http://openproblemgarden.org/op/counterexamples_to_the_baillie_psw_primality_test Comments for "Counterexamples to the Baillie-PSW primality test" en http://openproblemgarden.org/op/counterexamples_to_the_baillie_psw_primality_test <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/number_theory_0">Number Theory</a> » <a href="/category/computational_number_theory">Computational N.T.</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Problem&nbsp;&nbsp;(1)</b>&nbsp;&nbsp; Find a counterexample to <a href="http://en.wikipedia.org/wiki/Baillie-PSW primality test">Baillie-PSW primality test</a> or prove that there is no one. </div> <div class="envtheorem"><b>Problem&nbsp;&nbsp;(2)</b>&nbsp;&nbsp; Find a composite <img class="teximage" src="/files/tex/493f3d9bc88a631c25371ab6138625d0cbf08f52.png" alt="$ n\equiv 3 $" /> or <img class="teximage" src="/files/tex/1f85cdb6c4f3165da306e494803c7a7170153dfd.png" alt="$ 7\pmod{10} $" /> which divides both <img class="teximage" src="/files/tex/e9553e6870300b908f907d6edc486e5b87147e2d.png" alt="$ 2^{n-1} - 1 $" /> (see <a href="http://en.wikipedia.org/wiki/Fermat pseudoprime">Fermat pseudoprime</a>) and the Fibonacci number <img class="teximage" src="/files/tex/ada72b72f8ae80fb477cc7ba27cbb70b839959ff.png" alt="$ F_{n+1} $" /> (see <a href="http://en.wikipedia.org/wiki/Lucas pseudoprime">Lucas pseudoprime</a>), or prove that there is no such <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />. </div> </tr></td> </table> </td> </tr> </table> Number Theory Computational Number Theory http://openproblemgarden.org/op/counterexamples_to_the_baillie_psw_primality_test#comment Tue, 07 Aug 2007 12:36:47 +0200 maxal 511 at http://openproblemgarden.org