At 01:00 PM 6/18/99 +1200, Halliday, Ian wrote:
>Merely expressing an opinion as to whether or not you think there are an
>infinite or finite number of Mersenne primes doesn't add anything to the
>discussion unless you can furnish some argument one way or the other.
There are two main reasons:
(1) if you consider the prime number theorem to approximate the probability
that 2^p-1 is prime and sum that over all primes p, you get an infinite number
which means that you expect an infinite number of Mersenne primes.
(2) there are several conjectures concerning the growth rate of successive
Mersenne primes. They all suggest that on average, one exponent resulting in a
Mersenne prime is no more than twice the previous one. This implies an
infinite number of Mersenne primes. The known Mersenne primes are in very good
agreement with the conjecture that, on the average, an exponent resulting in a
Mersenne prime is about 3/2 as large as the previous one. That, of course,
would imply an infinite number of Mersenne primes.
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| Jud "program first and think later" McCranie |
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