Definition:Proth Number
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Definition
A Proth number is a natural number of the form:
- $N = k \times 2^n + 1$
where:
- $k$ is an odd integer
- $n$ is a positive integer
- $2^n > k$
The condition is included, otherwise every odd integer greater than $1$ would be a Proth number.
Sequence of Proth Numbers
The sequence of Proth numbers begins:
- $3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, \ldots$
Also see
Source of Name
This entry was named for François Proth.
Sources
- Weisstein, Eric W. "Proth Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProthNumber.html