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Difference between revisions of "Template:Generalized Fermat number"

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(a+b even -> no factor 2)
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|GFNRemarks=test
 
|GFNRemarks=test
 
}}
 
}}
[[Category:Prime collections]]</noinclude><includeonly>__NOTOC__{{#ifeq:{{NAMESPACENUMBER}}|0|{{#vardefine:Ta|{{#explode:{{PAGENAME}}||-3}}}}{{#vardefine:Tb|{{#explode:{{PAGENAME}}||-2}}}}{{#vardefine:Tn|{{#explode:{{PAGENAME}}||-1}}}}{{#ifeq:{{#var:Tb}}|1|{{#ifeq:{{#var:Ta}}|2|{{DISPLAYTITLE:Fermat number 2<sup>2<sup>{{#var:Tn}}</sup></sup>+1}}|{{DISPLAYTITLE:Generalized Fermat number {{#var:Ta}}<sup>2<sup>{{#var:Tn}}</sup></sup>+1}}}}|{{DISPLAYTITLE:Generalized Fermat number {{#var:Ta}}<sup>2<sup>{{#var:Tn}}</sup></sup>+{{#var:Tb}}<sup>2<sup>{{#var:Tn}}</sup></sup>{{#ifexpr:({{#var:Ta}}+{{#var:Tb}}) mod 2||/2}}}}}}}}
+
[[Category:Prime collections]]</noinclude><includeonly>__NOTOC__{{#ifeq:{{NAMESPACENUMBER}}|0|{{#vardefine:Ta|{{#explode:{{PAGENAME}}||-3}}}}{{#vardefine:Tb|{{#explode:{{PAGENAME}}||-2}}}}{{#vardefine:Tn|{{#explode:{{PAGENAME}}||-1}}}}{{#ifeq:{{#var:Tb}}|1|{{#ifeq:{{#var:Ta}}|2|{{DISPLAYTITLE:Fermat number 2<sup>2<sup>{{#var:Tn}}</sup></sup>+1}}|{{DISPLAYTITLE:Generalized Fermat number {{#var:Ta}}<sup>2<sup>{{#var:Tn}}</sup></sup>+1{{#ifexpr:({{#var:Ta}}+{{#var:Tb}}) mod 2||&nbsp;div 2}}}}}}|{{DISPLAYTITLE:Generalized Fermat number {{#var:Ta}}<sup>2<sup>{{#var:Tn}}</sup></sup>+{{#var:Tb}}<sup>2<sup>{{#var:Tn}}</sup></sup>{{#ifexpr:({{#var:Ta}}+{{#var:Tb}}) mod 2||&nbsp;div 2}}}}}}}}
 
==Current data==
 
==Current data==
 
{| class="primedata"
 
{| class="primedata"

Revision as of 08:41, 29 July 2021

Description

Template Generalized Fermat number

Collect the data of a Generalized Fermat number a2n + b2n, for b=1 this is a Fermat number a2n + 1.

If a+b is even, the numbers are always divisible by 2 and so this factor is not given here.

Prototype

{{Generalized Fermat number
|GFNa=
|GFNb=
|GFNn=
|GFNFDBid=
|GFNDigits=
|GFNFactors=
|GFNState=
|GFNRemarks=
}}

Parameters

See also

Example

{{Generalized Fermat number
|GFNa=2
|GFNb=1
|GFNn=207
|GFNFDBid=1000000000002000017
|GFNDigits=1234
|GFNFactors=
3,5
3,209
7,14
15288227662166113,8
N1100000000000108402,7
P345
C1133,1100000000212123761
|GFNState=CF
|GFNRemarks=test
}}

will create:

Current data

a b n : 2 1 207
FactorDB : ID: 1000000000002000017 / Formula: 22207+1
Digits : 1234
State : CF
Remarks :
test

Factors

Factorization

97 * 2468256835981809063232453773836025757474103798450369795022913537<64> * 114689 * 3913786281514524929<19> * Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI) * P<345> * C<1133>