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Difference between revisions of "Template:Proth prime"

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(cat. for Proth k=3k)
(display ktype changed)
 
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Template Proth prime
 
Template Proth prime
  
−
Display of current data for Proth primes, comments will be displayed as references at the bottom.
+
Display of current data for Proth primes {{Kbn|+|k|b|n}}, comments will be displayed as references at the bottom.
  
 
==Prototype==
 
==Prototype==
Line 9: Line 9:
 
{{Proth prime
 
{{Proth prime
 
|Pk=
 
|Pk=
 +
|Pb=
 +
|PCount=
 
|PNash=
 
|PNash=
 
|PMaxn=
 
|PMaxn=
Line 16: Line 18:
 
|PNlist=
 
|PNlist=
 
|PRemarks=
 
|PRemarks=
 +
|PSieve=
 
}}
 
}}
 
</pre>
 
</pre>
 +
 +
==Parameters==
 +
*'''Pk:''' the {{Vk}}-value of {{Kbn|+|k|b|n}}
 +
*'''Pb:''' the {{Vb}}-value of {{Kbn|+|k|b|n}}
 +
*'''PCount:''' the number of {{Vn}}-values given
 +
: If no count is given, this will be automatically counted. If given and differs from automated value, a warning will be shown.
 +
*'''PNash:''' the [[Nash weight]]
 +
*'''PMaxn:''' highest {{Vn}}-value of continuous searched range (from {{Vn}}=1)
 +
*'''PDate:''' last date of edit (latest history entry)
 +
*'''PReserved:''' person(s) who reserved this sequence (comma separated)
 +
*'''PMultiRes:''' number of [[:Category:Multi Reservation|Multi Reservation]]: PMaxn and PDate will be taken from there
 +
*'''PNlist:''' list of every {{Vn}}-value (one per row) with comments
 +
*'''PRemarks:''' any helpful text or links for this sequence
 +
*'''PSieve:''' if set a zip-file can be uploaded (filename is given then) if not available; if exists file is downloadable
  
 
==Explanations==
 
==Explanations==
−
In case of the following conditions special categories will be set automatically:
+
In case of the following conditions special categories will be set automatically ({{Vb}} = 2 only):
−
*k-value is disvisible by 15 &rarr; category [[:Category:Proth k=15k value|Proth 15k]] is set
+
*{{Vk}}-value is disvisible by 3 &rarr; category [[:Category:Proth 2 3k-value|Proth 3k]] is set
−
*k-value is disvisible by 2145 &rarr; category [[:Category:Proth k=2145k value|Proth 2145k]] is set
+
*{{Vk}}-value is disvisible by 15 &rarr; category [[:Category:Proth 2 15k-value|Proth 15k]] is set
−
*k-value is disvisible by 2805 &rarr; category [[:Category:Proth k=2805k value|Proth 2805k]] is set
+
*{{Vk}}-value is disvisible by 2145 &rarr; category [[:Category:Proth 2 2145k-value|Proth 2145k]] is set
−
*Nash-weight < 1000 &rarr; category [[:Category:Proth k=Low weight|Proth Low weight]] is set
+
*{{Vk}}-value is disvisible by 2805 &rarr; category [[:Category:Proth 2 2805k-value|Proth 2805k]] is set
 +
Any base:
 +
*Nash-weight < 1000 &rarr; category [[:Category:Proth 2 Low-weight|Proth Low-weight]] is set
 +
*If there are 100 {{Vn}}-values or more → [[:Category:Proth 2 Count-100|Proth Count-100]] is set
 +
*If PCount=0 &rarr; category [[:Category:Proth 2 Count-0|Proth Count 0]] is set
 +
*If PCount=0 & PNash=0 & PMaxn=0 → [[:Category:Proth 2 Sierpinski|Proth Sierpinski]] is set
  
−
The category [[:Category:Proth prime|Proth prime]] is set by default.
+
The category [[:Category:Proth prime|Proth prime]] for base {{Vb}} is set by default.
  
 
If "PMultiRes" is set, the parameters "PMaxn", "PDate" and "PReserved" (if given) will be ignored and replaced by the data from the [[:Category:Multi Reservation|Multi Reservation]] with ID given.
 
