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Re: Program for testing small numbers

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  • andrew_j_walker
    ... of small numbers (say under 25 digits). I know PFGW will do this but is there a faster program for small numbers? ... It might be worth testing pari, as
    Message 1 of 8 , Sep 2, 2004
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      --- In primenumbers@yahoogroups.com, Gary Chaffey <garychaffey2@y...>
      wrote:
      > Could somebody recommend a program that can PRP test large numbers
      of small numbers (say under 25 digits). I know PFGW will do this but
      is there a faster program for small numbers?
      > Regards
      > Gary
      >
      >

      It might be worth testing pari, as it's meant to be quite fast
      with mod-power operations. However if you're performing trial
      division as well it may not be as fast.

      Andrew
    • Bigfoot
      I did a quick scan of the files and didn t see a sieve for finding small primes. I may have missed one if it was there, can someone give me a link to one
      Message 2 of 8 , Sep 2, 2004
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        I did a quick scan of the files and didn't see a sieve for finding
        small primes. I may have missed one if it was there, can someone
        give me a link to one (written in c or c++)
      • Milton Brown
        A program in Java (C++) for small primes is attached. Milton L. Brown miltbrown at earthlink.net public class Prime { public static void main(String[] args) {
        Message 3 of 8 , Sep 2, 2004
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          A program in Java (C++) for small primes is attached.

          Milton L. Brown
          miltbrown at earthlink.net

          public class Prime
          {
          public static void main(String[] args)
          {

          int i, j, k;
          for (i = 2; i<3000; i++)
          { k = 1;
          for ( j=2; j<i; j++) {
          k = i %j;
          if (k == 0) break;
          }
          if ((i% 50)==0) System.out.println(" ");
          if (k !=0) System.out.print(i+" ");

          };

          }
          }


          > [Original Message]
          > From: Bigfoot <plano9@...>
          > To: <primenumbers@yahoogroups.com>
          > Date: 9/2/2004 5:48:35 PM
          > Subject: [PrimeNumbers] Re: Program for testing small numbers
          >
          > I did a quick scan of the files and didn't see a sieve for finding
          > small primes. I may have missed one if it was there, can someone
          > give me a link to one (written in c or c++)
          >
          >
          >
          >
          > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
          > The Prime Pages : http://www.primepages.org/
          >
          >
          > Yahoo! Groups Links
          >
          >
          >
          >
        • Bigfoot
          I m working on turning that into c++ code that I can use, but I don t see what the purpose of the lines k!==0 //pointless, no need to do factorial here and
          Message 4 of 8 , Sep 3, 2004
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            I'm working on turning that into c++ code that I can use, but I don't
            see what the purpose of the lines
            k!==0 //pointless, no need to do factorial here
            and
            i%50 //wouldn't that be if the remainder is 50?

            --- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
            wrote:
            > A program in Java (C++) for small primes is attached.
            >
            > Milton L. Brown
            > miltbrown at earthlink.net
            >
            > public class Prime
            > {
            > public static void main(String[] args)
            > {
            >
            > int i, j, k;
            > for (i = 2; i<3000; i++)
            > { k = 1;
            > for ( j=2; j<i; j++) {
            > k = i %j;
            > if (k == 0) break;
            > }
            > if ((i% 50)==0) System.out.println(" ");
            > if (k !=0) System.out.print(i+" ");
            >
            > };
            >
            > }
            > }
            >
            >
            > > [Original Message]
            > > From: Bigfoot <plano9@y...>
            > > To: <primenumbers@yahoogroups.com>
            > > Date: 9/2/2004 5:48:35 PM
            > > Subject: [PrimeNumbers] Re: Program for testing small numbers
            > >
            > > I did a quick scan of the files and didn't see a sieve for
            finding
            > > small primes. I may have missed one if it was there, can someone
            > > give me a link to one (written in c or c++)
            > >
            > >
            > >
            > >
            > > Unsubscribe by an email to: primenumbers-
            unsubscribe@yahoogroups.com
            > > The Prime Pages : http://www.primepages.org/
            > >
            > >
            > > Yahoo! Groups Links
            > >
            > >
            > >
            > >
          • Hadley, Thomas H (Tom), ALABS
            ... First of all, he wrote k != 0 , not k !== 0 and the first is basic C/C++ code. There is no confusion with the factorial. ... No, it s the remainder
            Message 5 of 8 , Sep 3, 2004
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              Bigfoot wrote:

