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(hidden reservations resolved)
(categorize for Riesel problem 4)
 
(38 intermediate revisions by the same user not shown)
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Template Riesel prime
 
Template Riesel prime
  
Display of current data for Riesel primes, comments will be displayed as references at the bottom.
+
Display of current data for Riesel primes {{Kbn|k|b|n}}, comments will be displayed as references at the bottom.
  
==Calling==
+
==Prototype==
 
<pre>
 
<pre>
 
{{Riesel prime
 
{{Riesel prime
 
|Rk=
 
|Rk=
 +
|Rb=
 +
|RCount=
 
|RNash=
 
|RNash=
 
|RMaxn=
 
|RMaxn=
Line 16: Line 18:
 
|RNlist=
 
|RNlist=
 
|RRemarks=
 
|RRemarks=
 +
|RSieve=
 
}}
 
}}
 
</pre>
 
</pre>
 +
 +
==Parameters==
 +
*'''Rk:''' the {{Vk}}-value of {{Kbn|k|b|n}}
 +
*'''Rb:''' the {{Vb}}-value of {{Kbn|k|b|n}}
 +
*'''RCount:''' 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.
 +
*'''RNash:''' the [[Nash weight]]
 +
*'''RMaxn:''' highest {{Vn}}-value of continuous searched range (from {{Vn}}=1)
 +
*'''RDate:''' last date of edit
 +
*'''RReserved:''' person(s) who reserved this sequence (comma separated)
 +
*'''RMultiRes:''' number of [[:Template:Multi Reservation]]: RMaxn and RDate will be taken from there
 +
*'''RNlist:''' list of every {{Vn}}-value (one per row) with comments
 +
*'''RRemarks:''' any helpful text or links for this sequence
 +
*'''RSieve:''' if set a zip-file can be uploaded (filename is given then) if not available; if exists file is downloadable
  
 
==Categories set==
 
==Categories set==
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:Riesel k=15k value|Riesel 15k]] is set
+
*If {{Vk}}-value is disvisible by 3 &rarr; category [[:Category:Riesel 2 3k-value|Riesel 3k]] is set
*k-value is disvisible by 2145 &rarr; category [[:Category:Riesel k=2145k value|Riesel 2145k]] is set
+
*If {{Vk}}-value is disvisible by 15 &rarr; category [[:Category:Riesel 2 15k-value|Riesel 15k]] is set
*k-value is disvisible by 2805 &rarr; category [[:Category:Riesel k=2805k value|Riesel 2805k]] is set
+
*If {{Vk}}-value is disvisible by 2145 &rarr; category [[:Category:Riesel 2 2145k-value|Riesel 2145k]] is set
*Nash-weight < 1000 &rarr; category [[:Category:Riesel k=Low weight|Riesel Low weight]] is set
+
*If {{Vk}}-value is disvisible by 2805 &rarr; category [[:Category:Riesel 2 2805k-value|Riesel 2805k]] is set
*remarks contain "Riesel" &rarr; category [[:Category:Riesel k=Riesel|Riesel number]] is set
+
*If RCount=0 & RNash=0 & RMaxn=0 &rarr; category [[:Category:Riesel 2 Riesel|Riesel number]] is set
 +
Any base (here given for base 2 only):
 +
*If Nash-weight < 1000 &rarr; category [[:Category:Riesel 2 Low-weight|Riesel Low weight]] is set
 +
*If there are 100 {{Vn}}-values or more &rarr; category [[:Category:Riesel 2 Count-100|Riesel Count 100]] is set
 +
*If RCount=0 &rarr; category [[:Category:Riesel 2 Count-0|Riesel Count 0]] is set
 +
*According to the {{Vk}}-value the corresponding category is set to the [[:Category:Riesel_prime_conjectures|Riesel problem]].
  
The category [[:Category:Riesel prime|Riesel prime]] is set by default.
+
The category [[:Category:Riesel prime|Riesel prime]] for base {{Vb}} is set by default.
  
