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Mersenne vs. LISP
- 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:
M = 2 - 1
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 ...