A search for prime factors of the generalized Fermat numbers
F
n
(
a
,
b
)
=
a
2
n
+
b
2
n
F_n(a,b)=a^{2^n}+b^{2^n}
has been carried out for all pairs
(
a
,
b
)
(a,b)
with
a
,
b
≤
12
a,b\leq 12
and GCD
(
a
,
b
)
=
1
(a,b)=1
. The search limit
k
k
on the factors, which all have the form
p
=
k
⋅
2
m
+
1
p=k\cdot 2^m+1
, was
k
=
10
9
k=10^9
for
m
≤
100
m\leq 100
and
k
=
3
⋅
10
6
k=3\cdot 10^6
for
101
≤
m
≤
1000
101\leq m\leq 1000
. Many larger primes of this form have also been tried as factors of
F
n
(
a
,
b
)
F_n(a,b)
. Several thousand new factors were found, which are given in our tables.—For the smaller of the numbers, i.e. for
n
≤
15
n\leq 15
, or, if
a
,
b
≤
8
a,b\leq 8
, for
n
≤
16
n\leq 16
, the cofactors, after removal of the factors found, were subjected to primality tests, and if composite with
n
≤
11
n\leq 11
, searched for larger factors by using the ECM, and in some cases the MPQS, PPMPQS, or SNFS. As a result all numbers with
n
≤
7
n\leq 7
are now completely factored.