Editing Fermat number (section)

===Generalized Fermat primes of the form F<sub>n</sub>(''a'', ''b'')===
It is also possible to construct generalized Fermat primes of the form <math>a^{2^n} + b^{2^n}</math>. As in the case where ''b''=1, numbers of this form will always be divisible by 2 if ''a+b'' is even, but it is still possible to define generalized half-Fermat primes of this type. For the smallest prime of the form <math>F_n(a,b)</math> (for odd <math>a+b</math>), see also {{oeis|id=A111635}}.

{|class="wikitable"
!<math>a</math>
!<math>b</math>
!numbers <math>n</math> such that<br/><math>F_n(a,b) = \frac{a^{2^n}+b^{2^n}}{\gcd(a+b, 2)}</math><br/>is prime<ref>{{cite web |title=Original GFN factors |url=http://www.prothsearch.com/OriginalGFNs.html |website=www.prothsearch.com}}</ref><ref name="bjorn"/>
|-
| 2
| 1
| 0, 1, 2, 3, 4, ...
|-
| 3
| 1
| 0, 1, 2, 4, 5, 6, ...
|-
| 3
| 2
| 0, 1, 2, ...
|-
| 4
| 1
| 0, 1, 2, 3, ... (equivalent to <math>F_n(2, 1)</math>)
|-
| 4
| 3
| 0, 2, 4, ...
|-
| 5
| 1
| 0, 1, 2, ...
|-
| 5
| 2
| 0, 1, 2, ...
|-
| 5
| 3
| 1, 2, 3, ...
|-
| 5
| 4
| 1, 2, ...
|-
| 6
| 1
| 0, 1, 2, ...
|-
| 6
| 5
| 0, 1, 3, 4, ...
|-
| 7
| 1
| 2, ...
|-
| 7
| 2
| 1, 2, ...
|-
| 7
| 3
| 0, 1, 8, ...
|-
| 7
| 4
| 0, 2, ...
|-
| 7
| 5
| 1, 4,
|-
| 7
| 6
| 0, 2, 4, ...
|-
| 8
| 1
| {{CNone|(none)}}
|-
| 8
| 3
| 0, 1, 2, ...
|-
| 8
| 5
| 0, 1, 2,
|-
| 8
| 7
| 1, 4, ...
|-
| 9
| 1
| 0, 1, 3, 4, 5, ... (equivalent to <math>F_n(3, 1)</math>)
|-
| 9
| 2
| 0, 2, ...
|-
| 9
| 4
| 0, 1, ... (equivalent to <math>F_n(3, 2)</math>)
|-
| 9
| 5
| 0, 1, 2, ...
|-
| 9
| 7
| 2, ...
|-
| 9
| 8
| 0, 2, 5, ...
|-
| 10
| 1
| 0, 1, ...
|-
| 10
| 3
| 0, 1, 3, ...
|-
| 10
| 7
| 0, 1, 2, ...
|-
| 10
| 9
| 0, 1, 2, ...
|-
| 11
| 1
| 1, 2, ...
|-
| 11
| 2
| 0, 2, ...
|-
| 11
| 3
| 0, 3, ...
|-
| 11
| 4
| 1, 2, ...
|-
| 11
| 5
| 1, ...
|-
| 11
| 6
| 0, 1, 2, ...
|-
| 11
| 7
| 2, 4, 5, ...
|-
| 11
| 8
| 0, 6, ...
|-
| 11
| 9
| 1, 2, ...
|-
| 11
| 10
| 5, ...
|-
| 12
| 1
| 0, ...
|-
| 12
| 5
| 0, 4, ...
|-
| 12
| 7
| 0, 1, 3, ...
|-
| 12
| 11
| 0, ...
|-
|}