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|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 {{Vk}}-value these are the [[Fermat prime]]s.
+
|PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s.
 
|PSieve=y
 
|PSieve=y
 
}}
 
}}
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|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 {{Vk}}-value these are the [[Fermat prime]]s.
+
|PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s.
 
|PSieve=
 
|PSieve=
 
}}
 
}}
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  {|  
 
  {|  
 
   | 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!]]}}}}
 
   | 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!]]}}}}
−
{{#ifeq:{{{Pb}}}|2|{{#if:{{{Pk|}}}|{{#ifeq:{{#var:_sir}}|0|{{#vardefine:ktype|{{K-type|Proth|{{{Pk}}}}}}}{{#if:{{#pos:{{#var:ktype}}|center}}|
+
{{#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>Type :</b> {{!}}{{!}} {{#var:ktype}}
−
}}}}}}}}
+
}}
 
   |-
 
   |-
 
   | 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!}}}}
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-->[[Category:Proth {{{Pb}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]<!--
 
-->[[Category:Proth {{{Pb}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]<!--
 
-->{{#ifeq:{{{Pb}}}|2|<!--
 
-->{{#ifeq:{{{Pb}}}|2|<!--
 +
  -->{{#ifexpr:{{{Pk}}} < 300|[[Category:Proth 2 1-300|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 300|{{#ifexpr:{{{Pk}}} < 2000|[[Category:Proth 2 300-2000|#.....{{padleft:{{{Pk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Pk}}} > 2000|{{#ifexpr:{{{Pk}}} < 4000|[[Category:Proth 2 2000-4000|#.....{{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 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 15||[[Category:Proth {{{Pb}}} 15k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!--

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. ↑ S.G. n=2, Twin n=2, Testtext
  2. ↑ S.G. n=3, Woodall, Examples
  3. ↑ Example
  4. ↑ with Top5000 entry
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