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MathGroup Archive 2000

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Re: speed of "PrimeQ"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg22865] Re: speed of "PrimeQ"
  • From: "Kai G. Gauer" <gauer at sk.sympatico.ca>
  • Date: Sun, 2 Apr 2000 15:33:35 -0400 (EDT)
  • References: <8c69qf$547@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Speaking of running prime tests,etc, I've got a few questions:

First, most number theorists probably know about the standard way of
publishing a number in the Cunningham tables which are kept on-line on
somebody's big webpage (sorry, I forgot his name). How do I convert his
format to a mathematica readable file format which could be appended
each 6 or 8 months?

Furthermore, I would also like to collect (a probably binary-style
file...two reasons: space and ensuring of proper readings (no
error-detectors unless way out at eof), etc added in to possibly, but
very unlikely, interfere with the read of) a table which contains a 0
for prime, a 1 for not completely factored composite, 2 for known
composite, but no factors/all but (a few #of factors known), 3 for a
unit (usually just 1,-1,-i,i, but others if you talk about formats other
than just the integers/gaussians), 4 being which behave like zero, 5 for
pseudoprimes of some particular type, 6 for odd perfects (if any), 7 for
other cool numbers, etc..... Anyone got a nice list that they might like
to share?

What's the best way to store the prime factorization of a list of
numbers (ie Is it good to call p(5)=11, or should we choose better
notations for storing bigger primes which need to be accessed more than
the prime = 11)

How big is the biggest list for which it is KNOWN the primality
(exactly) for all numbers on a certain interval? Presumably, the largest
interval starts with one, but what is the data file filled with, and up
to what...does it have everything for things like tau and phi of n, for
all n on that interval? Furthermore, we also (unless RSA already has it)
know that our largest currently known factored, composite or partially
factored number at almost any given time is say, x. Are there good ways
of estimating the size of how the ratio of the small interval of
prime/composite absolutely known compares to the larger interval and how
it fluctuates with the growth of computing time thru time?

I can't seem to find much of a web consensus on choosing any universally
accepted method of number primality storage that works nice for all
platforms. It's most likely because of the fact that when some people
like doing searches for wolfenstolhme numbers and others just want the
Mersenne primes or sequences that generate "nice arithmetic
progressions" that we won't come to agreement, but if you do have a
favoured method, please post it to me!


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