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.