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Assembly pgm for the decomposition of primes

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  • reismann@free.fr
    Dear SeqFans, My friend Fabien Sibenaler realized an Assembly program implementing the new algorithm that gives the decomposition of a prime number (prime =
    Message 1 of 2 , Apr 21, 2007
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      Dear SeqFans,

      My friend Fabien Sibenaler realized an Assembly program implementing the new
      algorithm that gives the decomposition of a prime number (prime = weight * level
      + gap, or A000040(n) = A117078(n) * A117563(n) + A001223(n)).

      This pgm is faster than the previous pgm said "naïf" for prime numbers
      classified by level.
      Ex (PIV 3 GHz, 512 Mo RAM) :
      Old pgm :
      Number : 979872743
      Gap : 204
      Weight : 979872539
      Level : 1
      Time in ms : 116656

      New pgm :
      Number : 979872743
      Gap : 204
      Weight : 979872539
      Level : 1
      Time in ms : 16

      The principle of the new algo :
      We look for the odd weights until sqrt(p) (1 red) and if we did not find the
      decomposition, we look for it by levels until (ln p)^2 by beginning with the
      highest level (2 red).
      This limit (ln p)^2 is arbitrary and can be improved.
      Whith the "naïf" algo, we looked for the odd weights until p-g (1 black) :
      http://reismann.free.fr/primeSieve.html
      The decomposition of primes in weight * level + gap is a generalisation of the
      Eratosthenes sieve :
      http://reismann.free.fr/sieveEra.html

      Assembly pgm :
      http://reismann.free.fr/download/class_asm.zip (the zip file contains exe and
      source code).
      Neil, the link on A117078 is OK.
      or on the "Download" page :
      http://reismann.free.fr/telechargements.php

      With this pgm I found a prime of level(1,24) :
      p(28106444831) - p(28106444830) = p(28106444830) - p(28106444830 - 24)
      738832928467 - 738832927927 = 738832927927 - 738832927387 = 540 = 6 * 90
      p(28106444830) is of level 1 in in A117563,
      p(28106444830) = 738832927927 is of level(1,24).

      With the Java pgm, I obtained a table of 25 million lines in 2h49min (PIV 3
      GHz, 512 Mo RAM).

      Best,

      Rémi Eismann
    • reismann@free.fr
      oups, sorry... Dear primenumbers group, My friend Fabien Sibenaler realized an Assembly program implementing the new algorithm that gives the decomposition of
      Message 2 of 2 , Apr 21, 2007
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        oups, sorry...


        Dear primenumbers group,

        My friend Fabien Sibenaler realized an Assembly program implementing the new
        algorithm that gives the decomposition of a prime number (prime = weight * level
        + gap, or A000040(n) = A117078(n) * A117563(n) + A001223(n)).

        This pgm is faster than the previous pgm said "naïf" for prime numbers
        classified by level.
        Ex (PIV 3 GHz, 512 Mo RAM) :
        Old pgm :
        Number : 979872743
        Gap : 204
        Weight : 979872539
        Level : 1
        Time in ms : 116656

        New pgm :
        Number : 979872743
        Gap : 204
        Weight : 979872539
        Level : 1
        Time in ms : 16

        The principle of the new algo :
        We look for the odd weights until sqrt(p) (1 red) and if we did not find the
        decomposition, we look for it by levels until (ln p)^2 by beginning with the
        highest level (2 red).
        This limit (ln p)^2 is arbitrary and can be improved.
        Whith the "naïf" algo, we looked for the odd weights until p-g (1 black) :
        http://reismann.free.fr/primeSieve.html
        The decomposition of primes in weight * level + gap is a generalisation of the
        Eratosthenes sieve :
        http://reismann.free.fr/sieveEra.html

        Assembly pgm :
        http://reismann.free.fr/download/class_asm.zip (the zip file contains exe and
        source code).
        or on the "Download" page :
        http://reismann.free.fr/telechargements.php

        With this pgm I found a prime of level(1,24) :
        p(28106444831) - p(28106444830) = p(28106444830) - p(28106444830 - 24)
        738832928467 - 738832927927 = 738832927927 - 738832927387 = 540 = 6 * 90
        p(28106444830) is of level 1 in in A117563,
        p(28106444830) = 738832927927 is of level(1,24).

        With the Java pgm, I obtained a table of 25 million lines in 2h49min (PIV 3
        GHz, 512 Mo RAM).

        Best,

        Rémi Eismann
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