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New Record Carol Prime!!!!

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  • Cletus Emmanuel
    Guys, Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has 105812 digits. This is a new record. To date, it is the largets Carol/Kynea prime
    Message 1 of 5 , Oct 8, 2004
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      Guys,
      Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has 105812 digits. This is a new record. To date, it is the largets Carol/Kynea prime found. It is the first 100K Carol or Kynea Prime. It took PFGW 30 minutes to test it 2-PRP and 2 hours 23 minutes to run an N+1 test. If only I could prove my conjecture, it would have saved me 2 hours.

      Steven, I've checked Carol from 150,001 - 175,928 with only this new prime in that range. This number is also the first 100K+ digits Carol or Kynea prime. This is one of my goals. The next goals is for anyone or us to find a Carol/Kynea prime with 1M+ digits and then 10M+ digits.

      I think that a 100K digit Kynea is near. The Kynea was at 110K and the search is up to 220K with no other Kynea Prime in sight. If we keep looking, I think that we will find one soon. I hope to submit a Carol/Kynea paper t a journal soon. I just have to find the time to do so.....

      ---Cletus Emmanuel


      P.S.: I tried to subimt this number to Chris Caldwell's page and it prompt me to enter a password to access the DB, but I don't know that I have access to the site via that route, muchless a password. Can someone help me submit?......


      ---Cletus Emmanuel



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    • Chris Caldwell
      ... Go to your page: http://primes.utm.edu/bios/page.php?id=374 and use the links at the bottom. There is one to submit the prime, another to change your
      Message 2 of 5 , Oct 8, 2004
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        At 01:40 PM 10/8/2004, Cletus Emmanuel wrote:
        >Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has 105812 digits. This is a new record. To date, it is the largets Carol/Kynea prime found. It is the first 100K Carol or Kynea Prime. It took PFGW 30 minutes to test it 2-PRP and 2 hours 23 minutes to run an N+1 test. If only I could prove my conjecture, it would have saved me 2 hours.
        >
        >P.S.: I tried to subimt this number to Chris Caldwell's page and it prompt me to enter a password to access the DB, but I don't know that I have access to the site via that route, muchless a password. Can someone help me submit?......

        Go to your page: http://primes.utm.edu/bios/page.php?id=374 and use the links at the bottom. There is one to submit the prime, another to change your password, and if you have lost yours, just click on edit entry--when you fail to enter the right password it will offer a link to send you a new one. (I should make this less hidden... but I haven't).

        "Carol Prime" is not an archivable comment, so don't bother adding it.

        Chris
      • Paul Underwood
        ... 105812 digits. This is a new record. To date, it is the largets Carol/Kynea prime found. It is the first 100K Carol or Kynea Prime. It took PFGW 30
        Message 3 of 5 , Oct 8, 2004
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          --- In primenumbers@yahoogroups.com, Cletus Emmanuel <cemmanu@y...> wrote:
          > Guys,
          > Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has
          105812 digits. This is a new record. To date, it is the largets
          Carol/Kynea prime found. It is the first 100K Carol or Kynea Prime.
          It took PFGW 30 minutes to test it 2-PRP and 2 hours 23 minutes to run
          an N+1 test. If only I could prove my conjecture, it would have saved
          me 2 hours.

          Congratulations on your find!

          I have tested n^2-2 is 2-PRP => n^2-2 is ( 5 miller rounds probable )
          prime for all odd n < 47,088,000,003 ( 1,851,251,401 PrP's )

          Paul
        • Cletus Emmanuel
          Paul, did you find any of those PRP s to be composite?..... ... 105812 digits. This is a new record. To date, it is the largets Carol/Kynea prime found. It
          Message 4 of 5 , Oct 9, 2004
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            Paul,
            did you find any of those PRP's to be composite?.....

            Paul Underwood <paulunderwood@...> wrote:

            --- In primenumbers@yahoogroups.com, Cletus Emmanuel <cemmanu@y...> wrote:
            > Guys,
            > Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has
            105812 digits. This is a new record. To date, it is the largets
            Carol/Kynea prime found. It is the first 100K Carol or Kynea Prime.
            It took PFGW 30 minutes to test it 2-PRP and 2 hours 23 minutes to run
            an N+1 test. If only I could prove my conjecture, it would have saved
            me 2 hours.