If "PMultiRes" is set, the parameters "PMaxn", "PDate" and "PReserved" (if given) will be ignored and replaced by the data from the [[:Category:Multi Reservation|Multi Reservation]] with ID given.
Line 37: Line 59:
 
{{Proth prime
 
{{Proth prime
 
|Pk=15
 
|Pk=15
 +
|Pb=2
 +
|PCount=4
 
|PNash=239
 
|PNash=239
 
|PMaxn=20
 
|PMaxn=20
Line 44: Line 68:
 
|PNlist=
 
|PNlist=
 
2;T:ST;C: Testtext
 
2;T:ST;C: Testtext
−
3;T:SW;C:[[Examples]]
+
3;T:SW;C:[[Help:Examples|Examples]]
 
5;C:'''Example'''
 
5;C:'''Example'''
 
15;43912;C:with Top5000 entry
 
15;43912;C:with Top5000 entry
−
|PRemarks=For this ''k''-value theses are the [[Fermat prime]]s.
+
|PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s.
 +
|PSieve=y
 
}}
 
}}
 
</pre>
 
</pre>
Line 53: Line 78:
 
{{Proth prime
 
{{Proth prime
 
|Pk=15
 
|Pk=15
 +
|Pb=2
 +
|PCount=4
 
|PNash=239
 
|PNash=239
 
|PMaxn=20
 
|PMaxn=20
Line 60: Line 87:
 
|PNlist=
 
|PNlist=
 
2;T:ST;C: Testtext
 
2;T:ST;C: Testtext
−
3;T:SW;C:[[Examples]]
+
3;T:SW;C:[[Help:Examples|Examples]]
 
5;C:'''Example'''
 
5;C:'''Example'''
 
15;43912;C:with Top5000 entry
 
15;43912;C:with Top5000 entry
−
|PRemarks=For this ''k''-value theses are the [[Fermat prime]]s.
+
|PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s.
 +
|PSieve=
 
}}
 
}}
−
[[Category:Prime collections]]</noinclude><includeonly>__NOTOC__{{#ifeq:{{NAMESPACENUMBER}}|0|{{DISPLAYTITLE:Proth primes of the form {{Kbn|+|{{#explode:{{PAGENAME}}||-1}}|2|n}}}}{{#if:{{{PMultiRes|}}}|{{ReservedM|{{{PMultiRes}}}}}|{{#if:{{{PReserved|}}}|{{Reserved|{{{PReserved}}}}}}}}}}}
+
[[Category:Prime collections]]</noinclude><includeonly>__NOTOC__{{#ifeq:{{NAMESPACENUMBER}}|0|{{DISPLAYTITLE:Proth primes of the form {{Kbn|+|{{#explode:{{PAGENAME}}||-1}}|{{#explode:{{PAGENAME}}||-2}}|n}}}}{{#if:{{{PMultiRes|}}}|{{ReservedM|{{{PMultiRes}}}}}|{{#if:{{{PReserved|}}}|{{Reserved|{{{PReserved}}}}}}}}}}}<!--
 +
-->{{#if:{{{PCount|}}}||[[Category:Missing XCount]]}}<!--
 +
-->{{#vardefine:_cnt|{{NVal list|{{{PNlist}}}|count}}}}<!--
 +
-->{{#vardefine:_sir|0}}{{#ifeq:{{{PCount}}}|0|{{#ifeq:{{{PNash}}}|0|{{#ifeq:{{{PMaxn}}}|0|{{#vardefine:_sir|1}}}}}}}}{{#ifeq:{{NAMESPACENUMBER}}|10|{{#vardefine:_cnt|4}}}}
 
==Current data==
 
==Current data==
 
{| class="primedata"
 
{| class="primedata"
−
| class="primetemplate" |
+
| class="primetemplate color-PrimeTemplate" |
 
