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 if is a prime of
the form .
The first few prime Cullen numbers are numbers 3, 393050634124102232869567034555427371542904833, ... (OEIS A050920 ),
corresponding to ,
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).
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. New York: Springer-Verlag, p. 77,
1994. 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. New York: Springer-Verlag, pp. 360-361,
1996. 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 --A Wolfram Web Resource. https://mathworld.wolfram.com/CullenNumber.html
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