- Of course I meant to say:

the set of prime numbers = 2, 3, 5 PLUS all odd numbers > 5, not ending

by

5 and not composite.

-----Original Message-----

From: Mazzarello Gianni

Sent: Monday, December 06, 2004 12:55 PM

To: Jim Doyle; primenumbers@yahoogroups.com

Subject: RE: [PrimeNumbers] another way to calculate primes

> It seems correct, but we can say it in an equivalent way:

by

> the set of prime numbers = 2, 5 PLUS all odd numbers > 5, not ending

> 5 and not composite.

- Gianni,

I think Jens is correct. You have to ask what it is that we are

trying to enumerate. We're trying to find the last digits for the

factors of some odd composite, N, call them p and q and we can let

p represent the smaller number, q the larger. The case, for

example where p=3(mod 10) and q=7(mod 10) is different from p=7(mod 10)

and q=3(mod 10) but the case p=1(mod 10) and q=1(mod 10) is not a different

case when the 1 and 1 are swapped.

Another way to think of it: Make a 4x4 multiplication table, mod 10.

With 4 digits there are 16 ways to combine them, with nice symmetry.

1 3 7 9

1 1 3 7 9

3 3 9 1 7

7 7 1 9 3

9 9 7 3 1

Tom Hadley

-----Original Message-----

From: Gianni Mazzarello [mailto:g.mazzarello@...]

Sent: Sunday, December 12, 2004 10:47 AM

To: Jens Kruse Andersen; primenumbers@yahoogroups.com

Subject: [PrimeNumbers] Re: another way to calculate primes

You say:

--

You have to count the "reverse" cases:

...1 => 1 x 1 or 3 x 7 or 7 x 3 or 9 x 9

...3 => 1 x 3 or 3 x 1 or 7 x 9 or 9 x 7

...7 => 1 x 7 or 7 x 1 or 3 x 9 or 9 x 3

...9 => 1 x 9 or 9 x 1 or 7 x 7 or 3 x 3

--

It seems to me you are right (more or less).

But haven't they "reverse" cases also 1x1 and 3x3 and 7 x 7 and 9 x 9?

Then we have to consider:

...1 => 1 x 1 or 3 x 7 or 7 x 3 or 9 x 9 or 1 x 1 or 9 x 9

...3 => 1 x 3 or 3 x 1 or 7 x 9 or 9 x 7

...7 => 1 x 7 or 7 x 1 or 3 x 9 or 9 x 3

...9 => 1 x 9 or 9 x 1 or 7 x 7 or 3 x 3 or 3 x 3 or 7 x 7

Gianni

______________________________________________________----- Original Message -----

From: "Jens Kruse Andersen" <jens.k.a@...>

To: "Mazzarello Gianni" <g.mazzarello@...>

Sent: Friday, December 10, 2004 4:54 PM

Subject: Re: another way to calculate primes

Re: another way to calculate primes

----- Original Message -----

From: "Mazzarello Gianni" <g.mazzarello@...>

To: <primenumbers@yahoogroups.com>

Sent: Friday, December 10, 2004 12:01 PM

Subject: RE: [PrimeNumbers] another way to calculate primes

> ...1 => 1 x 1 or 3 x 7 or 9 x 9

> ...3 => 1 x 3 or 7 x 9

> ...7 => 1 x 7 or 3 x 9

> ...9 => 1 x 9 or 7 x 7 or 3 x 3

You have to count the "reverse" cases:

...1 => 1 x 1 or 3 x 7 or 7 x 3 or 9 x 9

...3 => 1 x 3 or 3 x 1 or 7 x 9 or 9 x 7

...7 => 1 x 7 or 7 x 1 or 3 x 9 or 9 x 3

...9 => 1 x 9 or 9 x 1 or 7 x 7 or 3 x 3

4 cases for each digit.

--

Jens Kruse Andersen (off list)

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