 
==See also==
 
==See also==
Line 35: Line 57:
 
<pre>
 
<pre>
 
{{Riesel prime
 
{{Riesel prime
|Rk=19
+
|Rk=15
 +
|Rb=2
 +
|RCount=8
 
|RNash=2390
 
|RNash=2390
 
|RMaxn=20
 
|RMaxn=20
 
|RDate=2019-03-01
 
|RDate=2019-03-01
 
|RReserved=Karsten Bonath,Euclid
 
|RReserved=Karsten Bonath,Euclid
 +
|RMultiRes=
 
|RNlist=
 
|RNlist=
2;T:ST;C:'''[[M1]]''', Near Woodall: (1+1)*2^1-1, also (2-1)*2^2-1
+
2;T:ST;C:'''[[M1]]''', Near Woodall: (1+1)*2^1-1
 
3;T:SW;C:[[M2]], Woodall: 2*2^2-1
 
3;T:SW;C:[[M2]], Woodall: 2*2^2-1
 
5;C:[[M3]], Near Woodall: (3+1)*2^3-1
 
5;C:[[M3]], Near Woodall: (3+1)*2^3-1
Line 49: Line 74:
 
19;C:[[M7]], Near Woodall: (15+1)*2^15-1
 
19;C:[[M7]], Near Woodall: (15+1)*2^15-1
 
4253;43912;C:[[M19]]
 
4253;43912;C:[[M19]]
|RRemarks=For this ''k''-value theses are the [[Mersenne prime]]s.
+
|RRemarks=For this {{Vk}}-value theses are the [[Mersenne prime]]s.
 +
|RSieve=
 
}}
 
}}
 
</pre>
 
</pre>
 
will create:
 
will create:
 
{{Riesel prime
 
{{Riesel prime
|Rk=19
+
|Rk=15
 +
|Rb=2
 +
|RCount=8
 
|RNash=2390
 
|RNash=2390
 
|RMaxn=20
 
|RMaxn=20
 
|RDate=2019-03-01
 
|RDate=2019-03-01
 
|RReserved=Karsten Bonath,Euclid
 
|RReserved=Karsten Bonath,Euclid
 +
|RMultiRes=
 
|RNlist=
 
|RNlist=
2;T:ST;C:'''[[M1]]''', Near Woodall: (1+1)*2^1-1, also (2-1)*2^2-1
+
2;T:ST;C:'''[[M1]]''', Near Woodall: (1+1)*2^1-1
 
3;T:SW;C:[[M2]], Woodall: 2*2^2-1
 
3;T:SW;C:[[M2]], Woodall: 2*2^2-1
 
5;C:[[M3]], Near Woodall: (3+1)*2^3-1
 
5;C:[[M3]], Near Woodall: (3+1)*2^3-1
Line 68: Line 97:
 
19;C:[[M7]], Near Woodall: (15+1)*2^15-1
 
19;C:[[M7]], Near Woodall: (15+1)*2^15-1
 
4253;43912;C:[[M19]]
 
4253;43912;C:[[M19]]
|RRemarks=For this ''k''-value theses are the [[Mersenne prime]]s.
+
|RRemarks=For this {{Vk}}-value theses are the [[Mersenne prime]]s.
 +
|RSieve=
 
}}
 
}}
[[Category:Prime collections]]</noinclude><includeonly>__NOTOC__{{#ifeq:{{NAMESPACENUMBER}}|0|{{DISPLAYTITLE:Riesel primes of the form {{Kbn|{{#explode:{{PAGENAME}}||-1}}|2|n}}}}{{#if:{{{RMultiRes|}}}|{{ReservedM|{{{RMultiRes}}}}}|{{#if:{{{RReserved|}}}|{{Reserved|{{{RReserved}}}}}}}}}}}
+
[[Category:Prime collections]]</noinclude><includeonly>__NOTOC__{{#ifeq:{{NAMESPACENUMBER}}|0|{{DISPLAYTITLE:Riesel primes of the form {{Kbn|{{#explode:{{PAGENAME}}||-1}}|{{#explode:{{PAGENAME}}||-2}}|n}}}}{{#if:{{{RMultiRes|}}}|{{ReservedM|{{{RMultiRes}}}}}|{{#if:{{{RReserved|}}}|{{Reserved|{{{RReserved}}}}}}}}}}}<!--
 +
-->{{#if:{{{RCount|}}}||[[Category:Missing XCount]]}}<!--
 +
-->{{#vardefine:_cnt|{{NVal list|{{{RNlist}}}|count}}}}<!--
 +
-->{{#vardefine:_ris|0}}{{#ifeq:{{{RCount}}}|0|{{#ifeq:{{{RNash}}}|0|{{#ifeq:{{{RMaxn}}}|0|{{#vardefine:_ris|1}}}}}}
 +
}}{{#ifeq:{{NAMESPACENUMBER}}|10|{{#vardefine:_cnt|8}}}}
 
