prime sums 
Author Message
 prime sums

The sum of two prime numbers equals an even integer. an ex is 3+97=100 and
this is true for all even numbers greater than 2. So how do I go about
writing a program that will do this for a range of numbers that can be
changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.

------------------  Posted via CNET Help.com  ------------------
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Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums

Quote:

> The sum of two prime numbers equals an even integer. an ex is
> 3+97=100 and this is true for all even numbers greater than 2.
> So how do I go about writing a program that will do this for a
> range of numbers that can be changed. ie 700=23+677 ....to
> 1100=1+1069.Any help would be very welcome.

To begin with, you need to get your prime numbers straight.
One is not prime; two, OTOH, is, and 2+3 is not even.
However, every two _odd_ primes add up to an even integer;
and all even number greater than two are conjectured to be
the sum of two primes; for 4, you'll need 2+2, for all others,
you'll have to use odd primes. I don't know if this conjecture
has been proven or not, BTW.
All that said, this is not really a C question; more an algorithm
one. Show your C problem and people might be willing to help.

Richard
--



Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums

comp.lang.c:

Quote:
> The sum of two prime numbers equals an even integer. an ex is 3+97=100 and
> this is true for all even numbers greater than 2. So how do I go about
> writing a program that will do this for a range of numbers that can be
> changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.

See http://home.att.net/~jackklein/ctips01.html#homework for the help
you need.

Can you prove this is true for all even numbers greater than 2?

Jack Klein
--
Home: http://jackklein.home.att.net
--



Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums
I'm new to this group as well, and I have found that I get much, much
better answers if I post code that attempts to solve the problem first.

Neil


Quote:
> The sum of two prime numbers equals an even integer. an ex is 3+97=100 and
> this is true for all even numbers greater than 2. So how do I go about
> writing a program that will do this for a range of numbers that can be
> changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.
> ------------------  Posted via CNET Help.com  ------------------
>                       http://www.help.com/

--



Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums

Quote:

> The sum of two prime numbers equals an even integer.

Disproof:

1) Assume p is a prime of the sort 2n+1, n a positive integer, so p is
odd.
2) 2 is a prime.
3) p+2 = 2n+1+2 = 2(n+1) + 1, an odd number .
4) Since there are an infinite number of odd primes, there are infinite
number of odd numbers that can be expressed as the sum of two prime
numbers.

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Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums

Quote:
> The sum of two prime numbers equals an even integer. an ex is 3+97=100 and
> this is true for all even numbers greater than 2. So how do I go about
> writing a program that will do this for a range of numbers that can be
> changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.

Something like:

void Getprimesum(int,int *,int *);

int main(int argc, char **argv) {
  int i,from,to;
  int * a;
  int * b;
  if (argc == 3 && ((to = atoi(argv[2])) > (from = atoi(argv[1]))) {
    for(i = from;i<=to;i+=2) {
      Getprimesum(i,a,b);
/* get this function from comp.programming c.l.c is about the C language
and not about designing algorithms*/
    printf("%i=%i+%i",i,*a,*b)
  } else {
    printf("Use: %s fromnumber tonumber\n",argv[0]);
  }
  return 0;

Quote:
}

I havent tested this code... if you got any problems post your faulty
code to the group and we can examine it :P
--



Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums
IIRC, this is Goldbach's conjecture. Basically:

1. Create a list of all primes smaller than your upper limit.
2. For each prime smaller than or equal to 1/2 of the number being tested,
subtract the prime from the number and see if the result is in the list of
primes greater than or equal to 1/2 the number being tested (but smaller
than the tested number).

Note that even if all even numbers in your test range can be expressed as
the sum of two primes - this does not _prove_ the conjecture. You have to
provide a proof valid for _all_ even numbers, no matter how large.

--
Daniel Pfeffer
--------------
Remove 'nospam' from my address in order to contact me directly


Quote:
> The sum of two prime numbers equals an even integer. an ex is 3+97=100 and
> this is true for all even numbers greater than 2. So how do I go about
> writing a program that will do this for a range of numbers that can be
> changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.

