Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Difference between revisions of "Value k"

From Prime-Wiki
Jump to: navigation, search
(restored)
 
(Tagging variables)
Line 1: Line 1:
 +
{{DISPLAYTITLE:Value {{Vk}}}}
 
When discussing [[Mersenne number]]s, '''all''' [[factor]]s can be expressed in the following form:
 
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>
 
:<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]
 
See also: [http://www.mersenne.org/various/math.php http://www.mersenne.org/various/math.php]
 
[[Category:Math]]
 
[[Category:Math]]

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.

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