Value k

When discussing Mersenne numbers, all factors can be expressed in the following form:

[math]2kp+1[/math] where [math]p[/math] is the exponent in [math]2^p-1[/math].

An example:

[math]2^{23}-1 = 8388607 = 47 * 178481[/math]

[math]47 = 2 * 1 * 23 + 1[/math]

[math]178481 = 2 * 3880 * 23 + 1[/math]

So, we see that for the factor [math]47, k=1[/math] and for [math]178481, k=3880[/math].

When trial factoring finds a factor, it can either be written out and stored long hand, or just the k-value may be recorded.

See also: http://www.mersenne.org/various/math.php