> ------------------  Posted via CNET Help.com  ------------------
>                       http://www.help.com/
> --


--



Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums

: The sum of two prime numbers equals an even integer. an ex is 3+97=100 and

This is true for two prime numbers if neither or both of them is 2.

: this is true for all even numbers greater than 2. So how do I go about

It does not follow from "sum of two odd primes is an even number" that
"all even numbers can be expressed as the sum of to (odd) primes"; the
latter is (as of yet, unproved) conjecture called the (strong) Goldbach
conjecture. It has, however, been proven for even numbers up to 4x10^11,
which may be enough for your purposes. For more info, see the following
URL:
http://www.treasure-troves.com/math/GoldbachConjecture.html

: writing a program that will do this for a range of numbers that can be
: changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.

One solution would be to build a list of primes up to the higher limit;
the sieve of Erastothenes is quite straight-forward to implement and easy
to understand. Start by assuming all numbers are primes and start removing
composites.  When you are done, only primes remain.  This being
comp.lang.c, I give all the bughunters this:

#define MAXNUM 32766
char is_prime[MAXNUM + 1];
int i, j;

/* Start by assuming all numbers are prime unless proven composite */
for(i = 0; i < MAXNUM; i++) {
        is_prime[i] = 1;

Quote:
}

for(i = 2; i < MAXNUM; i++) {
        /*
         * Remove multiples of all numbers from list of primes
         * Be careful that i*j fits in the array!
         */
        for(j = 2; j <= MAXNUM / i; j++) {
                is_prime[i * j] = 0;
        }

Quote:
}

Now is_prime[i] is 1 if and only if i is a prime.  Now, to find out the
two primes the sum of which is n:

for all primes p:
        check if q = (n-p) is also a prime;
                is so, n = p + q
                if not, check next prime p

For a real program, dynamically allocate the is_prime array; you might
also want to consider using a bit vector rather than char array for
is_prime. Also, more sophisticated prime-checking methods are available.

--
Lasse Haataja
--



Sun, 31 Mar 2002 03:00:00 GMT  
 prime sums

Quote:
> The sum of two prime numbers equals an even integer. an ex is 3+97=100 and
> this is true for all even numbers greater than 2. So how do I go about
> writing a program that will do this for a range of numbers that can be
> changed. ie 700=23+677 ....to 1100=1+1069.Any help would be very welcome.

Happy to oblige.  Now all you have to do is explain to your prof. how it
works.

