Catalan-Mersenne Number
Catalan (1876, 1891) noted that the sequence of Mersenne numbers 
, 
, and 
, and 
(OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the numbers defined by
with 
are known in this work as Catalan-Mersenne numbers.
It is not known if 
is prime, but it is known that it has no prime factor less than 
(Noll; private correspondence with C. K. Caldwell, Aug. 10, 2003).
appeared in the Futurama movie The Beast with a Billion Backs (2008).
The Catalan-Mersenne numbers are a subset of the double Mersenne numbers.
REFERENCES:
Catalan, E. Sur la théorie des nombres premiers. Turin, p. 11, 1876.
Catalan, E. Théorie des nombres. p. 376, 1891.
Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, 2005.
Noll, L. K. "Prime Numbers, Mersenne Primes, Perfect Numbers, Etc." https://www.isthe.com/chongo/tech/math/prime/.
Sierpiński, W. A Selection of Problems in the Theory of Numbers. New York: Macmillan, p. 91, 1964.
Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, p. 81 1996.
Sloane, N. J. A. Sequence A007013/M0866 in "The On-Line Encyclopedia of Integer Sequences."