==Current data==
 
==Current data==
 
{| class="primedata"
 
{| class="primedata"
| class="primetemplate" |
+
| class="primetemplate color-PrimeTemplate" |
 
  {|  
 
  {|  
   | align="right"| <b>k-value :</b> || {{{Rk}}}<!--{{#if:{{{CKSieve|}}}|&nbsp;([[:File:{{PAGENAME}} sieve.zip|sieve]])|}}--> {{#if:{{{Rk|}}}|{{K-type|Riesel|{{{Rk}}}}}}}
+
   | align="right"| <b>{{Vk}} , {{Vb}} :</b> || {{{Rk}}} , {{{Rb}}} {{#if:{{{RSieve|}}}|{{#ifexist:File:{{PAGENAME}} sieve.zip|&nbsp;([[:File:{{PAGENAME}} sieve.zip|sieve]])|[[File:{{PAGENAME}} sieve.zip|Upload me!]]}}}}
 +
{{#ifeq:{{{Rb}}}|2|{{#if:{{{Rk|}}}|{{#ifeq:{{#var:_ris}}|0|{{#vardefine:ktype|{{K-type|Riesel|{{{Rk}}}}}}}{{#if:{{#pos:{{#var:ktype}}|center}}|
 +
{{!}}-
 +
{{!}} align="right"{{!}} <b>Type :</b> {{!}}{{!}} {{#var:ktype}}
 +
}}}}}}}}
 
   |-
 
   |-
   | align="right"| <b>Count :</b> || {{NVal list|{{{RNlist}}}|count}}
+
   | align="right"| <b>Count :</b> || {{#if:{{{RCount|}}}|{{#ifeq:{{{RCount|}}}|{{#var:_cnt}}|{{{RCount}}}|{{Alert|Attention!|Parameter RCount&#61;{{{RCount}}} differs from counting&#61;{{#var:_cnt}}}}[[Category:Wrong XCount]]}}|{{Alert|Attention!|Parameter RCount&#61;{{#var:_cnt}} not given!}}}}
 
   |-
 
   |-
 
   | align="right"| <b>Nash :</b> || {{{RNash}}}
 
   | align="right"| <b>Nash :</b> || {{{RNash}}}
 
   |-
 
   |-
   | align="right"| <b>Max&nbsp;<i>n</i> :</b> || {{#if:{{{RMultiRes|}}}|{{Num|{{Multi Reservation:{{{RMultiRes}}}-NMax}}}}|{{Num|{{{RMaxn}}}}}}}
+
   | align="right"| <b>Max&nbsp;{{Vn}} :</b> || {{#if:{{{RMultiRes|}}}|{{#if:{{{RMaxn|}}}|{{Num|{{{RMaxn}}}}} ({{Num|{{Multi Reservation:{{{RMultiRes}}}-NMax}}}})[[Category:Riesel {{{Rb}}} Missing-range|#.....{{padleft:{{{Rk}}}|5|0}}]]|{{Num|{{Multi Reservation:{{{RMultiRes}}}-NMax}}}}}}|{{#if:{{{RMaxn|}}}|{{Num|{{{RMaxn}}}}}|{{Alert|Attention!|Parameter RMaxn not given!}}}}}}
 
   |-
 
   |-
   | align="right"| <b>Date :</b> || {{#if:{{{RMultiRes|}}}|{{Multi Reservation:{{{RMultiRes}}}-Date}}|{{{RDate}}}}}
+
   | align="right"| <b>Date :</b> || {{#if:{{{RMultiRes|}}}|{{#if:{{{RDate|}}}|{{{RDate}}} ({{Multi Reservation:{{{RMultiRes}}}-Date}})|{{Multi Reservation:{{{RMultiRes}}}-Date}}}}|{{{RDate}}}}}
 
   |-
 
   |-
 
{{#if:{{{RMultiRes|}}}|{{#vardefine:_res|{{Multi Reservation:{{{RMultiRes}}}-Contributor}}}}|{{#if:{{{RReserved|}}}|{{#vardefine:_res|{{{RReserved}}}}}}}}}{{#if:{{#var:_res}}|
 
