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Difference between revisions of "Template:Generalized Fermat number"
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|#default={{#if:{{#var:n}}|{{NPr|{{#var:k}}|{{#var:n}}}} ([[GF Divisor {{#var:k}} {{#var:n}}|GF Divisor]]){{#ifexist:GF Divisor {{#var:k}} {{#var:n}}|{{#vardefine:dat|{{GFDivisor get disc|GF Divisor {{#var:k}} {{#var:n}}|{{{GFNa}}},{{{GFNb}}},}}}}{{#vardefine:factn|{{GP|GF Divisor {{#var:k}} {{#var:n}}|GFNumber}}}}{{#if:{{#var:factn}}|{{#vardefine:facts|{{#var:facts}} * {{#ifeq:{{Is Long number|{{#var:factn}}}}|1|{{Long number:{{#var:factn}}-NL}}<sub><{{Long number:{{#var:factn}}-DI}}></sub>|{{#var:factn}}{{#ifexpr:{{#len:{{#var:factn}}}}>9|<sub><{{#len:{{#var:factn}}}}></sub>}}}}}}}}}}|{{#var:k}}{{#vardefine:facts|{{#var:facts}} * {{#var:k}}}}}} | |#default={{#if:{{#var:n}}|{{NPr|{{#var:k}}|{{#var:n}}}} ([[GF Divisor {{#var:k}} {{#var:n}}|GF Divisor]]){{#ifexist:GF Divisor {{#var:k}} {{#var:n}}|{{#vardefine:dat|{{GFDivisor get disc|GF Divisor {{#var:k}} {{#var:n}}|{{{GFNa}}},{{{GFNb}}},}}}}{{#vardefine:factn|{{GP|GF Divisor {{#var:k}} {{#var:n}}|GFNumber}}}}{{#if:{{#var:factn}}|{{#vardefine:facts|{{#var:facts}} * {{#ifeq:{{Is Long number|{{#var:factn}}}}|1|{{Long number:{{#var:factn}}-NL}}<sub><{{Long number:{{#var:factn}}-DI}}></sub>|{{#var:factn}}{{#ifexpr:{{#len:{{#var:factn}}}}>9|<sub><{{#len:{{#var:factn}}}}></sub>}}}}}}}}}}|{{#var:k}}{{#vardefine:facts|{{#var:facts}} * {{#var:k}}}}}} | ||
}}<!-- | }}<!-- | ||
| − | -->{{#ifexpr:{{#len:{{#var:dat}}}}>0|, found {{#explode:{{#var:dat}}| |0}} by }}{{Contribs|{{#explode:{{#var:dat}}| |1}}|}} | + | -->{{#ifexpr:{{#len:{{#var:dat}}}}>0|, found {{#explode:{{#var:dat}}| |0}} by }}{{Contribs|{{#explode:{{#var:dat}}| |1}}|}} |
| − | + | }}{{#ifeq:{{NAMESPACENUMBER}}|0|[[Category:Generalized Fermat number {{{GFNa}}} {{{GFNb}}}|#.....{{padleft:{{{GFNn}}}|5|0}}]]}} | |
| − | }} | + | {{#if:{{#var:facts}}| |
==Factorization== | ==Factorization== | ||
| − | {{#vardefine:facts|{{#sub:{{#var:facts}}|2}}}}{{#var:facts}} | + | {{#vardefine:facts|{{#sub:{{#var:facts}}|2}}}}{{#var:facts}}}} |
</includeonly> | </includeonly> | ||
Revision as of 15:02, 5 July 2021
Description
Template Generalized Fermat number
Collect the data of a Generalized Fermat number (for b=1 this is a Fermat number).
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=
2
3,5
3,209
7,14
15288227662166113,8
N1100000000000108402,7
P345
C1133,1100000000212123761
|GFNState=CF
|GFNRemarks=test
}}
will create:
Current data
|
Remarks : |
test |
Factors
- 2
- Proth 3•25+1 (GF Divisor)
- Proth 3•2209+1 (GF Divisor), found 1956 by Raphael M. Robinson
- Proth 7•214+1 (GF Divisor), found 1877 by Ivan Mikheevich Pervushin, Édouard Lucas
- Proth 15288227662166113•28+1 (GF Divisor)
- [[Proth prime 2 Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI)|Proth Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI)•27+1]] ([[GF Divisor Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI) 7|GF Divisor]])Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI)
- Prime P<345>
- Composite C<1133>
Factorization
2 * 97 * 2468256835981809063232453773836025757474103798450369795022913537<64> * 114689 * 3913786281514524929<19> * Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI) * P<345> * C<1133>
