A Cullen number is a number of the form
The first few are 3, 9, 25, 65, 161, 385, ... (OEIS A002064 ).
Cullen numbers are divisible by prime of
the form
The first few prime Cullen numbers are numbers 3, 393050634124102232869567034555427371542904833, ... (OEIS A050920 ),
corresponding to A005849 ;
Caldwell). As of Nov. 2015, it is known that there are no other Cullen primes
for
See also Cunningham Number ,
Fermat Number ,
Integer Sequence Primes ,
Proth Number ,
Sierpiński
Number of the First Kind ,
Woodall Number ,
Woodall Prime
Explore with Wolfram|Alpha
References Caldwell, C. K. "The Top Twenty: Cullen Primes." http://primes.utm.edu/top20/page.php?id=6#records . Guy,
R. K. "Cullen Numbers." §B20 in Unsolved
Problems in Number Theory, 2nd ed. Keller, W. "New Cullen Primes." Math. Comput. 64 ,
1733-1741, 1995. Leyland, P. http://research.microsoft.com/~pleyland/factorization/cullen_woodall/cw.htm . PrimeGrid.
"PrimeGrid's Cullen Prime Search." Jul. 25, 2009. http://www.primegrid.com/download/Cullen6679881.pdf . PrimeGrid.
"Subprojects: Cullen Prime Search." http://www.primegrid.com/server_status_subprojects.php . PrimeGrid.
"PrimeGrid Primes: Subproject: (CUL) Cullen Prime Search." http://www.primegrid.com/primes/primes.php?project=CUL . Ribenboim,
P. The
New Book of Prime Number Records. Rodenkirch, M. and Ballinger, R. "Cullen Primes: Definition
and Status." http://www.prothsearch.net/cullen.html . Sloane,
N. J. A. Sequences A002064 /M2795,
A005849 /M5401, and A050920
in "The On-Line Encyclopedia of Integer Sequences." Referenced
on Wolfram|Alpha Cullen Number
Cite this as:
Weisstein, Eric W. "Cullen Number." From
MathWorld https://mathworld.wolfram.com/CullenNumber.html
Subject classifications
if 
is a prime of
the form 
.
,
141, 4713, 5795, 6611, 18496, 32292, 32469, 59656, 90825, 262419, 361275, 481899,
1354828, 6328548, 6679881, ... (OEIS A005849;
Caldwell). As of Nov. 2015, it is known that there are no other Cullen primes
for 
(PrimeGrid).