{{#if:{{{RMultiRes|}}}|{{#vardefine:_res|{{Multi Reservation:{{{RMultiRes}}}-Contributor}}}}|{{#if:{{{RReserved|}}}|{{#vardefine:_res|{{{RReserved}}}}}}}}}{{#if:{{#var:_res}}|
Line 89: Line 127:
 
| 0
 
| 0
 
| {{#arraysize:u}}
 
| {{#arraysize:u}}
| <span style="display:mnone">[[{{#arrayindex:u|{{#var:i}}}}/Reserved]]</span>}}}}
+
| <span style="display:none">[[{{#arrayindex:u|{{#var:i}}}}/Reserved]]</span>}}}}
 
   }}
 
   }}
 
  |}
 
  |}
|
+
| {{#ifeq:{{#var:_ris}}|1|class="color-PrimeTemplate"}} | {{#ifeq:{{#var:_ris}}|1|No primes possible!}}
 
  {|  
 
  {|  
  | {{NVal list|{{{RNlist}}}}}
+
  | {{#if:{{{RNlist|}}}|{{NVal list|{{{RNlist}}}}}}}
 
  |}
 
  |}
 
|}
 
|}
 
{{#if:{{{RRemarks|}}}|
 
{{#if:{{{RRemarks|}}}|
 
{{{!}}  
 
{{{!}}  
{{!}} <div height="120%" style="background-color:SkyBlue;"><b>Remarks : </b></div> {{!}}{{!}} {{{RRemarks}}}
+
{{!}} <div height="120%" class="color-PrimeTemplate"><b>Remarks : </b></div> {{!}}{{!}} {{{RRemarks}}}
 
{{!}}}
 
{{!}}}
}}
+
}}{{#ifeq:{{NAMESPACENUMBER}}|0|<!--
{{#ifeq:{{NAMESPACENUMBER}}|0|<!--
+
   -->[[Category:Riesel {{{Rb}}}|#.....{{padleft:{{{Rk}}}|5|0}}]]<!--
   -->{{#ifexpr:{{{Rk}}} mod 15||[[Category:Riesel k=15k value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
   -->{{#ifeq:{{{Rb}}}|2|<!--
   -->{{#ifexpr:{{{Rk}}} mod 2145||[[Category:Riesel k=2145k value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Rk}}} < 300|[[Category:Riesel 2 1-300|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
  -->{{#ifexpr:{{{Rk}}} mod 2805||[[Category:Riesel k=2805k value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 300|{{#ifexpr:{{{Rk}}} < 2000|[[Category:Riesel 2 300-2000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
 