#define bitget(buf,bit)(((buf[(bit)>>3]>>((bit)&7))&1))
typedef unsigned char uc;typedef unsigned short us;static uc d[]={111,
203,180,100,154,18,109,129,50,76,74,134,13,130,150,33,201,52,4,90,32,97,
137,164,68,17,134,41,209,130,40,74,48,64,66,50,33,153,52,8,75,6,37,66,
132,72,138,20,5,66,48,108,8,180,64,11,160,8,81,18,40,137,4,101,152,48,76
,128,150,68,18,128,33,66,18,65,201,4,33,192,50,45,152,0,0,73,4,8,129,150
,104,130,176,37,8,34,72,137,162,64,89,38,4,144,6,64,67,48,68,146,0,105,
16,130,8,8,164,13,65,18,96,192,0,36,210,34,97,8,132,4,27,130,1,211,16,1,
2,160,68,192,34,96,145,20,12,64,166,4,210,148,32,9,148,32,82,0,8,16,162,
76,0,130,1,81,16,8,139,164,37,154,48,68,129,16,76,3,2,37,82,128,8,73,132
,32,80,50,0,24,162,64,17,36,40,1,132,1,1,160,65,10,18,69,0,54,8,0,38,41,
131,130,97,192,128,4,16,16,109,0,34,72,88,38,12,194,16,72,137,36,32,88,
32,69,136,36,0,25,2,37,192,16,104,8,20,1,202,50,40,128,0,4,75,38,0,19,
144,96,130,128,37,208,0,1,16,50,12,67,134,33,17,0,8,67,36,4,72,16,12,144
,146,0,67,32,45,0,6,9,136,36,64,192,50,9,9,130,0,83,128,8,128,150,65,129
,0,64,72,16,72,8,150,72,88,32,41,195,128,32,2,148,96,146,0,32,129,34,68,
16,160,5,64,144,1,73,32,4,10,0,36,137,52,72,19,128,44,192,130,41,0,36,69
,8,0,8,152,54,4,82,132,4,208,4,0,138,144,68,130,50,101,24,144,0,10,2,1,
64,2,40,64,164,4,146,48,4,17,134,8,66,0,44,82,4,8,201,132,96,72,18,9,153
,36,68,0,36,0,3,20,33,0,16,1,26,50,5,136,32,64,64,6,9,195,132,64,1,48,96
,24,2,104,17,144,12,2,162,4,0,134,41,137,20,36,130,2,65,8,128,4,25,128,8
,16,18,104,66,164,4,0,2,97,16,6,12,16,0,1,18,16,32,3,148,33,66,18,101,24
,148,12,10,4,40,1,20,41,10,164,64,208,0,64,1,144,4,65,32,45,64,130,72,
193,32,0,16,48,1,8,36,4,89,132,36,0,2,41,130,0,97,88,2,72,129,22,72,16,0
,33,17,6,0,202,160,64,2,0,4,145,176,0,66,4,12,129,6,9,72,20,37,146,32,37
,17,160,0,10,134,12,193,2,72,0,32,69,8,50,0,152,6,4,19,34,0,130,4,72,129
,20,68,130,18,36,24,16,64,67,128,40,208,4,32,129,36,100,216,0,44,9,18,8,
65,162,0,0,2,65,202,32,65,192,16,1,24,164,4,24,164,32,18,148,32,131,160,
64,2,50,68,128,4,0,24,0,12,64,134,96,138,0,100,136,18,5,1,130,0,74,162,1
,193,16,97,9,4,1,136,0,96,1,180,64,8,6,1,3,128,8,64,148,4,138,32,41,128,
2,12,82,2,1,66,132,0,128,132,100,2,50,72,0,48,68,64,34,33,0,2,8,195,160,
4,208,32,64,24,22,64,64,0,40,82,144,8,130,20,1,24,16,8,9,130,64,10,160,
32,147,128,8,192,0,32,82,0,5,1,16,64,17,6,12,130,0,0,75,144,68,154,0,40,
128,144,4,74,6,9,67,2,40,0,52,1,24,0,101,9,128,68,3,0,36,2,130,97,72,20,
65,0,18,40,0,52,8,81,4,5,18,144,40,137,132,96,18,16,73,16,38,64,73,130,0
,145,16,1,10,36,64,136,16,76,16,4,0,80,162,44,64,144,72,10,176,1,80,18,8
,0,164,4,9,160,40,146,2,0,67,16,33,2,32,65,129,50,0,8,4,12,82,0,33,73,
