A Proth number is a positive integer of the form odd positive integer positive integer odd integer greater than 1 would qualify. The first few Proth
numbers are 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, ... (OEIS A080075 ).
The Cullen numbers are Proth numbers, since factors
of 2 in exponent . The Fermat
numbers are a special case of the Proth numbers with
See also Cullen Number ,
Cunningham Number ,
Proth Prime ,
Sierpiński
Number of the Second Kind ,
Sierpiński's
Composite Number Theorem
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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 https://mathworld.wolfram.com/ProthNumber.html
Subject classifications
for an odd positive integer 
, a positive integer 
, and 
. Without the 
condition, every odd integer greater than 1 would qualify. The first few Proth
numbers are 3, 5, 9, 13, 17, 25, 33, 41, 49, 57, 65, ... (OEIS A080075).
and any factors
of 2 in 
can be absorbed into the exponent. The Fermat
numbers are a special case of the Proth numbers with 
.
