# Determine whether M_{23} is prime

• July 20th 2010, 01:21 PM
dwsmith
Determine whether M_{23} is prime
$M_{23}=2^{23}-1=8388607$

$\left \lfloor \sqrt{8388607} \right \rfloor=2896$

$2kp+1=46k+1, \ 1\leq k \leq 62$

Since there are 62 possible values to check, how can this be done in a more efficient fashion?
• July 20th 2010, 01:30 PM
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Quote:

Originally Posted by dwsmith
$M_{23}=2^{23}-1=8388607$

$\left \lfloor \sqrt{8388607} \right \rfloor=2896$

$2kp+1=46k+1, \ 1\leq k \leq 62$

Since there are 62 possible values to check, how can this be done in a more efficient fashion?

Does this help? Lucas–Lehmer primality test

Edit: The MathWorld page is a bit cleaner than the Wikipedia article at the moment, in my opinion.