Conjecture on odd numbers
Felice Russo
Every odd number n>3 can be written as:
n=2*p+q
where p and q are two odd primes or 1.
I tested it by computer search up to 10^6.
Thanks Felice
Bob Silverman
fru...@micron.com (Felice Russo) wrote:
> Is the following conjecture already known or proved?
>
> Every odd number n>3 can be written as:
> n=2*p+q
> where p and q are two odd primes or 1.
It is easily seen to be a slight weakening of Goldbach's conjecture.
Bob Silverman
"You can lead a horse's ass to knowledge, but you can't make him think"
Sent via Deja.com http://www.deja.com/
Before you buy.
cea...@my-deja.com
fru...@micron.com (Felice Russo) wrote:
> Is the following conjecture already known or
proved?
>
> Every odd number n>3 can be written as:
> n=2*p+q
> where p and q are two odd primes or 1.
>
>
> Thanks Felice
related to Goldbach's ternary conjecture, that
any odd #>5 may be expressed as the sum of three
primes. I make a stronger conjecture: That any
odd #>5 may be expressed as 2*p+q, where p and q
are primes. This conjecture allows the use of
the prime "2", and does not require the use of
"1". For example, 7=2*2+3; 15=2*2+11=2*5+5;
17=2*2+13=2*3+11=2*5+7=2*7+3. I don't know how
to program, so I haven't tested it, except by
hand. Let me know if you are interested in
pursuing this.
You're welcome, and thanks,
Connie
John Savard
>I don't believe this has been proven. It is
>related to Goldbach's ternary conjecture, that
>any odd #>5 may be expressed as the sum of three
>primes.
I seem to vaguely recall that the ternary conjecture has been proved,
or at least something resembling it.
John Savard (don't snooze, don't snore)
http://www.ecn.ab.ca/~jsavard/crypto.htm
Dann Corbit
This program tests the Connie Conjecture. Supply one argument to the
command line to test odd numbers from 7 to that number for conjecture
compliance. Supply any additional argument to show only failures. E.g.:
connie 1000000 1
Will show any failures for odd numbers from 7 up to 1000000.
connie 1000
Sample runs:
D:\TMP>connie 10000000 1
Searching prime numbers to : 10000000
664579 prime numbers found in 1.00 secs.
Finished calculations in 6.00 secs.
D:\TMP>connie 50
Searching prime numbers to : 50
15 prime numbers found in 0.00 secs.
7 = 2*2 + 3
9 = 2*2 + 5
11 = 2*2 + 7
13 = 2*3 + 7
15 = 2*2 + 11
17 = 2*2 + 13
19 = 2*3 + 13
21 = 2*2 + 17
23 = 2*2 + 19
25 = 2*3 + 19
27 = 2*2 + 23
29 = 2*3 + 23
31 = 2*7 + 17
33 = 2*2 + 29
35 = 2*2 + 31
37 = 2*3 + 31
39 = 2*5 + 29
41 = 2*2 + 37
43 = 2*3 + 37
45 = 2*2 + 41
47 = 2*2 + 43
49 = 2*3 + 43
Finished calculations in 0.00 secs.
Will show the actual values found that complete the conjecture for odd
numbers up to 1000.
Here is the original email:
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From: cea...@my-deja.com
Newsgroups: sci.math
Subject: Re: Conjecture on odd numbers
Date: Fri, 19 Nov 1999 18:57:48 GMT
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In article <0vg2x4...@forum.swarthmore.edu>,
fru...@micron.com (Felice Russo) wrote:
> Is the following conjecture already known or
proved?
>
> Every odd number n>3 can be written as:
> n=2*p+q
> where p and q are two odd primes or 1.
>
> I tested it by computer search up to 10^6.
>
> Thanks Felice
I don't believe this has been proven. It is
related to Goldbach's ternary conjecture, that
any odd #>5 may be expressed as the sum of three
primes. I make a stronger conjecture: That any
odd #>5 may be expressed as 2*p+q, where p and q
are primes. This conjecture allows the use of
the prime "2", and does not require the use of
"1". For example, 7=2*2+3; 15=2*2+11=2*5+5;
17=2*2+13=2*3+11=2*5+7=2*7+3. I don't know how
to program, so I haven't tested it, except by
hand. Let me know if you are interested in
pursuing this.
