)/2</math> is termed a [[defining ingredient::Sophie Germain prime]].		The corresponding prime <math>(p-1)/2</math> is termed a [[defining ingredient::Sophie Germain prime]].

			==Relation with other properties==

			===Related properties of primes or pairs of primes===

			* [[Sophie Germain prime]] is a prime <math>q</math> such that <math>2q + 1</math> is also a prime.
			* [[Twin primes]] are primes that differ by two.

			===Related properties of longer chains of primes===

			* [[Cunningham chain]] is a chain of primes <math>q_1 < q_2 < \dots < q_k</math> such that <math>q_{i+1} = 2q_i + 1</math>.
			* [[Bitwin chain]] is a collection of multiple pairs of twin primes, each pair being double the previous one.

			==Facts==

			* [[Quadratic nonresidue that is not minus one is primitive root for safe prime]]
			* [[Safe prime has plus or minus two as a primitive root]]

Vipul: Created page with '{{prime number property}} ==Definition== A prime number $p$ is termed a '''safe prime''' if $p$ is odd and $(p-1)/2$ is also a [[prime numb...'

2009-04-20T15:52:49Z

Created page with '{{prime number property}} ==Definition== A prime number <math>p</math> is termed a '''safe prime''' if <math>p</math> is odd and <math>(p-1)/2</math> is also a [[prime numb...'

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