Difference between revisions of "Value k"

Revision as of 13:42, 20 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{ 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 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.

@@ Line 1: / Line 1: @@
+{{DISPLAYTITLE:Value {{Vk}}}}
 When discussing [[Mersenne number]]s, '''all''' [[factor]]s can be expressed in the following form:
@@ Line 9: / Line 10: @@
 :<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>.
+So, we see that for the factor 47, <math>k=1</math> and for 178481, <math>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.
+When [[trial factoring]] finds a factor, it can either be written out and stored long hand, or just the '''{{Vk}}-value''' may be recorded.
 See also: [http://www.mersenne.org/various/math.php http://www.mersenne.org/various/math.php]
 [[Category:Math]]