You're welcome, and thanks,
Connie
Sent via Deja.com http://www.deja.com/
Before you buy.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#define TEST( f, x ) ( *( f+( x )/16 )&( 1<<( ( ( x )%16L )/2 ) ) )
#define SET( f, x ) *( f+( x )/16 )|=1<<( ( ( x )%16L )/2 )
unsigned ip(unsigned long j, unsigned char *d)
{
if (j == 1)
return 0;
if ((j % 2) == 0) {
if (j == 2)
return 1;
else
return 0;
} else
return (!(*(d + (j) / 16) & (1 << (((j) % 16L) / 2))) && j != 1);
}
int main(int argc, char *argv[])
{
unsigned char *feld = NULL,
*zzz = NULL;
unsigned long teste = 1,
max,
mom,
hits = 1,
alloc;
time_t begin;
unsigned char quiet = 0;
if (argc > 1) {
max = atol(argv[1]) + 10000;
if (argc > 2)
quiet = 1;
} else
max = 14010000L;
zzz = feld = malloc(alloc = (((max -= 10000L) >> 4) + 1L));
if (feld) {
char found;
memset(zzz, 0, alloc);
printf("Searching prime numbers to : %lu\n", max);
begin = time(NULL);
while ((teste += 2) < max)
if (!TEST(feld, teste)) {
++hits;
for (mom = 3L * teste; mom < max; mom += teste << 1)
SET(feld, mom);
}
printf(" %ld prime numbers found in %.2f secs.\n\n",
hits, difftime(time(NULL), begin));
{
long o,
p,
q,
j;
for (o = 7; o <= max; o += 2) {
found = 0;
for (j = 2; j < o;) {
p = j;
q = o - 2 * p;
if (ip(p, feld) && ip(q, feld)) {
if (!quiet)
printf("%lu = 2*%lu + %lu\n", o, p, q);
found = 1;
break;
}
if (j == 2)
j++;
else
j += 2;
}
if (!found)
printf("*** Problem!! %lu\n", o);
}
free(feld);
printf(" Finished calculations in %.2f secs.\n\n",
difftime(time(NULL), begin));
}
} else {
puts("Memory allocation failure.");
exit(EXIT_FAILURE);
}
return 0;
}
--
C-FAQ: http://www.eskimo.com/~scs/C-faq/top.html
"The C-FAQ Book" ISBN 0-201-84519-9
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Tapio Hurme
After rearrangement 2*p=n-q is called de Polignac´s conjecture, where n is
also a prime as q -too. Note: n is also prime - not only odd. Use for
example Altavista to find Eric's treasure trove.(=CRC Handbook of Math's).
Tapio
Felice Russo <fru...@micron.com> kirjoitti
viestissä:0vg2x4...@forum.swarthmore.edu...
Jim Ferry
11/19/1999, are odd.
Enjoy it while it lasts. It won't happen again for a while.
| Jim Ferry | Center for Simulation |
+------------------------------------+ of Advanced Rockets |
| http://www.uiuc.edu/ph/www/jferry/ +------------------------+
| jferry@[delete_this]uiuc.edu | University of Illinois |
Dann Corbit
news:814ic3$96$1...@vixen.cso.uiuc.edu...
> Speaking of odd numbers, all the digits of today's date,
> 11/19/1999, are odd.
>
> Enjoy it while it lasts. It won't happen again for a while.
More than just odd -- they're all prime!
Richard Carr
:Date: Fri, 19 Nov 1999 14:38:55 -0800
:From: Dann Corbit <dco...@solutionsiq.com>
:Newsgroups: sci.math
:Subject: Prime dates
:
:Jim Ferry <"jferry"@[delete_this]uiuc.edu> wrote in message
:news:814ic3$96$1...@vixen.cso.uiuc.edu...
:> Speaking of odd numbers, all the digits of today's date,
:> 11/19/1999, are odd.
:>
:> Enjoy it while it lasts. It won't happen again for a while.
:
:More than just odd -- they're all prime!
In fact, none of the digits is prime, but 11, 19 and 1999 are prime.
:--
:
:
:
Dann Corbit
do on this workstation. It takes 62.5 megs of ram per billion entries
(roughly) so to get to a trillion would require a machine with 70 gigabytes
of memory or so. It would also take quite a while to complete.
D:\TMP\ioccc\RELEASE>connie 1000000000 1
Searching prime numbers to : 1000000000
50847534 prime numbers found in 250.00 secs.
Finished calculations in 1015.00 secs.
Erick Wong
>Yeah, it is known.