              >> k!==0 //pointless, no need to do factorial here

              First of all, he wrote "k != 0", not "k !== 0" and the first is
              basic C/C++ code. There is no confusion with the factorial.

              >>i%50 //wouldn't that be if the remainder is 50?

              No, it's the remainder after dividing by 50.

              Please read a book on intro to C or C++ before questioning someone's program. It looks to me like Milton's program is a valid, if inefficient, prime number generator.

              Tom Hadley

              -----Original Message-----
              From: Bigfoot [mailto:plano9@...]
              Sent: Friday, September 03, 2004 5:56 PM
              To: primenumbers@yahoogroups.com
              Subject: [PrimeNumbers] Re: Program for testing small numbers


              I'm working on turning that into c++ code that I can use, but I don't
              see what the purpose of the lines
              k!==0 //pointless, no need to do factorial here

              and
              i%50 //wouldn't that be if the remainder is 50?

              --- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
              wrote:
              > A program in Java (C++) for small primes is attached.
              >
              > Milton L. Brown
              > miltbrown at earthlink.net
              >
              > public class Prime
              > {
              > public static void main(String[] args)
              > {
              >
              > int i, j, k;
              > for (i = 2; i<3000; i++)
              > { k = 1;
              > for ( j=2; j<i; j++) {
              > k = i %j;
              > if (k == 0) break;
              > }
              > if ((i% 50)==0) System.out.println(" ");
              > if (k !=0) System.out.print(i+" ");
              >
              > };
              >
              > }
              > }
              >
              >
              > > [Original Message]
              > > From: Bigfoot <plano9@y...>
              > > To: <primenumbers@yahoogroups.com>
              > > Date: 9/2/2004 5:48:35 PM
              > > Subject: [PrimeNumbers] Re: Program for testing small numbers
              > >
              > > I did a quick scan of the files and didn't see a sieve for
              finding
              > > small primes. I may have missed one if it was there, can someone
              > > give me a link to one (written in c or c++)
              > >
              > >
              > >
              > >
              > > Unsubscribe by an email to: primenumbers-
              unsubscribe@yahoogroups.com
              > > The Prime Pages : http://www.primepages.org/
              > >
              > >
              > > Yahoo! Groups Links
              > >
              > >
              > >
              > >




              Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
              The Prime Pages : http://www.primepages.org/


              Yahoo! Groups Links
            • Milton Brown
              For the small prime lister program, the outer for-loop is exited as soon as i is found to be composite. The number is not composite (prime) when k != 0,
              Message 6 of 8 , Sep 3, 2004
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                For the small prime lister program, the outer for-loop
                is exited as soon as i is found to be composite. The
                number is not composite (prime) when k != 0, otherwise it
                is composite. This line is required to print the primes.

                The line with (i % 50) = = 0 will print a line-return, with less
                than 50 primes on a single line of out-put, so that many primes
                can be seen on a single page.

