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Difference between revisions of "Template:Generalized Fermat number"
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| − | }}{{#ifeq:{{NAMESPACENUMBER}}|0|[[Category:Generalized Fermat number {{{GFNa}}} {{{GFNb}}} | + | }}{{#ifeq:{{NAMESPACENUMBER}}|0|[[Category:Generalized Fermat number {{{GFNa}}} {{{GFNb}}} Nums]]}} |
{{#if:{{#var:facts}}| | {{#if:{{#var:facts}}| | ||
==Factorization== | ==Factorization== | ||
<span class="longline">{{#vardefine:facts|{{#sub:{{#var:facts}}|2}}}}{{#var:facts}}}}</span> | <span class="longline">{{#vardefine:facts|{{#sub:{{#var:facts}}|2}}}}{{#var:facts}}}}</span> | ||
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Revision as of 13:55, 10 September 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.
For the case (a,b) = (8,1) the number for Fn(8,1) div 22n+1 = 42n − 22n + 1 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>
