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  #1  
Old 14th March 2017, 06:13 AM
hiGuys Offline
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Programming Challenge - list prime numbers

Haven't seen one of these programming challenges in a while, so I thought I'd throw one out. Nothing esoteric, just list the prime numbers up to a(n) (arbitrary) point.

Here is one way to do it in python:

Code:
p = [2,3]
x = 5
counter = 1
k=[]
while counter < 10000:
    for i in p:
        y = x%i
        k.append(y)
    if 0 not in k:
        p.append(x)
    k = []
    x += 2
    counter += 1
print(p)
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  #2  
Old 14th March 2017, 09:47 AM
bobx001 Offline
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Re: Programming Challenge - list prime numbers

Just shot this in 10 mins, the first 3 give me zero calcs, due to the bitshifting I use to divide vy 2, which is to granular initially.

Code:
#include        <stdio.h>

int     main(int argc,char *argv[])
{
        register int    i=3, c, d, limit, modulo;
        long int     calculations,total_calculations=0;  /* EDITted to be long int */
        limit=abs(atoi(argv[1]));

        printf("Calculating primes up to: %lu\n",limit);
        for (i=3; i< limit; i+=2)
        {
                d=i>>2;
                modulo=1;
                calculations=0;
                for (c=2;(c<=d) && (modulo > 0);c++)
                {
                        modulo=i%c;
                        calculations++;
                        total_calculations++;
                }
                if (modulo)
                {
                        printf("%lu is prime : calculations: %lu -- total calcs: %lu\n", i,calculations,total_calculations);
                }
        }
}
after some high number runs, I changed the int declaration, to long int, then the total works.

Code:
time ./primes 1000000 > log

real    0m39.440s
user    0m39.275s
sys     0m0.025s

999983 is prime : calculations: 249994 -- total calcs: 9404063385
so, to get all first 1,000,000 prime numbers, it took my proggy 9404063385 iterations. (9.4 billion)

http://www.servermasters.com/stuff/log.txt.gz

will make some changes to avoid the 5's hehe, forgot about them.

of course this is for single-core running. I will make one for a 4-core cpu, where we just do the 1's 3's 7's and 9's in parallel. hehe, fun fun

Code:
on an old AMD 5300 CPU running the single-core proggy:

time ./primes 10000000 > 10mill.log.txt

real    56m16.989s
user    55m49.171s
sys     0m2.156s

tail -1 10mill.log.txt
9999991 is prime : calculations: 2499996 -- total calcs: 801205883487
[bobx@nova test]$ wc -l 10mill.log.txt
664580 10mill.log.txt
Here is a revised version, quicker too, since I figured out all dividers of odd numbers are always odd.
Code:
#include        <stdio.h>

int     main(int argc,char *argv[])
{
        register int    i=3, c, d, limit, modulo,divider_found;
        long int        primes_found=0,calculations,total_calculations=0;
        limit=abs(atoi(argv[1]));

        printf("Calculating primes up to: %lu\n",limit);
        for (i=3; i< limit; i+=2)
        {
                d=i>>2;
                modulo=1;
                calculations=0;
                for (c=3;(c<=d) && (modulo > 0);c+=2)
                {
                        modulo=i%c;
                        divider_found=c;
                        calculations++;
                        total_calculations++;
                }
                if (modulo)
                {
                        primes_found++;
                        printf("%lu is prime : calculations: %lu -- total calcs: %lu -- primes found: %lu\n", i,calculations,total_calculations,primes_found);
                }
                else
                {
                        printf("Divider found for: %lu --> %lu\n", i, divider_found);
                }
        }
}
Code:
time ./primes 1000000 > 1million_v3.log.txt

