| Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3). |
Navigation
| Topics | Help • Register • News • History • How to • Sequences statistics • Template prototypes |
Difference between revisions of "Template:Generalized Fermat number"
m |
(factor unknown) |
||
| Line 43: | Line 43: | ||
P345 | P345 | ||
C1133,1100000000212123761 | C1133,1100000000212123761 | ||
| + | U12345,4545 | ||
|GFNState=CF | |GFNState=CF | ||
|GFNRemarks=test | |GFNRemarks=test | ||
| Line 62: | Line 63: | ||
P345 | P345 | ||
C1133,1100000000212123761 | C1133,1100000000212123761 | ||
| + | U12345,4545 | ||
|GFNState=CF | |GFNState=CF | ||
|GFNRemarks=test | |GFNRemarks=test | ||
| Line 106: | Line 108: | ||
|C=Composite {{#vardefine:k|C<sub><{{#sub:{{#var:k}}|1}}></sub>}}{{#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 {{#vardefine:k|C<sub><{{#sub:{{#var:k}}|1}}></sub>}}{{#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 {{#vardefine:k|P<sub><{{#sub:{{#var:k}}|1}}></sub>}}{{#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 {{#vardefine:k|P<sub><{{#sub:{{#var:k}}|1}}></sub>}}{{#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}}}}}} | ||
| + | |U=Unknown {{#vardefine:k|U<sub><{{#sub:{{#var:k}}|1}}></sub>}}{{#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}}}}{{#ifeq:{{#sub:{{#var:factn}}|0|1}}|P|{{#vardefine:facts|{{#var:facts}} * P<sub><{{#sub:{{#var:factn}}|1}}></sub>}}|{{#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}}}}}}|{{#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}}}}{{#ifeq:{{#sub:{{#var:factn}}|0|1}}|P|{{#vardefine:facts|{{#var:facts}} * P<sub><{{#sub:{{#var:factn}}|1}}></sub>}}|{{#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}}}}}}|{{#var:k}}{{#vardefine:facts|{{#var:facts}} * {{#var:k}}}}}} | ||
}}<!-- | }}<!-- | ||
Revision as of 00:11, 23 August 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.
Prototype
{{Generalized Fermat number
|GFNa=
|GFNb=
|GFNn=
|GFNFDBid=
|GFNDigits=
|GFNFactors=
|GFNState=
|GFNRemarks=
}}
Parameters
If 'GFNa'+'GFNb' is even, the numbers are always divisible by 2 and so 2 is not given as factor here.
If 'GFNFDBid' is given, a link to the FactorDB is created, otherwise only the number in standard notation is given.
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
N1100000002618011261,9
P345
C1133,1100000000212123761
U12345,4545
|GFNState=CF
|GFNRemarks=test
}}
will create:
Current data
|
Remarks : |
test |
Factors
- 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 138139700146349586211941790195...83(88)•29+1 (GF Divisor)
- Prime P<345>
- Composite C<1133>
- Unknown U<12345>
Factorization
97 * 2468256835981809063232453773836025757474103798450369795022913537<64> * 114689 * 3913786281514524929<19> * 707275264749309881405141965802671548079179711820351316861777644606207216944972589404100097<90> * P<345> * C<1133> * U<12345>