  {|  
 
  {|  
−
   | align="right"| <b>k-value :</b> || {{{Pk}}}<!--{{#if:{{{CKSieve|}}}|&nbsp;([[:File:{{PAGENAME}} sieve.zip|sieve]])|}}--> {{K-type|Proth|{{{Pk}}}}}
+
   | align="right"| <b>{{Vk}} , {{Vb}} :</b> || {{{Pk}}} , {{{Pb}}} {{#if:{{{PSieve|}}}|{{#ifexist:File:{{PAGENAME}} sieve.zip|&nbsp;([[:File:{{PAGENAME}} sieve.zip|sieve]])|[[File:{{PAGENAME}} sieve.zip|Upload me!]]}}}}
 +
{{#vardefine:ktype|{{K-type|Proth|{{{Pk}}}|{{{Pb}}}}}}}{{#ifeq:{{{Pb}}}|2|{{#if:{{{Pk|}}}|{{#ifeq:{{#var:_sir}}|1|{{#vardefine:ktype|no}}}}}}}}{{#if:{{#pos:{{#var:ktype}}|center}}|
 +
{{!}}-
 +
{{!}} align="right"{{!}} <b>Type :</b> {{!}}{{!}} {{#var:ktype}}
 +
}}
 
   |-
 
   |-
−
   | align="right"| <b>Count :</b> || {{NVal list|{{{PNlist}}}|count}}
+
   | align="right"| <b>Count :</b> || {{#if:{{{PCount|}}}|{{#ifeq:{{{PCount|}}}|{{#var:_cnt}}|{{{PCount}}}|{{Alert|Attention!|Parameter PCount&#61;{{{PCount}}} differs from counting&#61;{{#var:_cnt}}}}[[Category:Wrong XCount]]}}|{{Alert|Attention!|Parameter PCount&#61;{{#var:_cnt}} not given!}}}}
 
   |-
 
   |-
 
   | align="right"| <b>Nash :</b> || {{{PNash}}}
 
   | align="right"| <b>Nash :</b> || {{{PNash}}}
 
   |-
 
   |-
−
   | align="right"| <b>Max&nbsp;<i>n</i> :</b> || {{#if:{{{PMultiRes|}}}|{{Num|{{Multi Reservation:{{{PMultiRes}}}-NMax}}}}|{{Num|{{{PMaxn}}}}}}}
+
   | align="right"| <b>Max&nbsp;{{Vn}} :</b> || {{#if:{{{PMultiRes|}}}|{{#if:{{{PMaxn|}}}|{{Num|{{{PMaxn}}}}} ({{Num|{{Multi Reservation:{{{PMultiRes}}}-NMax}}}})[[Category:Proth {{{Pb}}} Missing-range|#.....{{padleft:{{{Pk}}}|5|0}}]]|{{Num|{{Multi Reservation:{{{PMultiRes}}}-NMax}}}}}}|{{#if:{{{PMaxn|}}}|{{Num|{{{PMaxn}}}}}|{{Alert|Attention!|Parameter PMaxn not given!}}}}}}
 
   |-
 
   |-
−
   | align="right"| <b>Date :</b> || {{#if:{{{PMultiRes|}}}|{{Multi Reservation:{{{PMultiRes}}}-Date}}|{{{PDate}}}}}
+
   | align="right"| <b>Date :</b> || {{#if:{{{PMultiRes|}}}|{{#if:{{{PDate|}}}|{{{PDate}}} ({{Multi Reservation:{{{PMultiRes}}}-Date}})|{{Multi Reservation:{{{PMultiRes}}}-Date}}}}|{{{PDate}}}}}
 
   |-
 
   |-
 
{{#if:{{{PMultiRes|}}}|{{#vardefine:_res|{{Multi Reservation:{{{PMultiRes}}}-Contributor}}}}|{{#if:{{{PReserved|}}}|{{#vardefine:_res|{{{PReserved}}}}}}}}}{{#if:{{#var:_res}}|
 
{{#if:{{{PMultiRes|}}}|{{#vardefine:_res|{{Multi Reservation:{{{PMultiRes}}}-Contributor}}}}|{{#if:{{{PReserved|}}}|{{#vardefine:_res|{{{PReserved}}}}}}}}}{{#if:{{#var:_res}}|
−
   {{!}} align="right" {{!}} <b>Reserved :</b> {{!}}{{!}} [[{{#var:_res}}]]{{#ifeq:{{NAMESPACENUMBER}}|0|<span style="display:none">[[{{#var:_res}}/Reserved]]</span>}}
+
   {{!}} align="right" {{!}} <b>Reserved :</b> {{!}}{{!}} {{Contribs|{{#var:_res}}}}{{#ifeq:{{NAMESPACENUMBER}}|0|<span style="display:none">[[{{#var:_res}}/Reserved]]</span>}}
 
