Difference between revisions of "Proth number"

Latest revision as of 10:59, 9 July 2021

In number theory, a Proth number is a number of the form

N = k•2ⁿ+1

where k is an odd positive integer and n is a positive integer such that 2ⁿ > k.

Without the condition that 2ⁿ > k, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too.

A Proth prime is a Proth number, which is prime.

Cullen numbers (n•2ⁿ+1) and Fermat numbers (2^2ⁿ+1) are special forms of Proth numbers.

Number classes

General numbers

Special numbers

Prime numbers

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 In [[number theory]], a '''Proth number''' is a number of the form
-:N = k &times; 2<sup>n</sup> + 1
+:{{V|N}} = {{Kbn|+|k|2|n}}
-where ''k'' is an odd positive [[integer]] and ''n'' is a positive integer such that 2<sup>n</sup> > k.
+where {{Vk}} is an odd positive [[integer]] and {{Vn}} is a positive integer such that 2<sup>{{Vn}}</sup> > {{Vk}}.
-Without the condition that 2<sup>n</sup> > k, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too.
+Without the condition that 2<sup>{{Vn}}</sup> > {{Vk}}, all odd integers greater than 1 would be Proth numbers, but most pages lists them, too.
 A [[Proth prime]] is a Proth number, which is prime.
-[[Cullen number]]s (n &times; 2<sup>n</sup>+1) and [[Fermat number]]s (2<sup>2<sup>n</sup></sup>+1) are special forms of Proth numbers.
+[[Cullen number]]s ({{Kbn|+|n|2|n}}) and [[Fermat number]]s ({{Kbn|+|2<sup>n</sup>}}) are special forms of Proth numbers.
 ==See also==