Template:Generalized Fermat number

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=
}}

Example

{{Generalized Fermat number
|GFNa=2
|GFNb=1
|GFNn=207
|GFNFDBid=1000000000002000017
|GFNDigits=1234
|GFNFactors=
2
3,41
7,14
17353230210429594579133099699123162989482444520899,15
P345
C1133,1100000000212123761
|GFNState=Composite
|GFNRemarks=test
}}

will create:

Current data

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

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 17353230210429594579133099699123162989482444520899•2¹⁵+1 (GF Divisor)17353230210429594579133099699123162989482444520899
• Prime P_<345>
• Composite C_<1133>

Factorization

2 * 6597069766657_<13> * 114689 * 17353230210429594579133099699123162989482444520899 * P_<345> * C_<1133>