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Re: executor-digest V1 #349
Dear Charlie:
On your primes problems, there's a discussion of it in Chapter
1 of Ribenboim's "Book of Prime Number Records". For a prime p,
define p# to be the product of all primes q <= p. Then
p# + 1 is prime for p = 2,3,5,7,11,31,379, 1019, 1021, 2657 and
composite for all other primes < 11213. Thus 13# + 1 = 30,031
is the first for which it's composite, as you say. It's not
known whether there are infinitely many p for which p# + 1 is
prime, nor is it known whether there are infinitely many p for
which p# + 1 is composite.
All these relativistic arguments are bull. I don't put
any stock in 'em. I agree with what you say about logic
being used as a weapon of intimidation.
Maple and Mathematica are both slow. I recently came across
a free software package called Pari written by some number-theorists
from Paris. For factoring large numbers, I found it *much* better
than Maple. I don't know if it would be good for the combinatorial
problems I am currently interested in. The authors of Pari claim
it can be 300 to 500 times faster than Mathematica etc. which is
impressive if true.
Alasdair