132,32,16,2,1,129,16,72,64,34,1,1,132,105,193,48,1,200,2,68,136,0,12,1,2
,45,192,18,97,0,160,0,192,48,64,1,18,8,11,32,0,128,148,64,1,132,64,0,50,
0,16,132,0,11,36,0,1,6,41,138,132,65,128,16,8,8,148,76,3,128,1,64,150,64
,65,32,32,80,34,37,137,162,64,64,164,32,2,134,40,1,32,33,74,16,8,0,20,8,
64,4,37,66,2,33,67,16,4,146,0,33,17,160,76,24,34,9,3,132,65,137,16,4,130
,34,36,1,20,8,8,132,8,193,0,9,66,176,65,138,2,0,128,54,4,73,160,36,145,0
,0,2,148,65,146,2,1,8,6,8,9,0,1,208,22,40,137,128,96,0,0,104,1,144,12,80
,32,1,64,128,64,66,48,65,0,32,37,129,6,64,73,0,8,1,18,73,0,160,32,24,48,
5,1,166,0,16,36,40,0,2,32,200,32,0,136,18,12,144,146,0,2,38,1,66,22,73,0
,4,36,66,2,1,136,128,12,26,128,8,16,0,96,2,148,68,136,0,105,17,48,8,18,
160,36,19,132,0,130,0,101,192,16,40,0,48,4,3,32,1,17,6,1,200,128,0,194,
32,8,16,130,12,19,2,12,82,6,64,0,176,97,64,16,1,152,134,4,16,132,8,146,
20,96,65,128,65,26,16,4,129,34,64,65,32,41,82,0,65,8,52,96,16,0,40,1,16,
64,0,132,8,66,144,32,72,4,4,82,2,0,8,32,4,0,130,13,0,130,64,2,16,5,72,32
,64,153,0,0,1,6,36,192,0,104,130,4,33,18,16,68,8,4,0,64,166,32,208,22,9,
201,36,65,2,32,12,9,146,64,18,0,0,64,0,9,67,132,32,152,2,1,17,36,0,67,36
,0,3,144,8,65,48,36,88,32,76,128,130,8,16,36,37,129,6,65,9,16,32,24,16,
68,128,16,0,74,36,13,1,148,40,128,48,0,192,2,96,16,132,12,2,0,9,2,130,1,
8,16,4,194,32,104,9,6,4,24,0,0,17,144,8,11,16,33,130,2,12,16,182,8,0,38,
0,65,2,1,74,36,33,26,32,36,128,0,68,2,0,45,64,2,0,139,148,32,16,0,32,144
,166,64,19,0,44,17,134,97,1,128,65,16,2,4,129,48,72,72,32,40,80,128,33,
138,16,4,8,16,9,16,16,72,66,160,12,130,146,96,192,32,5,210,32,64,1,0,4,8
,130,45,130,2,0,72,128,65,72,16,0,145,4,4,3,132,0,194,4,104,0,0,100,192,
34,64,8,50,68,9,134,0,145,2,40,1,0,100,72,0,36,16,144,0,67,0,33,82,134,
65,139,144,32,64,32,8,136,4,68,19,32,0,2,132,96,129,144,36,64,48,0,8,16,
8,8,2,1,16,4,32,67,180,64,144,18,104,1,128,76,24,0,8,192,18,73,64,16,36,
26,0,65,137,36,76,16,0,4,82,16,9,74,32,65,72,34,105,17,20,8,16,6,36,128,
132,40,0,16,0,64,16,1,8,38,8,72,6,40,0,20,1,66,132,4,10,32,0,1,130,8,0,
130,36,18,4,64,64,160,64,144,16,4,144,34,64,16,32,44,128,16,40,67,0,4,88
,0,1,129,16,72,9,32,33,131,4,0,66,164,68,0,0,108,16,160,68,72,128,0,131,
128,72,201,0,0,0,2,5,16,176,4,19,4,41,16,146,64,8,4,68,130,34,0,25,32,0,
25,32,1,129,144,96,138,0,65,192,2,69,16,4,0,2,162,9,64,16,33,73,32,1,66,
48,44,0,20,68,1,34,4,2,146,8,137,4,33,128,16,5,1,32,64,65,128,4,0,18,9,
64,176,100,88,50,1,8,144,0,65,4,9,193,128,97,8,144,0,154,0,36,1,18,8,2,
38,5,130,6,8,8,0,32,72,32,0,24,36,72,3,2,0,17,0,9,0,132,1,74,16,1,152,0,
4,24,134,0,192,0,32,129,128,4,16,48,5,0,180,12,74,130,41,145,2,40,0,32,