real    0m20.020s
user    0m19.862s
sys     0m0.043s
[bobx@nova test]$ tail -20 1million_v3.log.txt
999961 is prime : calculations: 124994 -- total calcs: 4701762062 -- primes found: 78496
Divider found for: 999963 --> 3
Divider found for: 999965 --> 5
Divider found for: 999967 --> 31
Divider found for: 999969 --> 3
Divider found for: 999971 --> 7
Divider found for: 999973 --> 13
Divider found for: 999975 --> 3
Divider found for: 999977 --> 11
999979 is prime : calculations: 124996 -- total calcs: 4701887092 -- primes found: 78497
Divider found for: 999981 --> 3
999983 is prime : calculations: 124997 -- total calcs: 4702012090 -- primes found: 78498
Divider found for: 999985 --> 5
Divider found for: 999987 --> 3
Divider found for: 999989 --> 19
Divider found for: 999991 --> 17
Divider found for: 999993 --> 3
Divider found for: 999995 --> 5
Divider found for: 999997 --> 757
Divider found for: 999999 --> 3
So, half the number of iterations as before, including much bigger log, but about 1/2 of the CPU time.


Interestingly:
grep Divider 1million_v3.log.txt | cut -f6 -d' ' | sort -rn | more
997
991
.
.
.
The max divider found for up to 1,000,000 is almost exactly 1000 times smaller. That's gotta be of significance, and I will see if I put some contraints on the divider search loop, and test/compare it up to waz00 numbers, to see if it works.

Last edited by bobx001; 14th March 2017 at 12:16 PM.
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  #3  
Old 16th March 2017, 04:52 AM
RupertPupkin Offline
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Re: Programming Challenge - list prime numbers

One-liner using Octave to list the first 10,000 primes:
Code:
$ octave --eval 'printf("%d ", list_primes(10000))'
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  #4  
Old 16th March 2017, 07:18 AM
hiGuys Offline
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Re: Programming Challenge - list prime numbers

Quote:
Originally Posted by RupertPupkin View Post
One-liner using Octave to list the first 10,000 primes:
Code:
$ octave --eval 'printf("%d ", list_primes(10000))'
Very impressive. I was going to install this mysterious Octave, but, at least on the machine I am currently in front of, it looks like a 237 MB installation with the necessary dependencies yet to be installed. Maybe in future...
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Last edited by hiGuys; 16th March 2017 at 07:26 AM. Reason: clarification
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  #5  
Old 16th March 2017, 07:25 AM
hiGuys Offline
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linuxubuntufirefox
Re: Programming Challenge - list prime numbers

Quote:
Originally Posted by bobx001 View Post
Code:
time ./primes 1000000 > 1million_v3.log.txt

real    0m20.020s
user    0m19.862s
sys     0m0.043s
[bobx@nova test]$ tail -20 1million_v3.log.txt
999961 is prime : calculations: 124994 -- total calcs: 4701762062 -- primes found: 78496
Divider found for: 999963 --> 3
Divider found for: 999965 --> 5
Divider found for: 999967 --> 31
Divider found for: 999969 --> 3
Divider found for: 999971 --> 7
Divider found for: 999973 --> 13
Divider found for: 999975 --> 3
Divider found for: 999977 --> 11
999979 is prime : calculations: 124996 -- total calcs: 4701887092 -- primes found: 78497
Divider found for: 999981 --> 3
999983 is prime : calculations: 124997 -- total calcs: 4702012090 -- primes found: 78498
Divider found for: 999985 --> 5
Divider found for: 999987 --> 3
Divider found for: 999989 --> 19
Divider found for: 999991 --> 17
Divider found for: 999993 --> 3
Divider found for: 999995 --> 5
Divider found for: 999997 --> 757
Divider found for: 999999 --> 3
So, half the number of iterations as before, including much bigger log, but about 1/2 of the CPU time.


Interestingly:
grep Divider 1million_v3.log.txt | cut -f6 -d' ' | sort -rn | more
997
991
.
.
.
The max divider found for up to 1,000,000 is almost exactly 1000 times smaller. That's gotta be of significance, and I will see if I put some contraints on the divider search loop, and test/compare it up to waz00 numbers, to see if it works.
I like showing the divisors. That could be useful depending what one wanted to do with primes.
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  #6  
Old 16th March 2017, 01:19 PM
ocratato Online
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linuxfirefox
Re: Programming Challenge - list prime numbers

Hmmm, a one line call to a function called list_primes is hardly in the spirit of a programming challenge thread.

As for a solution involving division operators when the ancient Greeks had a much more efficient solution .
Might I suggest doing just a smidgin of research before launching into writing code.