+
  -->{{#ifexpr:{{{Rk}}} > 2000|{{#ifexpr:{{{Rk}}} < 4000|[[Category:Riesel 2 2000-4000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} < 300|[[Category:Riesel k=1-300|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 4000|{{#ifexpr:{{{Rk}}} < 6000|[[Category:Riesel 2 4000-6000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 300|{{#ifexpr:{{{Rk}}} < 2000|[[Category:Riesel k=300-2000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 6000|{{#ifexpr:{{{Rk}}} < 8000|[[Category:Riesel 2 6000-8000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 2000|{{#ifexpr:{{{Rk}}} < 4000|[[Category:Riesel k=2000-4000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 8000|{{#ifexpr:{{{Rk}}} < 1e4|[[Category:Riesel 2 8000-10000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 4000|{{#ifexpr:{{{Rk}}} < 6000|[[Category:Riesel k=4000-6000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e4|{{#ifexpr:{{{Rk}}} < 1e5|[[Category:Riesel 2 10e4-10e5|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 6000|{{#ifexpr:{{{Rk}}} < 8000|[[Category:Riesel k=6000-8000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e5|{{#ifexpr:{{{Rk}}} < 1e6|[[Category:Riesel 2 10e5-10e6|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 8000|{{#ifexpr:{{{Rk}}} < 10000|[[Category:Riesel k=8000-10000|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e6|{{#ifexpr:{{{Rk}}} < 1e7|[[Category:Riesel 2 10e6-10e7|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 10000|{{#ifexpr:{{{Rk}}} < 100000|[[Category:Riesel k=10e4-10e5|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e7|{{#ifexpr:{{{Rk}}} < 1e8|[[Category:Riesel 2 10e7-10e8|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 100000|{{#ifexpr:{{{Rk}}} < 1000000|[[Category:Riesel k=10e5-10e6|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e8|{{#ifexpr:{{{Rk}}} < 1e9|[[Category:Riesel 2 10e8-10e9|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 1000000|{{#ifexpr:{{{Rk}}} < 10000000|[[Category:Riesel k=10e6-10e7|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e9|{{#ifexpr:{{{Rk}}} < 1e10|[[Category:Riesel 2 10e9-10e10|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 10000000|{{#ifexpr:{{{Rk}}} < 100000000|[[Category:Riesel k=10e7-10e8|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexpr:{{{Rk}}} > 1e10|[[Category:Riesel 2 10e10-infinity|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
  -->{{#ifexpr:{{{Rk}}} > 100000000|{{#ifexpr:{{{Rk}}} < 1000000000|[[Category:Riesel k=10e8-10e9|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifeq:{{#var:_ris}}|1|[[Category:Riesel 2 Riesel|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
  -->{{#ifexpr:{{{Rk}}} > 1000000000|{{#ifexpr:{{{Rk}}} < 10000000000|[[Category:Riesel k=10e9-10e10|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
+
  -->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Rk}}}<509203|{{#if:{{{RCount|}}}|{{#ifexpr:{{{RCount}}}>0|[[Category:Riesel 2 1Intervals‎{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}}}}}<!--
  -->{{#ifexpr:{{{Rk}}} > 10000000000|[[Category:Riesel k=10e10-infinity|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
  -->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Rk}}}>509203|{{#ifexpr:{{{Rk}}}<762701|{{#if:{{{RCount|}}}|{{#ifexpr:{{{RCount}}}>0|[[Category:Riesel 2 2Intervals{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}}}}}}}<!--
 +
  -->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Rk}}}>762701|{{#ifexpr:{{{Rk}}}<777149|{{#if:{{{RCount|}}}|{{#ifexpr:{{{RCount}}}>0|[[Category:Riesel 2 3Intervals{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}}}}}}}<!--
 +
  -->{{#ifexist:{{PAGENAME}}|{{#ifexpr:{{{Rk}}}>777149|{{#ifexpr:{{{Rk}}}<790841|{{#if:{{{RCount|}}}|{{#ifexpr:{{{RCount}}}>0|[[Category:Riesel 2 4Intervals{{Exponent interval|{{GNn|{{PAGENAME}}|1}}}}|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}}}}}}}<!--
 +
  -->{{#ifexpr:{{{Rk}}} mod 3||{{#if:{{#pos:{{{RNlist}}}|T:S}}{{#pos:{{{RNlist}}}|T:CS}}||[[Category:Riesel 2 no-SG|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Rk}}} mod 3||{{#if:{{#pos:{{{RNlist}}}|T:T}}{{#pos:{{{RNlist}}}|T:ST}}{{#pos:{{{RNlist}}}|T:CT}}{{#pos:{{{RNlist}}}|T:CST}}||[[Category:Riesel 2 no-twin|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
 +
  -->{{#ifexpr:{{{Rk}}} mod 3||[[Category:Riesel {{{Rb}}} 3k-value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
 +
  -->{{#ifexpr:{{{Rk}}} mod 15||[[Category:Riesel {{{Rb}}} 15k-value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
 +
  -->{{#ifexpr:{{{Rk}}} mod 2145||[[Category:Riesel {{{Rb}}} 2145k-value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
 +
  -->{{#ifexpr:{{{Rk}}} mod 2805||[[Category:Riesel {{{Rb}}} 2805k-value|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
 +
  -->}}<!--
  
