Mersenne vs. LISP

[WGD at MIT-MC (William G. Dubuque)]

	Consider the infamous Mersenne numbers defined by:
		                 K
	                   M  = 2  - 1
		            K
Besides being useful for generating the worlds largest known primes 
(k = 44497 at the present) it seems that they may also be useful for
debugging numerical routines; or at least that seems so for LISP.
	Since GCD(M(P),M(Q)) = M(GCD(P,Q)) we see that
M(K) divides M(2*K) (this may also be seen by factoring M(2*k)).
However, LISP does not seem to think that this identity holds ...
for all k > 105 we get (from LISP):

	        	(GCD (M K) (M 2*K))) => 1

(DIFFERENCE (M 2*K) (TIMES (M K) (QUOTIENT (M 2*K) (M K)))) => unequal 0

It also seems rather suspicious that 105 is exactly the 3-word boundary ...