We have shown by machine proof that
F
22
=
2
2
22
+
1
{F_{22}} = {2^2}^{^{22}} + 1
is composite. In addition, we reenacted Young and Buell’s 1988 resolution of
F
20
{F_{20}}
as composite, finding agreement with their final Selfridge-Hurwitz residues. We also resolved the character of all extant cofactors of
F
n
,
n
≤
22
{F_n}, n \leq 22
, finding no new primes, and ruling out prime powers.