From: Lee Corbin (lcorbin@tsoft.com)
Date: Thu May 02 2002 - 01:28:10 MDT
Hi Spike,
Yes, it looks like you can add to the "abundant" and
"deficient" numbers with this classification. I've
never heard of it before.
Don't let me impede your efforts to foment more
NewSpeak, but don't you think that "superb" and
"sublime" and so on might be preferable to
"kilovery" "kilodamn"? ;-)
Hmm. Well, maybe not.
By the way, since you're up late running strange
programs, here's one that might interest you that
I recently wrote:
// This program tries to figure out how many
// solutions exist for each positive N to the
// equation x^2 == 1 (mod N). (When N is prime,
// solutions depend on "The Law of Quadratic
// Residues".)
// But I may have made an interesting discovery
// for composite N. Something very strange happens
// when N is greater than 46334. Run the following
// program, and you'll see!
#include <stdio.h>
int N;
int count;
void trial( int N )
{
count = 0;
for ( int i=1; i<N; i++ )
{
if ( (i*i)%N == 1 )
count++;
}
if ( count == 2 ) // Are there exactly two solutions?
printf( "%5d ", N );
}
void main()
{
for ( int i=4; i<300000; i+=2 )
{
if ( i%100 == 0 ) // only check 100 per line of output
printf( "\n" );
trial( i );
}
}
Lee
> -----Original Message-----
> From: owner-extropians@extropy.org
> [mailto:owner-extropians@extropy.org]On Behalf Of spike66
> Sent: Wednesday, May 01, 2002 11:14 PM
> To: extropians@extropy.org
> Subject: oh my goodness
>
>
> A perfect number is one whose factors exactly
> equal the number itself, examples being 6 and 28.
> Another way to look at it is the ratio of the sum
> of the factors to the number is unity. Thirty-nine
> perfect numbers are known, all of them even.
>
> What about odd numbers whose factor ratio is
> almost unity? We could refer to those numbers
> with a sum of factors ratio (goodness ratio) between
> 0.9 and 1.1 as good numbers. Numbers with
> goodness ratio is between 0.99 and 1.01 could
> be very good numbers, and goodness ratios
> between 0.999 and 1.001 are damn good numbers.
> Then for each order of magnitude approaching the
> perfect number, we could use the usual prefixes,
> kilogood, kilovery good, kilodamn good, and so on.
>
> I have written a program to discover good numbers.
> The even numbers are better, as might be expected.
> For instance, 262144 has a factor sum of 262143,
> for a goodness ratio of 0.9999962, making it a
> kilovery good number. The best (goodest?) odd
> number it has found so far is 32445 whose factor
> sum is 32451 for a goodness ratio of 1.00018,
> making it a damn good number, very close to the
> kilogood range. And that's pretty close to perfect,
> even the FRENCH judge would have to agree.
>
> There are no known odd perfect numbers. What is the
> record goodest known odd number? What if extropians
> were to raise a team to do background calculations on
> our confusers to search for the goodest known odd
> number? We could snag the record! Who knows,
> perhaps we could discover the illusive odd perfect
> number.
>
> spike
>
>
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