>After rearrangement 2*p=n-q is called de Polignac´s conjecture, where n is
>also a prime as q -too. Note: n is also prime - not only odd. Use for
>example Altavista to find Eric's treasure trove.(=CRC Handbook of Math's).
First of all, "known" would mean that it has been proven, which it hasn't
to my knowledge. Secondly, the question is whether the equation can hold
for any odd n, not any natural p, which would correspond to de Polignac.
Basically, I don't see any connection between the two :).
-- Erick
Erick Wong
>cea...@my-deja.com wrote, in part:
>>I don't believe this has been proven. It is
>>related to Goldbach's ternary conjecture, that
>>any odd #>5 may be expressed as the sum of three
>>primes.
>
>or at least something resembling it.
Vinogradov showed that it was true for sufficiently large n. Under the
Riemann hypothesis, Deshouillers, Effinger, te Riele and Zinoviev (1997)
have established it for all n. The best bound I can find in the absence
of Riemann is 10^7194 by Chen and Wang (1996).
-- Erick
Nico Benschop
>
> On Fri, 19 Nov 1999, Dann Corbit wrote:
>
> :Date: Fri, 19 Nov 1999 14:38:55 -0800
> :From: Dann Corbit <dco...@solutionsiq.com>
> :Newsgroups: sci.math
> :Subject: Prime dates
> :
> :Jim Ferry <"jferry"@[delete_this]uiuc.edu> wrote in message
> :news:814ic3$96$1...@vixen.cso.uiuc.edu...
> :> Speaking of odd numbers, all the digits of today's date,
> :> 11/19/1999, are odd.
> :>
> :> Enjoy it while it lasts. It won't happen again for a while.
> :
> :More than just odd -- they're all prime!
>
> In fact, none of the digits is prime,
Very sharp indeed (funny even, those exact mathematicians;-)
[*] But in what number base representation?
Assumptions galore....
--
Ciao, Nico Benschop. | AHA: One is Always Halfway Anyway
http://www.iae.nl/users/benschop | Institute of Advanced Engineering
Richard Carr
:Date: Sun, 21 Nov 1999 02:45:31 +0800
:From: Dirichlet <anty...@hotmail.com>
:Newsgroups: sci.math
:Subject: Re: Prime dates
:
:And in fact, 19111999 is also prime (this is the way we write dates in my
:part of the world).
Mine too, except we usually have something to separate day, month and
year, viz 19/11/1999.
:
:Richard Carr <ca...@math.columbia.edu> wrote in message
:news:Pine.LNX.4.21.991119...@cpw.math.columbia.edu...
:> On Fri, 19 Nov 1999, Dann Corbit wrote:
:>
:> :Date: Fri, 19 Nov 1999 14:38:55 -0800
:> :From: Dann Corbit <dco...@solutionsiq.com>
:> :Newsgroups: sci.math
:> :Subject: Prime dates
:> :
:> :Jim Ferry <"jferry"@[delete_this]uiuc.edu> wrote in message
:> :news:814ic3$96$1...@vixen.cso.uiuc.edu...
:> :> Speaking of odd numbers, all the digits of today's date,
:> :> 11/19/1999, are odd.
:> :>
:> :> Enjoy it while it lasts. It won't happen again for a while.
:> :
:> :More than just odd -- they're all prime!
:>
:> In fact, none of the digits is prime, but 11, 19 and 1999 are prime.
:>
:> :--
:> :
:> :
:> :
:>
:
:
:
Dirichlet
part of the world).
Richard Carr <ca...@math.columbia.edu> wrote in message
Dirichlet
Dirichlet
Richard Carr <ca...@math.columbia.edu> wrote in message
news:Pine.LNX.4.21.991120...@cpw.math.columbia.edu...
> On Sun, 21 Nov 1999, Dirichlet wrote:
>
> :Date: Sun, 21 Nov 1999 02:45:31 +0800
> :From: Dirichlet <anty...@hotmail.com>
> :Newsgroups: sci.math
> :Subject: Re: Prime dates
> :
> :And in fact, 19111999 is also prime (this is the way we write dates in my
> :part of the world).
>
> Mine too, except we usually have something to separate day, month and
> year, viz 19/11/1999.
>
> :
> :Richard Carr <ca...@math.columbia.edu> wrote in message
> :> :
> :> :
> :>
> :
> :
> :
>
Richard Carr
Yeah, it was implied- just messing around, although we do write dates that
way too.