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Value k
When discussing Mersenne numbers, all factors can be expressed in the following form:
- [math]\displaystyle{ 2kp+1 }[/math] where [math]\displaystyle{ p }[/math] is the exponent in [math]\displaystyle{ 2^p-1 }[/math].
An example:
- [math]\displaystyle{ 2^{23}-1 = 8388607 = 47 * 178481 }[/math]
- [math]\displaystyle{ 47 = 2 * 1 * 23 + 1 }[/math]
- [math]\displaystyle{ 178481 = 2 * 3880 * 23 + 1 }[/math]
So, we see that for the factor [math]\displaystyle{ 47, k=1 }[/math] and for [math]\displaystyle{ 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
