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Difference between revisions of "Value k"

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An example:
 
An example:
  
:<math>2^{23}-1 = 8388607 = 47 * 178481</math>
+
<math>\begin{align}2^{23}-1 &= 8388607\\&= 47 * 178481\\
:<math>47 = 2 * 1 * 23 + 1</math>
+
\\
:<math>178481 = 2 * 3880 * 23 + 1</math>
+
47 &= 2 * 1 * 23 + 1\\
 +
178481 &= 2 * 3880 * 23 + 1
 +
\end{align}</math>
  
 
So, we see that for the factor 47, <math>k=1</math> and for 178481, <math>k=3880</math>.
 
So, we see that for the factor 47, <math>k=1</math> and for 178481, <math>k=3880</math>.

Latest revision as of 10:43, 25 October 2020

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{ \begin{align}2^{23}-1 &= 8388607\\&= 47 * 178481\\ \\ 47 &= 2 * 1 * 23 + 1\\ 178481 &= 2 * 3880 * 23 + 1 \end{align} }[/math]

So, we see that for the factor 47, [math]\displaystyle{ k=1 }[/math] and for 178481, [math]\displaystyle{ 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