12862Re: [PrimeNumbers] Re: primes and John Harrison
- Jul 9, 2003Hello:
I don't know if I missunderstood what you wanted to say, but...
the fact that every prime is either in 6n+1 or 6n-1 is trivial, watching at the residues modulo 6: 6n,6n+2,6n+4 = 2·(3n),2·(3n+1),2·(3n+2) ; 6n+3 = 3·(2n+1) ... the residues 0,2,3,4 can't generate primes because they actually become in composite numbers. This only gives us the residues 1,5 to generate the primes (but of course they also bring a lot of composites).
I think you are computing something similar to the Erathostenes Sieve (as Dècio said), but I'll wait to see your base theory.
Good luck, Jose Brox
----- Original Message -----
Sent: Wednesday, July 09, 2003 6:32 AM
Subject: [PrimeNumbers] Re: primes and John Harrison
--- In firstname.lastname@example.org, "Mark Underwood"
> Hi bejjinks,
> First, it seems we are not receiving your replies. Please note that
> on your replies you have to override the default value which
> only to the individual and change it so it sends to the group.
Actually, I am not replying to every email I recieve. Most of the
emails repeat the same basic messages and so I've sent more group
replies than individual replies. With the individual replies, I may
have accidentally sent them to the individual I haven't sent very
many individual replies.
> Secondly, I would very much like to hear what you have to say. I
> think that your theory can be explained even in text like this if
> define your symbols beforehand.
I've chosen one individual from this group and I've asked him to help
me clear up my terminology so that I can post it to this group in an
understandable manner. I should have that email ready soon.
> So I look forward to hearing more from you on this, if you wish.
> instance, do I correctly recall you saying something to the effect
> that finding larger primes took *less* time than finding smaller
> primes? I would like to hear more about that one! And also, can
> idea be used to demonstrate a numbers primality, or is it strictly
> for prime generation?
Yes, in a way, finding larger primes takes less time than finding
smaller primes. More accurately, it's not that it takes less time,
but that the number of primes produced is greater when working with
larger numbers. In other words, it takes approximately 5 seconds to
use my formula to calculate that 2 is a prime number. It also takes
approximately 5 seconds to calculate all the prime numbers between
30,000 and 500,000. In other words, it doesn't reduce the amount of
time for calculation, it increases the productivity of the process to
work in larger numbers. The only reason I haven't been working in
larger numbers is because at a certain point, the process becomes so
productive that my computer crashes from the sheer volume of numbers.
Although this process is mostly useful for generating prime numbers,
it does also offer some insight into the demonstration of numbers
primality that can lead to further understanding of the nature of
prime numbers. In particular, I know why all primes except 2 and 3
either equal a multiple of six minus one or a multiple of six plus
one. With a little help, I can prove that this is true of all primes
except 2 and 3 and I can prove that there are other "magic" numbers
p.s. not all the responses I've recieved have been so rude. A few
people, in this group and in other places, have been at least civil
if not impressed by what I've got.
Thank you for your questions.
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