Proth number: Difference between revisions

Revision as of 00:03, 30 May 2010

Definition

Suppose $n$ is a natural number and $k$ is a natural number such that $2^{n} > k$ . The Proth number with parameters $n$ and $k$ is defined as the number:

$k \cdot 2^{n} + 1$ .

A Proth number that is also a prime is termed a Proth prime.

Relation with other properties

Stronger properties

Fermat number: The $m^{t h}$ Fermat number is the Proth number with $k = 1$ and $n = 2^{m}$ .
Cullen number

Other related properties

Mersenne number is a number of the form $2^{n} - 1$ .
Sierpinski number is a number of the form $k \cdot 2^{n} - 1$ with $k < 2^{n}$

@@ Line 13: / Line 13: @@
 * [[Weaker than::Fermat number]]: The <math>m^{th}</math> Fermat number is the Proth number with <math>k = 1</math> and <math>n = 2^m</math>.
 * [[Weaker than::Cullen number]]
+===Other related properties===
+* [[Mersenne number]] is a number of the form <math>2^n - 1</math>.
+* [[Sierpinski number]] is a number of the form <math>k \cdot 2^n - 1</math> with <math>k < 2^n</math>