            Congratulations on your find!

            I have tested n^2-2 is 2-PRP => n^2-2 is ( 5 miller rounds probable )
            prime for all odd n < 47,088,000,003 ( 1,851,251,401 PrP's )

            Paul







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          • Paul Underwood
            Cletus, no, I did not find any of those 2-PRP s composite by using 5 rounds of the Miller-Rabin test on each one found. The process is slow ~ 120 MHz Here is
            Message 5 of 5 , Oct 9, 2004
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              Cletus,

              no, I did not find any of those 2-PRP's composite by using 5 rounds of
              the Miller-Rabin test on each one found.

              The process is slow ~ 120 MHz

              Here is the GNU Multiple Precision program:

              //outputs x:x^f-x is NOT 5 times Miller Rabin where f=x^2-2
              is 2-PRP
              //(PU/22/03/04)



              #include <stdio.h>

              #include <gmp.h>



              int main( int argc, char *argv[] ) {

              mpz_t x; //inputted minimum

              mpz_t f; //=x^2-2

              mpz_t k; //prp counter

              mpz_t t; //temporary variable

              int i, j; //loop counter

              FILE *fp; //for x-PRP.out

              if ( argc != 3 ) {

              printf( "usage : quadratic minimum_x prp_count\n" );

              exit( 1 ); }

              else printf( "Working...\n" );

              mpz_init_set_str( x, *++argv, 10 );

              mpz_init_set_str( k, *++argv, 10 );

              mpz_init( f );

              mpz_init( t );

              while ( 1 ) {

              for( i=0; i<1000000; i++ ) {

              mpz_add_ui( x, x, 2 );

              mpz_pow_ui( f, x, 2 );

              mpz_sub_ui( f, f, 2 );

              mpz_set_ui( t, 2 );

              mpz_powm( t, t, f, f );

              if ( mpz_cmp_ui( t, 2 ) == 0 ) {

              if( mpz_probab_prime_p( f, 5 ) ) mpz_add_ui( k, k, 1 );

              else {

              printf( "x-PRP:x=" ); mpz_out_str( NULL, 10, x );

              printf( "\n" );

              fp = fopen( "x-PRP.out", "a" );

              fprintf( fp, "x-PRP:x=" ); mpz_out_str( fp, 10, x );

              fprintf( fp, "\n" );

              fclose( fp ); } } }

              printf( "status: x=" ); mpz_out_str( NULL, 10, x );

              printf( " x-prp_count=" ); mpz_out_str( NULL, 10, k );

              printf( "\n" );

              fp = fopen( "x-PRP.out", "a" );

              fprintf( fp, "status: x=" ); mpz_out_str( fp, 10, x );

              fprintf( fp, " x-prp_count=" ); mpz_out_str( fp, 10, k );

              fprintf( fp, "\n" );

              fclose( fp );

              }

              }


              Of course I can unroll my loops by using the method of differences.
              And I need only test 2^((n^2-3)/2)=1 mod n^2-2. But speed up in these
              tricks are insignificant compared to the modular exponentiation and
              any of subsequent Miller Rabin probable prime tests.

              Paul

              --- In primenumbers@yahoogroups.com, Cletus Emmanuel <cemmanu@y...> wrote:
              > Paul,
              > did you find any of those PRP's to be composite?.....
              >
              > Paul Underwood <paulunderwood@m...> wrote:
              >
              > --- In primenumbers@yahoogroups.com, Cletus Emmanuel <cemmanu@y...>
              wrote:
              > > Guys,
              > > Here is a new Carol Prime....(2^175749 - 1)^2 - 2. This number has
              > 105812 digits. This is a new record. To date, it is the largets
              > Carol/Kynea prime found. It is the first 100K Carol or Kynea Prime.
              > It took PFGW 30 minutes to test it 2-PRP and 2 hours 23 minutes to run
              > an N+1 test. If only I could prove my conjecture, it would have saved
              > me 2 hours.
              >
              > Congratulations on your find!
              >
              > I have tested n^2-2 is 2-PRP => n^2-2 is ( 5 miller rounds probable )
              > prime for all odd n < 47,088,000,003 ( 1,851,251,401 PrP's )
              >
              > Paul
              >
              >
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