TOPICS
Search

Proth Number


A Proth number is a number of the form N=k·2^n+1 for odd k, n a positive integer, and 2^n>k. The 2^n>k condition is needed since otherwise, every odd number >1 would be a Proth number. The first few Proth numbers are 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, ... (OEIS A080075).

The Cullen numbers are a special case of the Proth numbers with k=n (and the inequality restriction dropped). The Fermat numbers are a special case of the Proth numbers with k=1.


See also

Cullen Number, Cunningham Number, Proth Prime, Sierpiński's Composite Number Theorem, Sierpiński Number of the Second Kind

Explore with Wolfram|Alpha

References

McNamara, J. and Mills, M. "Factoring of Proth Numbers." http://www.fidn.org/proth1.html.Sloane, N. J. A. Sequence A080075 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Proth Number

Cite this as:

Weisstein, Eric W. "Proth Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProthNumber.html

Subject classifications