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 -----

From: bejjinks

To: primenumbers@yahoogroups.com

Sent: Wednesday, July 09, 2003 6:32 AM

Subject: [PrimeNumbers] Re: primes and John Harrison

--- In primenumbers@yahoogroups.com, "Mark Underwood"

<mark.underwood@s...> wrote:

>

> 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

replies

> 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

you

> 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.

For

> 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

your

> 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

besides 6.

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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