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Difference between revisions of "Template:Proth prime"
(more param & checks) |
(display ktype changed) |
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Template Proth prime | Template Proth prime | ||
− | Display of current data for Proth primes {{Kbn|+|k| | + | 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| | + | *'''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 ( | + | *'''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 [[: | + | *'''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 | + | *{{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 | + | *{{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 | + | *{{Vk}}-value is disvisible by 2145 → category [[:Category:Proth 2 2145k-value|Proth 2145k]] is set |
− | *Nash-weight < 1000 → category [[:Category:Proth | + | *{{Vk}}-value is disvisible by 2805 → category [[:Category:Proth 2 2805k-value|Proth 2805k]] is set |
+ | Any base: | ||
+ | *Nash-weight < 1000 → 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 → 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 53: | Line 59: | ||
{{Proth prime | {{Proth prime | ||
|Pk=15 | |Pk=15 | ||
+ | |Pb=2 | ||
|PCount=4 | |PCount=4 | ||
|PNash=239 | |PNash=239 | ||
Line 61: | 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 {{Vk}}-value these are the [[Fermat prime]]s. | + | |PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s. |
|PSieve=y | |PSieve=y | ||
}} | }} | ||
Line 71: | Line 78: | ||
{{Proth prime | {{Proth prime | ||
|Pk=15 | |Pk=15 | ||
+ | |Pb=2 | ||
|PCount=4 | |PCount=4 | ||
|PNash=239 | |PNash=239 | ||
Line 79: | 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 {{Vk}}-value these are the [[Fermat prime]]s. | + | |PRemarks=For this {{Vk}}-value these are the [[Generalized Fermat prime]]s. |
− | |PSieve= | + | |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]]}}<!-- | -->{{#if:{{{PCount|}}}||[[Category:Missing XCount]]}}<!-- | ||
-->{{#vardefine:_cnt|{{NVal list|{{{PNlist}}}|count}}}}<!-- | -->{{#vardefine:_cnt|{{NVal list|{{{PNlist}}}|count}}}}<!-- | ||
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==Current data== | ==Current data== | ||
{| class="primedata" | {| class="primedata" | ||
− | | class="primetemplate" | | + | | class="primetemplate color-PrimeTemplate" | |
{| | {| | ||
− | | align="right"| <b>{{Vk}} | + | | align="right"| <b>{{Vk}} , {{Vb}} :</b> || {{{Pk}}} , {{{Pb}}} {{#if:{{{PSieve|}}}|{{#ifexist:File:{{PAGENAME}} sieve.zip| ([[: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> || {{#if:{{{PCount|}}}|{{#ifeq:{{{PCount|}}}|{{#var:_cnt}}|{{{PCount}}}|{{Alert|Attention!|Parameter PCount={{{PCount}}} differs from counting={{#var:_cnt}}}}[[Category:Wrong XCount]]}}|{{Alert|Attention!|Parameter PCount={{#var:_cnt}} not given!}}}} | | align="right"| <b>Count :</b> || {{#if:{{{PCount|}}}|{{#ifeq:{{{PCount|}}}|{{#var:_cnt}}|{{{PCount}}}|{{Alert|Attention!|Parameter PCount={{{PCount}}} differs from counting={{#var:_cnt}}}}[[Category:Wrong XCount]]}}|{{Alert|Attention!|Parameter PCount={{#var:_cnt}} not given!}}}} | ||
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| align="right"| <b>Nash :</b> || {{{PNash}}} | | align="right"| <b>Nash :</b> || {{{PNash}}} | ||
|- | |- | ||
− | | align="right"| <b>Max {{Vn}} :</b> || {{#if:{{{PMultiRes|}}}|{{#if:{{{PMaxn|}}}|{{Num|{{{PMaxn}}}}} ({{Num|{{Multi Reservation:{{{PMultiRes}}}-NMax}}}})[[Category:Proth | + | | align="right"| <b>Max {{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 114: | Line 126: | ||
{{#if:{{{PRemarks|}}}| | {{#if:{{{PRemarks|}}}| | ||
{{{!}} | {{{!}} | ||
− | {{!}} <div height="120%" | + | {{!}} <div height="120%" class="color-PrimeTemplate"><b>Remarks : </b></div> {{!}}{{!}} {{{PRemarks}}} |
{{!}}} | {{!}}} | ||
}} | }} | ||
{{#ifeq:{{NAMESPACENUMBER}}|0|<!-- | {{#ifeq:{{NAMESPACENUMBER}}|0|<!-- | ||
− | -->{{#ifexpr:{{{Pk}}} | + | -->[[Category:Proth {{{Pb}}}|#.....{{padleft:{{{Pk}}}|5|0}}]]<!-- |
− | -->{{#ifexpr:{{{Pk}}} | + | -->{{#ifeq:{{{Pb}}}|2|<!-- |
− | -->{{#ifexpr:{{{Pk}}} | + | -->{{#ifexpr:{{{Pk}}} < 300|[[Category:Proth 2 1-300|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!-- |
− | -->{{#ifexpr:{{{Pk}}} | + | -->{{#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}}]]}}<!-- |
− | -->{{#ifeq:{{#var:_sir}}| | + | -->{{#ifexpr:{{{Pk}}} mod 15||[[Category:Proth {{{Pb}}} 15k-value|#.....{{padleft:{{{Pk}}}|5|0}}]]}}<!-- |
− | -->{{#if:{{{PCount|}}}|{{#ifexpr:{{{PCount}}}> | + | -->{{#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}}]]}}<!-- | |
− | -->[[Category:Proth | + | -->{{#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:
- Nash-weight < 1000 → category Proth Low-weight is set
- If there are 100 n-values or more → Proth Count-100 is set
- If PCount=0 → category Proth Count 0 is set
- If PCount=0 & PNash=0 & PMaxn=0 → Proth Sierpinski is set
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
|
|
Remarks : |
For this k-value these are the Generalized Fermat primes. |
Notes
- ↑ Sophie Germain n=2, Twin n=2, Testtext
- ↑ Sophie Germain n=3, Woodall, Examples
- ↑ Example
- ↑ with Top5000 entry