Solutions to this problem get much more interesting when you try to make the best use of the available cores and keep as much as possible in the local cache.
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  #7  
Old 16th March 2017, 04:10 PM
hiGuys Offline
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Re: Programming Challenge - list prime numbers

It's interesting you mention research first, because part of my thinking in this was to independently come up with a solution without reference to pre-existing knowledge of the solutions. Yes, there is a huge database of research into primes, but my personal interest was in creating home brew solutions, not discovering or optimizing the solution to millennia of thinking on a chat forum. But since you mention the Greeks, I look forward to seeing what they had to say on the matter.
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  #8  
Old 16th March 2017, 05:38 PM
bobx001 Offline
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Re: Programming Challenge - list prime numbers

I just like to walk the walk, and come up with my own conclusions. It's the fun of programming that keeps me alive. Besides number theorems and their logic implementations are more expensive programatically than simple iteration most of the times.
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Old 16th March 2017, 07:05 PM
lsatenstein Online
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Re: Programming Challenge - list prime numbers

Is there still a better method? I was thinking of looking at the prime factors of the integer immediately bow the prime and start by manipulating those integers by adding one to each, one at a time. I think we know enough info to avoid unnecessary recalcs
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  #10  
Old 16th March 2017, 11:11 PM
ocratato Online
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Re: Programming Challenge - list prime numbers

Quote:
Originally Posted by bobx001 View Post
I just like to walk the walk, and come up with my own conclusions. It's the fun of programming that keeps me alive. Besides number theorems and their logic implementations are more expensive programatically than simple iteration most of the times.
You are quite right about keeping it simple. There are some improved variations on the "Sieve of Eratosthenes" but they don't overtake the basic form until you start to get into very large numbers.

The SoE algorithm starts with a bitmap of all the numbers in the desired range and then, using just addition, flags all the multiples of each prime number. An obvious speed-up is to skip the even numbers.

Advanced versions subdivide the bitmap into cache sized chunks to avoid slow external memory addressing, and spread the work over all available cores. (These are in addition to the improved algorithms, mentioned above.)
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  #11  
Old 17th March 2017, 12:06 AM
RupertPupkin Offline
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Re: Programming Challenge - list prime numbers

Quote:
Originally Posted by hiGuys View Post
I was going to install this mysterious Octave, but, ...
I think Octave is definitely worth installing. It's basically a free Matlab clone. But there are alternatives with smaller footprints.

IDL is one such alternative. Here's an IDL one-liner to list the first 10,000 primes (using GDL, a free GNU implementation of IDL, which is in the Fedora repos: dnf install gdl):
Code:
$ gdl -q -e 'print, primes(10000)'
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  #12  
Old 17th March 2017, 01:18 AM
RupertPupkin Offline
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Re: Programming Challenge - list prime numbers

Here's a way in Java to get the first N > 1 primes:
Code:
public class getPrimes {
   public static void main(String[] args) {
      int N = Integer.parseInt(args[0]), p = 3, counter = 1;
      System.out.print("2");
      while (counter < N) {
         if (isPrime(p)) {
            System.out.print(", " + p);
            counter++;
         }
         p += 2;
      }
      System.out.println("");
   }

   private static boolean isPrime(int odd) {
      boolean result = true;
      if (odd > 3) {
         if (odd%3 == 0) {
            result = false;
         } else {
            for (int i = 5; i*i <= odd; i += 6) {
               if (odd%i == 0 || odd%(i+2) == 0) {
                  result = false;
                  break;
               }
            }
         }
      }
      return result;
   }
}
Compile and run:
Code:
$ javac getPrimes.java

$ java getPrimes 10
2, 3, 5, 7, 11, 13, 17, 19, 23, 29

$ java getPrimes 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349,
 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541
Takes just under 5 seconds to get the first 1 million primes, and just over 2 minutes to get the first 10 million primes:
Code:
$ time java getPrimes 1000000 > primes.log

real    0m4.912s
user    0m4.141s
sys     0m0.859s

$ time java getPrimes 10000000 > primes.log

real    2m8.225s
user    1m57.553s
sys     0m8.833s
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  #13  
Old 17th March 2017, 02:37 AM
lsatenstein Online
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Re: Programming Challenge - list prime numbers

Quote:
Originally Posted by bobx001 View Post
Just shot this in 10 mins, the first 3 give me zero calcs, due to the bitshifting I use to divide vy 2, which is to granular initially.