68,192,0,44,145,128,64,1,162,0,18,4,9,195,32,0,8,2,12,16,34,4,0,0,44,17,
134,0,192,0,0,18,50,64,137,128,64,64,2,5,80,134,96,130,164,96,10,18,77,
128,144,8,18,128,9,2,20,72,1,36,32,138,0,68,144,4,4,1,2,0,209,18,0,10,4,
64,0,50,33,129,36,8,25,132,32,2,4,8,137,128,36,2,2,104,24,130,68,66,0,33
,64,0,40,1,128,69,130,32,64,17,128,12,2,0,36,64,144,1,64,32,32,80,32,40,
25,0,64,9,32,8,128,4,96,64,128,32,8,48,73,9,52,0,17,36,36,130,0,65,194,0
,4,146,2,36,128,0,12,2,160,0,1,6,96,65,4,33,208,0,1,1,0,72,18,132,4,145,
18,8,0,36,68,0,18,65,24,38,12,65,128,0,82,4,32,9,0,36,144,32,72,24,2,0,3
,162,9,208,20,0,138,132,37,74,0,32,152,20,64,0,162,5,0,0,0,64,20,1,88,32
,44,128,132,0,9,32,32,145,2,8,2,176,65,8,48,0,9,16,0,24,2,33,2,2,0,0,36,
68,8,18,96,0,178,68,18,2,12,192,128,64,200,32,4,80,32,5,0,176,4,11,4,41,
83,0,97,72,48,0,130,32,41,0,22,0,83,34,32,67,16,72,0,128,4,210,0,64,0,
162,68,3,128,41,0,4,8,192,4,100,64,48,40,9,132,68,80,128,33,2,146,0,192,
16,96,136,34,8,128,0,0,24,132,4,131,150,0,129,32,5,2,0,69,136,132,0,81,
32,32,81,134,65,75,148,0,128,0,8,17,32,76,88,128,4,3,6,32,137,0,5,8,34,5
,144,0,64,0,130,9,80,0,0,0,160,65,194,32,8,0,22,8,64,38,33,208,144,8,129
,144,65,0,2,68,8,16,12,10,134,9,144,4,0,200,160,4,8,48,32,137,132,0,17,
34,44,64,0,8,2,176,1,72,2,1,9,32,4,3,4,0,128,2,96,66,48,33,74,16,68,9,2,
0,1,36,0,18,130,33,128,164,32,16,2,4,145,160,64,24,4,0,2,6,105,9,0,5,88,
2,1,0,0,72,0,0,0,3,146,32,0,52,1,200,32,72,8,48,8,66,128,32,145,144,104,
1,4,64,18,2,97,0,18,8,1,160,0,17,4,33,72,4,36,146,0,12,1,132,4,0,0,1,18,
150,64,1,160,65,136,34,40,136,0,68,66,128,36,18,20,1,66,144,96,26,16,4,
129,16,72,8,6,41,131,2,64,2,36,100,128,16,5,128,16,64,2,2,8,66,132,1,9,
32,4,80,0,96,17,48,64,19,2,4,129,0,9,8,32,69,74,16,97,144,38,12,8,2,33,
145,0,96,2,4,0,2,0,12,8,6,8,72,132,8,17,2,0,128,164,0,90,32,0,136,4,4,2,
0,9,0,20,8,73,20,32,200,0,4,145,160,64,89,128,0,18,16,0,128,128,101,0,0,
4,0,128,64,25,0,33,3,132,96,192,4,36,26,18,97,128,128,8,2,4,9,66,18,32,8
,52,4,144,32,1,1,160,0,11,0,8,145,146,64,2,52,64,136,16,97,25,2,0,64,4,
37,192,128,104,8,4,33,128,34,4,0,160,12,1,132,32,65,0,8,138,0,32,138,0,
72,136,4,4,17,130,8,64,134,9,73,164,64,0,16,1,1,162,4,80,128,12,128,0,72
,130,160,1,24,18,65,1,4,72,65,0,36,1,0,0,136,20,0,2,0,104,1,32,8,74,34,8
,131,128,0,137,4,1,194,0,0,0,52,4,0,130,40,2,2,65,74,144,5,130,2,9,128,
36,4,65,0,1,146,128,40,1,20,0,80,32,76,16,176,4,67,164,33,144,4,1,2,0,68
,72,0,100,8,6,0,66,32,8,2,146,1,74,0,32,80,50,37,144,34,4,9,0,8,17,128,
33,1,16,5,0,50,8,136,148,8,8,36,13,193,128,64,11,32,64,24,18,4,0,34,64,
16,38,5,193,130,0,1,48,36,2,34,65,8,36,72,26,0,37,210,18,40,66,0,4,64,48
,65,0,2,0,19,32,36,209,132,8,137,128,4,82,0,68,24,164,0,0,6,32,145,16,9,