   }}
 
   }}
 
  |}
 
  |}
−
|
+
| {{#ifeq:{{#var:_sir}}|1|style="background-color:SkyBlue;"}} | {{#ifeq:{{#var:_sir}}|1|No primes possible!}}
 
  {|  
 
  {|  
 
  | {{NVal list|{{{PNlist}}}}}
 
  | {{NVal list|{{{PNlist}}}}}
Line 91: Line 126:
 
{{#if:{{{PRemarks|}}}|
 
{{#if:{{{PRemarks|}}}|
 
{{{!}}  
 
{{{!}}  
−
{{!}} <div height="120%" style="background-color:SkyBlue;"><b>Remarks : </b></div> {{!}}{{!}} {{{PRemarks}}}
+
{{!}} <div height="120%" class="color-PrimeTemplate"><b>Remarks : </b></div> {{!}}{{!}} {{{PRemarks}}}
 
{{!}}}
 
{{!}}}
 
}}
 
}}
 
{{#ifeq:{{NAMESPACENUMBER}}|0|<!--
 
{{#ifeq:{{NAMESPACENUMBER}}|0|<!--
−
-->{{#ifexpr:{{{Pk}}} mod 3||[[Category:Proth k=3k value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
-->[[Category:Proth {{{Pb}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]<!--
−
-->{{#ifexpr:{{{Pk}}} mod 15||[[Category:Proth k=15k value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
-->{{#ifeq:{{{Pb}}}|2|<!--
−
-->{{#ifexpr:{{{Pk}}} mod 2145||[[Category:Proth k=2145k value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Pk}}} < 300|[[Category:Proth 2 1-300|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
−
-->{{#ifexpr:{{{Pk}}} mod 2805||[[Category:Proth k=2805k value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Pk}}} > 300|{{#ifexpr:{{{Pk}}} < 2000|[[Category:Proth 2 300-2000|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
−
-->{{#ifexpr:{{{PNash}}}<1000|[[Category:Proth k=Low weight|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Pk}}} > 2000|{{#ifexpr:{{{Pk}}} < 4000|[[Category:Proth 2 2000-4000|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
−
-->[[Category:Proth prime|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Pk}}} > 4000|{{#ifexpr:{{{Pk}}} < 6000|[[Category:Proth 2 4000-6000|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 6000|{{#ifexpr:{{{Pk}}} < 8000|[[Category:Proth 2 6000-8000|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 8000|{{#ifexpr:{{{Pk}}} < 1e4|[[Category:Proth 2 8000-10000|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e4|{{#ifexpr:{{{Pk}}} < 1e5|[[Category:Proth 2 10e4-10e5|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e5|{{#ifexpr:{{{Pk}}} < 1e6|[[Category:Proth 2 10e5-10e6|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e6|{{#ifexpr:{{{Pk}}} < 1e7|[[Category:Proth 2 10e6-10e7|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e7|{{#ifexpr:{{{Pk}}} < 1e8|[[Category:Proth 2 10e7-10e8|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e8|{{#ifexpr:{{{Pk}}} < 1e9|[[Category:Proth 2 10e8-10e9|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e9|{{#ifexpr:{{{Pk}}} < 1e10|[[Category:Proth 2 10e9-10e10|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 1e10|[[Category:Proth 2 10e10-infinity|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
 