Code:
#include        <stdio.h>

int     main(int argc,char *argv[])
{
        register int    i=3, c, d, limit, modulo;
        long int     calculations,total_calculations=0;  /* EDITted to be long int */
        limit=abs(atoi(argv[1]));

        printf("Calculating primes up to: %lu\n",limit);
        for (i=3; i< limit; i+=2)
        {
                d=i>>2;
                modulo=1;
                calculations=0;
                for (c=2;(c<=d) && (modulo > 0);c++)
                {
                        modulo=i%c;
                        calculations++;
                        total_calculations++;
                }
                if (modulo)
                {
                        printf("%lu is prime : calculations: %lu -- total calcs: %lu\n", i,calculations,total_calculations);
                }
        }
}
after some high number runs, I changed the int declaration, to long int, then the total works.

Code:
time ./primes 1000000 > log

real    0m39.440s
user    0m39.275s
sys     0m0.025s

999983 is prime : calculations: 249994 -- total calcs: 9404063385
so, to get all first 1,000,000 prime numbers, it took my proggy 9404063385 iterations. (9.4 billion)

http://www.servermasters.com/stuff/log.txt.gz

will make some changes to avoid the 5's hehe, forgot about them.

of course this is for single-core running. I will make one for a 4-core cpu, where we just do the 1's 3's 7's and 9's in parallel. hehe, fun fun

Code:
on an old AMD 5300 CPU running the single-core proggy:

time ./primes 10000000 > 10mill.log.txt

real    56m16.989s
user    55m49.171s
sys     0m2.156s

tail -1 10mill.log.txt
9999991 is prime : calculations: 2499996 -- total calcs: 801205883487
[bobx@nova test]$ wc -l 10mill.log.txt
664580 10mill.log.txt
Here is a revised version, quicker too, since I figured out all dividers of odd numbers are always odd.
Code:
#include        <stdio.h>

int     main(int argc,char *argv[])
{
        register int    i=3, c, d, limit, modulo,divider_found;
        long int        primes_found=0,calculations,total_calculations=0;
        limit=abs(atoi(argv[1]));

        printf("Calculating primes up to: %lu\n",limit);
        for (i=3; i< limit; i+=2)
        {
                d=i>>2;
                modulo=1;
                calculations=0;
                for (c=3;(c<=d) && (modulo > 0);c+=2)
                {
                        modulo=i%c;
                        divider_found=c;
                        calculations++;
                        total_calculations++;
                }
                if (modulo)
                {
                        primes_found++;
                        printf("%lu is prime : calculations: %lu -- total calcs: %lu -- primes found: %lu\n", i,calculations,total_calculations,primes_found);
                }
                else
                {
                        printf("Divider found for: %lu --> %lu\n", i, divider_found);
                }
        }
}
Code:
time ./primes 1000000 > 1million_v3.log.txt

real    0m20.020s
user    0m19.862s
sys     0m0.043s
[bobx@nova test]$ tail -20 1million_v3.log.txt
999961 is prime : calculations: 124994 -- total calcs: 4701762062 -- primes found: 78496
Divider found for: 999963 --> 3
Divider found for: 999965 --> 5
Divider found for: 999967 --> 31
Divider found for: 999969 --> 3
Divider found for: 999971 --> 7
Divider found for: 999973 --> 13
Divider found for: 999975 --> 3
Divider found for: 999977 --> 11
999979 is prime : calculations: 124996 -- total calcs: 4701887092 -- primes found: 78497
Divider found for: 999981 --> 3
999983 is prime : calculations: 124997 -- total calcs: 4702012090 -- primes found: 78498
Divider found for: 999985 --> 5
Divider found for: 999987 --> 3
Divider found for: 999989 --> 19
Divider found for: 999991 --> 17
Divider found for: 999993 --> 3
Divider found for: 999995 --> 5
Divider found for: 999997 --> 757
Divider found for: 999999 --> 3
So, half the number of iterations as before, including much bigger log, but about 1/2 of the CPU time.


