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 "Template:Proth prime"

From Prime-Wiki
Jump to: navigation, search
(class)
(including base b)
Line 3: Line 3:
 
Template Proth prime
 
Template Proth prime
  
−
Display of current data for Proth primes {{Kbn|+|k|2|n}}, 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=
 
|PCount=
 
|PNash=
 
|PNash=
Line 22: Line 23:
  
 
==Parameters==
 
==Parameters==
−
*'''Pk:''' the {{Vk}}-value of {{Kbn|+|k|2|n}}
+
*'''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
 
*'''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.
 
: 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]]
 
*'''PNash:''' the [[Nash weight]]
 
*'''PMaxn:''' highest {{Vn}}-value of continuous searched range (from {{Vn}}=1)
 
*'''PMaxn:''' highest {{Vn}}-value of continuous searched range (from {{Vn}}=1)
−
*'''PDate:''' last date of edit (mostly latest history entry)
+
*'''PDate:''' last date of edit (latest history entry)
 
*'''PReserved:''' person(s) who reserved this sequence (comma separated)
 
*'''PReserved:''' person(s) who reserved this sequence (comma separated)
−
*'''PMultiRes:''' number of [[:Template:Multi Reservation]]: PMaxn and PDate will be taken from there
+
*'''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
 
*'''PNlist:''' list of every {{Vn}}-value (one per row) with comments
 
*'''PRemarks:''' any helpful text or links for this sequence
 
*'''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
 
*'''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):
−
*{{Vk}}-value is disvisible by 15 → category [[:Category:Proth k=15k value|Proth 15k]] is set
+
*{{Vk}}-value is disvisible by 3 → category [[:Category:Proth 2 3k-value|Proth 3k]] is set
−
*{{Vk}}-value is disvisible by 2145 → category [[:Category:Proth k=2145k value|Proth 2145k]] is set
+
*{{Vk}}-value is disvisible by 15 → category [[:Category:Proth 2 15k-value|Proth 15k]] is set
−
*{{Vk}}-value is disvisible by 2805 → category [[:Category:Proth k=2805k value|Proth 2805k]] is set
+
*{{Vk}}-value is disvisible by 2145 → 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 & 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 53: Line 58:
 
{{Proth prime
 
{{Proth prime
 
|Pk=15
 
|Pk=15
 +
|Pb=2
 
|PCount=4
 
|PCount=4
 
|PNash=239
 
|PNash=239
Line 71: Line 77:
 
{{Proth prime
 
{{Proth prime
 
|Pk=15
 
|Pk=15
 +
|Pb=2
 
|PCount=4
 
|PCount=4
 
|PNash=239
 
|PNash=239
Line 85: Line 92:
 
|PSieve=y
 
|PSieve=y
 
}}
 
}}
−
[[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]]}}<!--
 
-->{{#if:{{{PCount|}}}||[[Category:Missing XCount]]}}<!--
 
-->{{#vardefine:_cnt|{{NVal list|{{{PNlist}}}|count}}}}<!--
 
-->{{#vardefine:_cnt|{{NVal list|{{{PNlist}}}|count}}}}<!--
Line 93: Line 100:
 
| class="primetemplate color-PrimeTemplate" |
 
| class="primetemplate color-PrimeTemplate" |
 
  {|  
 
  {|  
−
   | align="right"| <b>{{Vk}}-value :</b> || {{{Pk}}}<!--{{#if:{{{CKSieve|}}}|&nbsp;([[:File:{{PAGENAME}} sieve.zip|sieve]])|}}--> {{K-type|Proth|{{{Pk}}}}}
+
   | align="right"| <b>{{Vk}} :</b> || {{{Pk}}}{{#if:{{{PSieve|}}}|&nbsp;([[:File:{{PAGENAME}} sieve.zip|sieve]])|}} {{K-type|Proth|{{{Pk}}}|{{{Pb}}}}}
 +
  |-
 +
  | align="right"| <b>{{Vb}} :</b> || {{{Pb}}}
 
   |-
 
   |-
 
   | 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>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!}}}}
Line 99: Line 108:
 