 +
-->{{#ifexpr:{{{Pk}}} mod 3||[[Category:Proth {{{Pb}}} 3k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
-->{{#ifexpr:{{{Pk}}} mod 15||[[Category:Proth {{{Pb}}} 15k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
-->{{#ifexpr:{{{Pk}}} mod 2145||[[Category:Proth {{{Pb}}} 2145k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
-->{{#ifexpr:{{{Pk}}} mod 2805||[[Category:Proth {{{Pb}}} 2805k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
-->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Pk}}}<78557|{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>0|[[Category:Proth {{{Pb}}} Interval{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}}}}}
 +
}}<!--
 +
-->{{#if:{{{PCount|}}}|{{#ifeq:{{{PCount}}}|0|{{#ifeq:{{#var:_sir}}|0|[[Category:Proth {{{Pb}}} Count-0|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
-->{{#ifexist:{{PAGENAME}}|{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>0|{{#ifexpr:{{GNn|{{PAGENAME}}|{{GP|{{PAGENAME}}|PCount}} }} > {{GP|{{PAGENAME}}|PMaxn}}|[[Category:Proth {{{Pb}}} Missing-range|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}}}}}<!--Exp err-->
 +
}}<!--
 +
-->{{#ifeq:{{#var:_sir}}|0|{{#ifexpr:{{{PNash}}}<1000|[[Category:Proth {{{Pb}}} Low-weight|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
-->{{#ifeq:{{#var:_sir}}|1|[[Category:Proth {{{Pb}}} Sierpinski|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
-->{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>99|[[Category:Proth {{{Pb}}} Count-100|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 
-->{{#if:{{{PMultiRes|}}}|[[Category:{{Multi Reservation:{{{PMultiRes}}}-Name}}|#.....{{padleft:{{{Pk}}}|5|0}}]]}}
 
-->{{#if:{{{PMultiRes|}}}|[[Category:{{Multi Reservation:{{{PMultiRes}}}-Name}}|#.....{{padleft:{{{Pk}}}|5|0}}]]}}
 +
}}
 
{{#if:{{#pos:{{{PNlist}}}|:}}|
 
{{#if:{{#pos:{{{PNlist}}}|:}}|
 
==Notes==
 
==Notes==
 
<references />}}</includeonly>
 
<references />}}</includeonly>

Latest revision as of 06:38, 31 May 2024

Description

Template Proth prime

Display of current data for Proth primes k•bn+1, comments will be displayed as references at the bottom.

Prototype

{{Proth prime
|Pk=
|Pb=
|PCount=
|PNash=
|PMaxn=
|PDate=
|PReserved=
|PMultiRes=
|PNlist=
|PRemarks=
|PSieve=
}}

Parameters

  • Pk: the k-value of k•bn+1
  • Pb: the b-value of k•bn+1
  • PCount: the number of n-values given
If no count is given, this will be automatically counted. If given and differs from automated value, a warning will be shown.
  • PNash: the Nash weight
  • PMaxn: highest n-value of continuous searched range (from n=1)
  • PDate: last date of edit (latest history entry)
  • PReserved: person(s) who reserved this sequence (comma separated)
  • PMultiRes: number of Multi Reservation: PMaxn and PDate will be taken from there
  • PNlist: list of every n-value (one per row) with comments
  • PRemarks: any helpful text or links for this sequence
  • PSieve: if set a zip-file can be uploaded (filename is given then) if not available; if exists file is downloadable

Explanations

In case of the following conditions special categories will be set automatically (b = 2 only):

  • k-value is disvisible by 3 → category Proth 3k is set
  • k-value is disvisible by 15 → category Proth 15k is set
  • k-value is disvisible by 2145 → category Proth 2145k is set
  • k-value is disvisible by 2805 → category Proth 2805k is set

Any base:

The category Proth prime for base b is set by default.

If "PMultiRes" is set, the parameters "PMaxn", "PDate" and "PReserved" (if given) will be ignored and replaced by the data from the Multi Reservation with ID given.

See also

Example

{{Proth prime
|Pk=15
|Pb=2
|PCount=4
|PNash=239
|PMaxn=20
|PDate=2019-03-01
|PReserved=Karsten Bonath
|PMultiRes=
|PNlist=
2;T:ST;C: Testtext
3;T:SW;C:[[Help:Examples|Examples]]
5;C:'''Example'''
15;43912;C:with Top5000 entry
|PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s.
|PSieve=y
}}

will create:

Current data

k , b : 15 , 2
Type : 315
Count : 4
Nash : 239
Max n : 20
Date : 2019-03-01
Reserved : Karsten Bonath
2[1], 3[2], 5[3], 15[4]
Remarks :
For this k-value these are the Generalized Fermat primes.

Notes

  1. ↑ Sophie Germain n=2, Twin n=2, Testtext
  2. ↑ Sophie Germain n=3, Woodall, Examples
  3. ↑ Example
  4. ↑ with Top5000 entry
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