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Value k

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

2kp+1 where p is the exponent in 2p1.

An example:

2231=8388607=4717848147=2123+1178481=2388023+1

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

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