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*To*: (BUG LISP) at MIT-MC, MATHLAB at MIT-MC*Subject*: Mersenne vs. LISP*From*: WGD at MIT-MC (William G. Dubuque)*Date*: Tue, 22 Jan 80 03:24:00 GMT*Original-date*: 21 JAN 1980 2224-EST

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 ...

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