   | align="right"| <b>Nash :</b> || {{{PNash}}}
 
   | align="right"| <b>Nash :</b> || {{{PNash}}}
 
   |-
 
   |-
−
   | align="right"| <b>Max&nbsp;{{Vn}} :</b> || {{#if:{{{PMultiRes|}}}|{{#if:{{{PMaxn|}}}|{{Num|{{{PMaxn}}}}} ({{Num|{{Multi Reservation:{{{PMultiRes}}}-NMax}}}})[[Category:Proth prime missing range|#.....{{padleft:{{{Pk}}}|5|0}}]]|{{Num|{{Multi Reservation:{{{PMultiRes}}}-NMax}}}}}}|{{#if:{{{PMaxn|}}}|{{Num|{{{PMaxn}}}}}|{{Alert|Attention!|Parameter PMaxn not given!}}}}}}
+
   | 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|}}}|{{#if:{{{PDate|}}}|{{{PDate}}} ({{Multi Reservation:{{{PMultiRes}}}-Date}})|{{Multi Reservation:{{{PMultiRes}}}-Date}}}}|{{{PDate}}}}}
 
   | align="right"| <b>Date :</b> || {{#if:{{{PMultiRes|}}}|{{#if:{{{PDate|}}}|{{{PDate}}} ({{Multi Reservation:{{{PMultiRes}}}-Date}})|{{Multi Reservation:{{{PMultiRes}}}-Date}}}}|{{{PDate}}}}}
Line 118: Line 127:
 
}}
 
}}
 
{{#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}}} mod 3||[[Category:Proth {{{Pb}}} 3k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
−
-->{{#ifexpr:{{{Pk}}} mod 2805||[[Category:Proth k=2805k value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
+
-->{{#ifexpr:{{{Pk}}} mod 15||[[Category:Proth {{{Pb}}} 15k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
−
-->{{#if:{{{PCount|}}}|{{#ifeq:{{{PCount}}}|0|{{#ifeq:{{#var:_sir}}|0|[[Category:Zero PCount|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}}}<!--
+
-->{{#ifexpr:{{{Pk}}} mod 2145||[[Category:Proth {{{Pb}}} 2145k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
−
-->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Pk}}}<78557|{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>0|[[Category:Proth prime Sierpinski f{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}}}}}<!--
+
-->{{#ifexpr:{{{Pk}}} mod 2805||[[Category:Proth {{{Pb}}} 2805k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
−
-->{{#ifexist:{{PAGENAME}}|{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>0|{{#ifexpr:{{GNn|{{PAGENAME}}|{{GP|{{PAGENAME}}|PCount}} }} > {{GP|{{PAGENAME}}|PMaxn}}|[[Category:Proth prime missing range|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}}}}}<!--Exp err
+
-->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Pk}}}<78557|{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>0|[[Category:Proth {{{Pb}}} interval{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}}}}}
−
 
+
}}<!--
−
-->{{#ifeq:{{#var:_sir}}|0|{{#ifexpr:{{{PNash}}}<1000|[[Category:Proth k=Low weight|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
+
-->{{#if:{{{PCount|}}}|{{#ifeq:{{{PCount}}}|0|{{#ifeq:{{#var:_sir}}|1|[[Category:Zero PCount|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
−
-->{{#ifeq:{{#var:_sir}}|1|[[Category:Proth k=Sierpinski|#.....{{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-->
−
-->{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}>99|[[Category:Proth count 100|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
+
}}<!--
−
 
+
-->{{#ifeq:{{#var:_sir}}|0|{{#ifexpr:{{{PNash}}}<1000|[[Category:Proth {{{Pb}}} Low-weight|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
−
-->[[Category:Proth prime|#.....{{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>

Revision as of 14:52, 11 July 2021

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:[[Examples]]
5;C:'''Example'''
15;43912;C:with Top5000 entry
|PRemarks=For this {{Vk}}-value these are the [[Fermat prime]]s.
|PSieve=y
}}

will create:

Current data

k , b : 15 , 2 Upload me!
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 Fermat primes.

Notes

  1. ↑ S.G. n=2, Twin n=2, Testtext
  2. ↑ S.G. n=3, Woodall, Examples
  3. ↑ Example
  4. ↑ with Top5000 entry
Retrieved from "https://www.rieselprime.de/z/index.php?title=Template:Proth_prime&oldid=15049"