The way I read the algorithm ..., you're looping too much in your middle loop. I believe you're supposed to choose a fixed accuracy k, and then a random set of k bases. You're using *all* numbers less than n as a base, and that is way too strong, especially for very large numbers, for which this algorithm is designed.

Yes, that's pretty much right. Furthermore, for any number less than 341550071728322, if the Miller-Rabin test doesn't return "composite" for any of the bases 2, 3, 5, 7, 11, 13 and 17, then the number in question is proven to be prime. For numbers less than 1373653 it is sufficient to test only for bases 2 and 3. See http://primes.utm.edu/prove/prove2_3.html

For large numbers Math::BigInt's bmodpow (pure perl) function is just way too slow. You'll be wanting to use something like Math::Pari or Math::GMP (as rhesa has suggested).

Cheers,
Rob

In reply to Re^2: optimizing the miller-rabin algorithm by syphilis
in thread optimizing the miller-rabin algorithm by punklrokk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.