Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Difference between revisions of "Sophie Germain prime"

From Prime-Wiki
Jump to: navigation, search
(restored)
 
(Tagging variables)
 
(3 intermediate revisions by one other user not shown)
Line 1: Line 1:
A [[prime number]] p is called a '''Sophie Germain prime''' if 2p + 1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2*23+1 = 47, also prime.
+
A [[prime]] number {{V|p}} is called a '''Sophie Germain prime''' if 2{{V|p}}+1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2*23+1 = 47, also prime.
  
 
It is not known whether there are infinitely many Sophie Germain primes.
 
It is not known whether there are infinitely many Sophie Germain primes.
Line 6: Line 6:
 
The next table includes the first 500 Sophie Germain primes.
 
The next table includes the first 500 Sophie Germain primes.
  
 +
==Table==
 
'''''ToDo: List of primes as document'''''
 
'''''ToDo: List of primes as document'''''
 +
 +
This is only a test.
 +
{| class="wikitable"
 +
! No. !! {{V|p}} !! Link
 +
|-
 +
| 1 || 2 || -
 +
|-
 +
| 2 || 3 || {{NRi|2}}
 +
|-
 +
| 3 || 5 || {{NRi|3|1}}
 +
|-
 +
| 4 || 11 || {{NRi|3|2}}
 +
|-
 +
| 5 || 23 || {{NRi|3|3}}
 +
|-
 +
| 6 || 29 || {{NRi|15|1}}
 +
|-
 +
| 7 || 41 || {{NRi|21|1}}
 +
|-
 +
| 8 || 53 || {{NRi|27|1}}
 +
|-
 +
| 9 || 83 || {{NRi|21|2}}
 +
|-
 +
| 10 || 89 || {{NRi|45|1}}
 +
|-
 +
| 11 || 113 || {{NRi|57|1}}
 +
|-
 +
| 12 || 131 || {{NRi|33|2}}
 +
|-
 +
| 13 || 173 || {{NRi|87|1}}
 +
|-
 +
| 14 || 179 || {{NRi|45|2}}
 +
|-
 +
| 15 || 191 || {{NRi|3|6}}
 +
|-
 +
| 16 || 233 || {{NRi|117|1}}
 +
|-
 +
| 17 || 239 || {{NRi|15|4}}
 +
|-
 +
| 18 || 251 || {{NRi|63|2}}
 +
|-
 +
| 19 || 281 || {{NRi|141|1}}
 +
|-
 +
| 20 || 293 || {{NRi|147|1}}
 +
|-
 +
| 212 || 11519 || {{NRi|45|8}}
 +
|-
 +
| 100000 || 19391363 || {{NRi|4847841|2}}
 +
|-
 +
| || 145135534866431 || {{NRi|33|42}}
 +
|}
 +
:Note: Possible to give the No. (if available) in the comments of the [[Riesel prime]] page (see [[:Template:NVal|Template NVal]])?
  
 
==External links==
 
==External links==
 
*[http://primes.utm.edu/top20/page.php?id=2 Top 20 known Sophie Germain primes]
 
*[http://primes.utm.edu/top20/page.php?id=2 Top 20 known Sophie Germain primes]
 
*[[Wikipedia:Sophie Germain prime|Sophie Germain prime]]
 
*[[Wikipedia:Sophie Germain prime|Sophie Germain prime]]
[[Category:Primes]]
+
*The {{OEIS|l|A005384}}
 +
[[Category:Prime]]

Latest revision as of 04:26, 3 November 2020

A prime number p is called a Sophie Germain prime if 2p+1 is also prime. For example, 23 is a Sophie Germain prime because it is a prime and 2*23+1 = 47, also prime.

It is not known whether there are infinitely many Sophie Germain primes.

List of Sophie Germain primes

The next table includes the first 500 Sophie Germain primes.

Table

ToDo: List of primes as document

This is only a test.

No. p Link
1 2 -
2 3 Mersenne 22-1
3 5 Riesel 3•21-1
4 11 Riesel 3•22-1
5 23 Riesel 3•23-1
6 29 Riesel 15•21-1
7 41 Riesel 21•21-1
8 53 Riesel 27•21-1
9 83 Riesel 21•22-1
10 89 Riesel 45•21-1
11 113 Riesel 57•21-1
12 131 Riesel 33•22-1
13 173 Riesel 87•21-1
14 179 Riesel 45•22-1
15 191 Riesel 3•26-1
16 233 Riesel 117•21-1
17 239 Riesel 15•24-1
18 251 Riesel 63•22-1
19 281 Riesel 141•21-1
20 293 Riesel 147•21-1
212 11519 Riesel 45•28-1
100000 19391363 Riesel 4847841•22-1
145135534866431 Riesel 33•242-1
Note: Possible to give the No. (if available) in the comments of the Riesel prime page (see Template NVal)?

External links