Let

A1 := 118464154434645263860267343997297625073515299575810526009609590494555875212753237432077051783988309701763476345132077575492035913941539680031806906994000003063163805121640021467690282290325426999148751;

and

A2 := 2;

Now consider the differential operator (in Maple notation):

_Envdiffopdomain := [Dx,x]; # Means that Dx = d/dx

L4 := Dx^4+(-2*A2*x^2-2*A1)*Dx^2-4*A2*x*Dx+A1^2-3*A2+A2^2*x^4+2*A2*x^2*A1;

This L4 is reducible in Q(x)[Dx].  Given a factorization of A1 one
can quickly factor L4 in Q(x)[Dx].  The difficulty is that at the moment
(in 2002) the integer A1 is too large for currently available integer
factorizers.

I offer a $100 reward (valid until 2012) for anyone who can find
an irreducible factor of L4 in Q(x)[Dx]  (send to hoeij@math.fsu.edu).