I am a little bit impatient about the divulgation of the value of the
exponent of the (probably)recently found new Mersenne Prime.According to Chris
Caldwell's home-page,M37 was found on 1/27/98 and Slowinsky finished the
double checking on 1/30/98.Since the exponent of the new prime is close to
the double of the exponent 3021377,it is reasonable to expect that a double
check could be done in not much more time than 4*3=12 days,say 2 weeks,so,if
these considerations make sense we should expect to know the new exponent
very soon.
However,I am a little bit concerned about the meaning of the "bad news" of
Woltman's announce of the discovery.GIMPS(and Woltman's work in particular)
was a great contribution to computational number theory.One of GIMPS
greatest virtues is it's transparence,and the collective character of its
work and information.Moreover,I am convinced that the main motivation of
the great majority of GIMPS participants is the intelectual satisfaction of
contributing somehow to human's knowledge.Money prizes are very positive
iniciatives,but should not affect the transparence of the traditional
information policy of such a nice project as GIMPS. According to these
considerations,I consider that it doesn't make sense to keep the exponent in
secret until publication on a paper review.It is important to notice that
almost all important mathematical results are announced,and preprints of
them are distributed before actual publication,and the magazines do not
create obstacles to it.Moreover,the rules of EFF's prize are very reasonable
ones,and do not request the discovers of a prime to keep it's value in secret.
As I mentioned before,it is not the policy of math magazines such as Math.
Comp. to do this kind of requirement.To give an example,according again to
Caldwell's home-page,the 29th Mersenne prime 2^110503-1 was found by Colquitt
and Welsh on 1988 and was published in Math. Comp. only on 1991.I'm quite sure
that they didn't keep the secret about the exponent for 3 years(and,as this
example shows,we have no control on the time that a magazine spend for
publishing a paper).
Carlos Gustavo Moreira
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