   -->{{#ifexpr:{{{RNash}}}<1000|[[Category:Riesel k=Low weight|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
   -->{{#ifeq:{{#var:_ris}}|0|{{#ifexpr:{{{RNash}}}<1000|[[Category:Riesel {{{Rb}}} Low-weight|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
   -->{{#if:{{#pos:{{{RRemarks}}}|Riesel}}|[[Category:Riesel k=Riesel|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
+
   -->{{#if:{{{RCount|}}}|{{#ifexpr:{{{RCount}}}>99|[[Category:Riesel {{{Rb}}} Count-100|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}<!--
   -->[[Category:Riesel prime|#.....{{padleft:{{{Rk}}}|5|0}}]]<!--
+
  -->{{#if:{{{RCount|}}}|{{#ifeq:{{{RCount}}}|0|{{#ifeq:{{#var:_ris}}|0|[[Category:Riesel {{{Rb}}} Count-0|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}}}<!--
 +
   -->{{#ifexist:{{PAGENAME}}|{{#if:{{{RCount|}}}|{{#ifexpr:{{{RCount}}}>0|{{#ifexpr:{{GNn|{{PAGENAME}}|{{GP|{{PAGENAME}}|RCount}} }} > {{GP|{{PAGENAME}}|RMaxn}}|[[Category:Riesel {{{Rb}}} Missing-range‎|#.....{{padleft:{{{Rk}}}|5|0}}]]}}}}}}}}<!--Exp err
 
   -->{{#if:{{{RMultiRes|}}}|[[Category:{{Multi Reservation:{{{RMultiRes}}}-Name}}|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
 
   -->{{#if:{{{RMultiRes|}}}|[[Category:{{Multi Reservation:{{{RMultiRes}}}-Name}}|#.....{{padleft:{{{Rk}}}|5|0}}]]}}<!--
 
-->}}
 
-->}}

Latest revision as of 11:05, 25 March 2024

Description

Template Riesel prime

Display of current data for Riesel primes kbn-1, comments will be displayed as references at the bottom.

Prototype

{{Riesel prime
|Rk=
|Rb=
|RCount=
|RNash=
|RMaxn=
|RDate=
|RReserved=
|RMultiRes=
|RNlist=
|RRemarks=
|RSieve=
}}

Parameters

  • Rk: the k-value of kbn-1
  • Rb: the b-value of kbn-1
  • RCount: 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.
  • RNash: the Nash weight
  • RMaxn: highest n-value of continuous searched range (from n=1)
  • RDate: last date of edit
  • RReserved: person(s) who reserved this sequence (comma separated)
  • RMultiRes: number of Template:Multi Reservation: RMaxn and RDate will be taken from there
  • RNlist: list of every n-value (one per row) with comments
  • RRemarks: any helpful text or links for this sequence
  • RSieve: if set a zip-file can be uploaded (filename is given then) if not available; if exists file is downloadable

Categories set

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

  • If k-value is disvisible by 3 → category Riesel 3k is set
  • If k-value is disvisible by 15 → category Riesel 15k is set
  • If k-value is disvisible by 2145 → category Riesel 2145k is set
  • If k-value is disvisible by 2805 → category Riesel 2805k is set
  • If RCount=0 & RNash=0 & RMaxn=0 → category Riesel number is set

Any base (here given for base 2 only):

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

See also

Example

{{Riesel prime
|Rk=15
|Rb=2
|RCount=8
|RNash=2390
|RMaxn=20
|RDate=2019-03-01
|RReserved=Karsten Bonath,Euclid
|RMultiRes=
|RNlist=
2;T:ST;C:'''[[M1]]''', Near Woodall: (1+1)*2^1-1
3;T:SW;C:[[M2]], Woodall: 2*2^2-1
5;C:[[M3]], Near Woodall: (3+1)*2^3-1
7;C:[[M4]], Near Woodall: (5-1)*2^5-1
13;C:[[M5]]
17;C:[[M6]]
19;C:[[M7]], Near Woodall: (15+1)*2^15-1
4253;43912;C:[[M19]]
|RRemarks=For this {{Vk}}-value theses are the [[Mersenne prime]]s.
|RSieve=
}}

will create:

Current data

k , b : 15 , 2
Type : 315
Count : 8
Nash : 2390
Max n : 20
Date : 2019-03-01
Reserved : Karsten Bonath, Euclid
2[1], 3[2], 5[3], 7[4], 13[5], 17[6], 19[7], 4253[8]
Remarks :
For this k-value theses are the Mersenne primes.

Notes

  1. Sophie Germain n=2, Twin n=2, M1, Near Woodall: (1+1)*2^1-1
  2. Sophie Germain n=3, Woodall, M2, Woodall: 2*2^2-1
  3. M3, Near Woodall: (3+1)*2^3-1
  4. M4, Near Woodall: (5-1)*2^5-1
  5. M5
  6. M6
  7. M7, Near Woodall: (15+1)*2^15-1
  8. M19