66,32,36,64,48,40,0,132,64,64,128,8,16,4,9,8,4,64,8,34,0,25,2,0,0,128,44
,2,2,33,1,144,32,64,0,12,0,52,72,88,32,1,67,4,32,128,20,0,144,0,109,17,0
,0,64,32,0,3,16,64,136,48,5,74,0,101,16,36,8,24,132,40,3,128,32,66,176,
64,0,16,105,25,4,0,0,128,4,194,4,0,1,0,5,0,34,37,8,150,4,2,34,0,208,16,
41,1,160,96,8,16,4,1,22,68,16,2,40,2,130,72,64,132,32,144,34,40,128,4,0,
64,4,36,0,128,41,3,16,96,72,0,0,129,160,0,81,32,12,209,0,1,65,32,4,146,0
,0,16,146,0,66,4,5,1,134,64,128,16,32,82,32,33,0,16,72,10,2,0,208,18,65,
72,128,4,0,0,72,9,34,4,0,36,0,67,16,96,10,0,68,18,32,44,8,32,68,0,132,9,
64,6,8,193,0,64,128,32,0,152,18,72,16,162,32,0,132,72,192,16,32,144,18,8
,152,130,0,10,160,4,3,0,40,195,0,68,66,16,4,8,4,64,0,0,5,16,0,33,3,128,4
,136,18,105,16,0,4,8,4,4,2,132,72,73,4,32,24,2,100,128,48,8,1,2,0,82,18,
73,8,32,65,136,16,72,8,52,0,1,134,5,208,0,0,131,132,33,64,2,65,16,128,72
,64,162,32,81,0,0,73,0,1,144,32,64,24,2,64,2,34,5,64,128,8,130,16,32,24,
0,5,1,130,64,88,0,4,129,144,41,1,160,100,0,34,64,1,162,0,24,4,13,0,0,96,
128,148,96,130,16,13,128,48,12,18,32,0,0,18,64,192,32,33,88,2,65,16,128,
68,3,2,4,19,144,41,8,0,68,192,0,33,0,38,0,26,128,1,19,20,32,10,20,32,0,
50,97,8,0,64,66,32,9,128,6,1,129,128,96,66,0,104,144,130,8,66,128,4,2,
128,9,11,4,0,152,0,12,129,6,68,72,132,40,3,146,0,1,128,64,10,0,12,129,2,
8,81,4,40,144,2,32,9,16,96,0,0,9,129,160,12,0,164,9,0,2,40,128,32,0,2,2,
4,129,20,4,0,4,9,17,18,96,64,32,1,72,48,64,17,0,8,10,134,0,0,4,96,129,4,
1,208,2,65,24,144,0,10,32,0,193,6,1,8,128,100,202,16,4,153,128,72,1,130, ...

read more »



Mon, 01 Apr 2002 03:00:00 GMT  
 prime sums

True, but the goldbach conjecture says that for every even integer number
greater than 2 and not all 2n+1 numbers are prime numbers.....

On Wed, 13 Oct 1999, Martin Ambuhl wrote

Quote:


> > The sum of two prime numbers equals an even integer.

> Disproof:

> 1) Assume p is a prime of the sort 2n+1, n a positive integer, so p is
> odd.
> 2) 2 is a prime.
> 3) p+2 = 2n+1+2 = 2(n+1) + 1, an odd number .
> 4) Since there are an infinite number of odd primes, there are infinite
> number of odd numbers that can be expressed as the sum of two prime
> numbers.

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Mon, 01 Apr 2002 03:00:00 GMT  
 prime sums


Quote:
>True, but the goldbach conjecture says that for every even integer number
>greater than 2 and not all 2n+1 numbers are prime numbers.....
>> > The sum of two prime numbers equals an even integer.

These statements are unrelated; the one with 3 >'s is false.  :)

-s
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Mon, 01 Apr 2002 03:00:00 GMT  
 
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