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Difference between revisions of "Template:Generalized Fermat number"
(short k-value but long number for factor) |
(lengths in factorization) |
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|C=Composite {{#if:{{#var:n}}|[http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]{{#vardefine:facts|{{#var:facts}} * [http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]}}|{{#var:k}}{{#vardefine:facts|{{#var:facts}} * {{#var:k}}}}}} | |C=Composite {{#if:{{#var:n}}|[http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]{{#vardefine:facts|{{#var:facts}} * [http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]}}|{{#var:k}}{{#vardefine:facts|{{#var:facts}} * {{#var:k}}}}}} | ||
|P=Prime {{#if:{{#var:n}}|[http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]{{#vardefine:facts|{{#var:facts}} * [http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]}}|{{#var:k}}{{#vardefine:facts|{{#var:facts}} * {{#var:k}}}}}} | |P=Prime {{#if:{{#var:n}}|[http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]{{#vardefine:facts|{{#var:facts}} * [http://factordb.com/index.php?id={{#var:n}} {{#var:k}}]}}|{{#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}}|{{#var:factn}}}}}}}}}}|{{#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}}}}}} |
}}<!-- | }}<!-- | ||
-->{{#if:{{#var:dat}}|{{#arraydefine:disc|{{#explode:{{#var:dat}}| |1}}|/;/}}{{#ifexpr:{{#arraysize:disc}}>0|, found {{#explode:{{#var:dat}}| |0}} by }}{{#arrayprint:disc|, |@@@|[[@@@]]}}}}<!-- | -->{{#if:{{#var:dat}}|{{#arraydefine:disc|{{#explode:{{#var:dat}}| |1}}|/;/}}{{#ifexpr:{{#arraysize:disc}}>0|, found {{#explode:{{#var:dat}}| |0}} by }}{{#arrayprint:disc|, |@@@|[[@@@]]}}}}<!-- | ||
Revision as of 12:19, 30 June 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
3,41
7,14
15288227662166113,8
N1100000000000108402,7
P345
C1133,1100000000212123761
|GFNState=Composite
|GFNRemarks=test
}}
will create:
Current data
|
Remarks : |
test |
Factors
- 2
- Proth 3•241+1 (GF Divisor), found 1903 by James Cullen, Allan Cunningham, Alfred Edward Western
- 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 * 6597069766657<13> * 114689 * 3913786281514524929<19> * Long number:N1100000000000108402-NS(Long number:N1100000000000108402-DI) * P<345> * C<1133>