Interestingly:
grep Divider 1million_v3.log.txt | cut -f6 -d' ' | sort -rn | more
997
991
.
.
.
The max divider found for up to 1,000,000 is almost exactly 1000 times smaller. That's gotta be of significance, and I will see if I put some contraints on the divider search loop, and test/compare it up to waz00 numbers, to see if it works.
If a number ends in a 5, it is not prime. There was also another rule about the sum of the digits. (Sum of digits divisible by 3) can be factored -- not prime
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  #14  
Old 17th March 2017, 04:07 AM
ocratato Online
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Re: Programming Challenge - list prime numbers

Here is my simple Sieve of Eratosthenes solution (taken from Wikipedia pseudocode):
Code:
#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <math.h>

using namespace std;
typedef unsigned long int ul64;

int     main(int argc,char *argv[])
{
        ul64 limit=abs(atol(argv[1]));
        printf("Calculating primes up to: %lu\n",limit);
        limit++;
        vector<bool> primes(limit, true);

        ul64 range = sqrt(limit);
        for( ul64 i=2; i<=range; i++)
        {
                if( primes[i] )
                {
                        ul64 ii = i*i;
                        ul64 k = ii;
                        for ( ul64 j=0; k<limit; j++ )
                        {
                                primes[k] = false;
                                k += i;
                        }
                }
        }

        for(ul64 i=2; i<limit; i++)
        {
                if( primes[i] ) printf("%lu\n", i );
        }
}
~
For comparison, on my machine bobx001's solution takes 46.6 seconds for 1 million.

Code:
[brenton@acer primes]$ time ./primes3 1000000 > primes3.dat

real	0m0.024s
user	0m0.021s
sys	0m0.003s
[brenton@acer primes]$ time ./primes3 1000000000 > primes3.dat

real	0m18.232s
user	0m17.725s
sys	0m0.513s
I did a diff to make sure it got the same results.
__________________
Has anyone seriously considered that it might be turtles all the way down?
That's very old fashioned thinking.
The current model is that it's holographic nested virtualities of turtles, all the way down.

Last edited by ocratato; 17th March 2017 at 12:49 PM.
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  #15  
Old 17th March 2017, 05:24 AM
RupertPupkin Offline
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Re: Programming Challenge - list prime numbers

Quote:
Originally Posted by ocratato View Post
Here is my simple Sieve of Eratosthenes solution (taken from Wikipedia pseudocode):
Code:
#include <stdio.h>
#include <stdlib.h>
#include <vector>
#include <math.h>

using namespace std;
typedef unsigned long int ul32;

int     main(int argc,char *argv[])
{
        ul32 limit=abs(atoi(argv[1]));
        printf("Calculating primes up to: %lu\n",limit);
        vector<bool> primes(limit, true);

        ul32 range = sqrt(limit);
        for( ul32 i=2; i<range; i++)
        {
                if( primes[i] )
                {
                        ul32 ii = i*i;
                        ul32 k;
                        for ( ul32 j=0; (k=ii+j*i)<limit; j++ )
                        {
                                primes[k] = false;
                        }
                }
        }

        for(ul32 i=3; i<limit; i++)
        {
                if( primes[i] ) printf("%lu\n", i );
        }
}
For comparison, on my machine bobx001's solution takes 46.6 seconds for 1 million.
In fact, I just compiled and ran your program, and it doesn't quite do what it says:
Code:
$ ./getPrimes 11
Calculating primes up to: 11
3
5
7
9
So not only is the non-prime number 9 listed, but 11 is missing (so that it's not "up to" 11), and even 2 is missing!

Maybe you should do a little research before writing code, and not blindly copy code from Wikipedia.

Edit: To be fair, bobx001's program also wrongly lists 9 as a prime number and makes the same mistakes that yours does. His program does print out more info (like divisors), though, so the time comparisons are kind of apples to oranges.
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Last edited by RupertPupkin; 17th March 2017 at 05:51 AM. Reason: Read the wrong post for bobx001.
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[BASH]: Prime Numbers sea Guides & Solutions (Not For Questions) 14 21st November 2012 09:18 AM
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