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: <email@example.com>
- 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!