                Milton L. Brown
                miltbrown at earthlink.net


                > [Original Message]
                > From: Bigfoot <plano9@...>
                > To: <primenumbers@yahoogroups.com>
                > Date: 9/3/2004 3:56:43 PM
                > Subject: [PrimeNumbers] Re: Program for testing small numbers
                >
                > I'm working on turning that into c++ code that I can use, but I don't
                > see what the purpose of the lines
                > k!==0 //pointless, no need to do factorial here
                > and
                > i%50 //wouldn't that be if the remainder is 50?
                >
                > --- In primenumbers@yahoogroups.com, "Milton Brown" <miltbrown@e...>
                > wrote:
                > > A program in Java (C++) for small primes is attached.
                > >
                > > Milton L. Brown
                > > miltbrown at earthlink.net
                > >
                > > public class Prime
                > > {
                > > public static void main(String[] args)
                > > {
                > >
                > > int i, j, k;
                > > for (i = 2; i<3000; i++)
                > > { k = 1;
                > > for ( j=2; j<i; j++) {
                > > k = i %j;
                > > if (k == 0) break;
                > > }
                > > if ((i% 50)==0) System.out.println(" ");
                > > if (k !=0) System.out.print(i+" ");
                > >
                > > };
                > >
                > > }
                > > }
                > >
                > >
                > > > [Original Message]
                > > > From: Bigfoot <plano9@y...>
                > > > To: <primenumbers@yahoogroups.com>
                > > > Date: 9/2/2004 5:48:35 PM
                > > > Subject: [PrimeNumbers] Re: Program for testing small numbers
                > > >
                > > > I did a quick scan of the files and didn't see a sieve for
                > finding
                > > > small primes. I may have missed one if it was there, can someone
                > > > give me a link to one (written in c or c++)
                > > >
                > > >
                > > >
                > > >
                > > > Unsubscribe by an email to: primenumbers-
                > unsubscribe@yahoogroups.com
                > > > The Prime Pages : http://www.primepages.org/
                > > >
                > > >
                > > > Yahoo! Groups Links
                > > >
                > > >
                > > >
                > > >
                >
                >
                >
                >
                > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
                > The Prime Pages : http://www.primepages.org/
                >
                >
                > Yahoo! Groups Links
                >
                >
                >
                >
              • Jim Laird
                Here s a simple, simple prime number tester for very small numbers. It saves the previous results of test searches in memory, so it will be impractical if you
                Message 7 of 8 , Sep 7, 2004
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                  Here's a simple, simple prime number tester for very small numbers. It
                  saves the previous results of test searches in memory, so it will be
                  impractical if you search for primes that are too large (depending on
                  how much memory is on your system). It also uses STL classes for
                  containers etc. Worked on my system. Change main() as required. Only
                  checks up to the square root of the test number as a slight
                  optimization.

                  Cheers, Jim

                  ========================================================================
                  =====

                  #include <string>
                  #include <vector>
                  #include <ostream>

                  using namespace std;

                  // loads the prime list with the initial primes
                  void preload_pl(vector<int> &v)
                  {
                  v.resize(6);
                  v[0]=2; v[1]=3; v[2]=5;
                  v[3]=7; v[4]=11; v[5]=13;
                  return;
                  }

                  // returns true if testnum is prime. Adds primes to v as necessary
                  bool test_prime(int testnum, vector<int> &v)
                  {
                  // check the first few primes
                  for (unsigned int i = 0; i < 5; i++)
                  if (testnum % v[i] == 0) return false;

                  // check the rest of the list
                  for (unsigned int i = 5; i < v.size(); i++) {
                  if (testnum % v[i] == 0) return false;
                  if (testnum < (v[i]*v[i])) return true;
                  }

                  // at the end of the prime list, increase it till you hit the
                  test
                  // or determine that testnum is composite

                  for(int x = v[v.size()-1] + 2; ; x += 2) {
                  if (test_prime(x, v) == true) {
                  v.push_back(x);
                  if (testnum % x == 0) return false;
                  if ((x*x) > testnum) return true;
                  }
                  }
                  }



                  void main(int argv, char **argc)
                  {
                  vector<int> base_primes;

                  // initialize vector
                  base_primes.reserve(1000); // make room for 1000
                  entries to begin with
                  preload_pl(base_primes); // initialize the prime
                  list

                  // sieve numbers between 1001 and 10000
                  cout << "Primes between 1001 and 10000\n";
                  for (int test = 1001; test < 10000; test += 2) {
                  if (test_prime(test, base_primes) == true) {
                  cout << test << ", ";
                  }
                  }

                  return;
                  }
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